Pendulum device, vibration damping device and design method of vibration damping device

Abstract

The invention provides a pendulum device capable of adjusting the amplitude dependence of the restoring force of a pendulum based on gravity to a desired characteristic. To this end, a pendulum device (1) is configured so as to be provided with: a pendulum member (2) having pendulum-side magnetic members (22a, 22b) on which a restoring force based on gravity acts and which performs pendulum motion about a fulcrum (32); and fixed magnetic members (4a, 4b) that provide a repulsive force or an attractive force based on the magnetic force to the pendulum member (2) as a restoring force based on the magnetic force. At least one of the magnetic flux density of at least one of the pendulum-side magnetic members (22a, 22b) and the fixed magnetic members (4a, 4b), the relative position of the pendulum-side magnetic members (22a, 22b) and the fixed magnetic members (4a, 4b), and the mass of the pendulum member (2) is adjusted. Thus, the pendulum member (2) has a restoring force based on magnetic force that counteracts a nonlinear component of a restoring force based on gravity acting on the pendulum member (2).

Description

Technical Field

[0001] This invention relates to a pendulum device, a vibration damping device, and a design method for the vibration damping device. Background Technology

[0002] Vibration damping devices for reducing the swaying of structures caused by wind and earthquakes are known in the past. For example, vibration damping devices that use a pendulum for vibration damping are known (see, for example, Patent Document 1).

[0003] In such vibration damping devices utilizing a pendulum, for example, a method is known to achieve a vibration damping effect by using a pendulum whose natural frequency is 1:1 with the natural frequency of the object being damped. Furthermore, in vibration damping devices utilizing a pendulum, a method has also been proposed for constructing a pendulum-type dynamic vibration absorber system using autoparametric excitation, and using a pendulum whose natural frequency is 1:1 / 2 with the natural frequency of the object being damped to achieve a vibration damping effect (for example, see Non-Patent Literature 1).

[0004] Existing technical documents Patent documents Patent Document 1: Japanese Patent Application Publication No. 2021-125976 Non-patent literature Non-Patent Document 1: "Response of a Dynamic Vibration Absorber System Based on Parametric Excitation of a Pendulum", Proceedings of the Japan Society of Mechanical Engineers (C), Vol. 67, No. 661 (2001-9), Paper No. 00-1494, pp. 15-21 Summary of the Invention

[0005] Technical issues However, when the pendulum is allowed to vibrate freely, in regions with large swing angles and amplitudes, the restoring force caused by gravity acting on the pendulum is disproportionate to the swing angle and is nonlinear, causing the pendulum's natural frequency to change. Therefore, in vibration damping devices utilizing a pendulum, in regions where the pendulum's amplitude is large and the restoring force is nonlinear, it is impossible to maintain the required ratio (e.g., 1:1, 1:1 / 2, etc.) between the pendulum's natural frequency and the natural frequency of the object being damped, resulting in reduced damping effectiveness or chaotic pendulum motion. Therefore, the pendulum is limited to a small amplitude range where its nonlinear effects are negligible in order to achieve a damping effect within this range.

[0006] In a pendulum-type dynamic vibration absorber system that utilizes self-parameter excitation, the required restoring force can be obtained by setting half of the natural frequency of the object to be damped as the natural frequency of the pendulum, reducing the mass of the pendulum, and correspondingly increasing the amplitude of the pendulum.

[0007] However, in regions with large pendulum amplitudes, the restoring force caused by the gravity applied to the pendulum is disproportionate to the angle of the pendulum, and the natural frequency varies depending on the amplitude of the pendulum. If the natural frequency changes, it will lead to a deviation from the aforementioned condition of "setting half of the natural frequency of the object to be damped as the natural frequency of the pendulum," resulting in insufficient damping effect and a decrease in the damping performance of the damping device.

[0008] Therefore, the present invention was made in view of the above-mentioned previously unsolved problems, and its object is to provide a pendulum device that can adjust the amplitude dependence of the gravity-based restoring force of a pendulum to a desired characteristic, a vibration damping device using the pendulum device, and a design method for the vibration damping device.

[0009] Technical solution According to one aspect of the present invention, a pendulum device is provided, comprising: a pendulum member acting with a gravity-based restoring force, performing pendulum motion around a fulcrum, at least a portion of which is composed of a first magnetic member; and a fixing member providing a magnetically repulsive or attractive force to the pendulum member as a magnetically based restoring force, at least a portion of which is composed of a second magnetic member, wherein the pendulum device has a magnetically based restoring force that counteracts the nonlinear component of the gravity-based restoring force acting on the pendulum member by adjusting at least one of the magnetic flux density of at least one of the first magnetic member and the second magnetic member, the relative position of the first magnetic member and the second magnetic member, and the mass of the pendulum member.

[0010] In addition, according to another aspect of the present invention, a vibration damping device is provided, which is a vibration damping device that uses a pendulum device that performs pendulum motion to dampen vibration, wherein the pendulum device uses a pendulum device of the above-described manner.

[0011] Furthermore, according to another aspect of the present invention, a method for designing a vibration damping device is provided, which is a method for designing a vibration damping device that uses a pendulum component acting with a gravity-based restoring force and moving like a pendulum around a fulcrum to dampen the vibration of an object. The method includes: arranging a first magnetic component on at least a portion of the pendulum component; arranging a second magnetic component at a position that provides a magnetic repulsive force or attractive force to the first magnetic component as a magnetic-based restoring force; and adjusting at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component, so that the nonlinear component of the gravity-based restoring force acting on the pendulum component and the nonlinear component of the magnetic force restoring force based on the magnetic force between the first magnetic component and the second magnetic component are canceled out.

[0012] Furthermore, according to another aspect of the present invention, a pendulum device is provided, wherein a first magnetic member is disposed on at least a portion of a pendulum member which experiences a gravity-based restoring force and performs pendulum motion around a fulcrum, and a second magnetic member is disposed at a position that provides a magnetically repulsive or attractive force to the first magnetic member as a magnetically restoring force. At least one of the magnetic flux density of the first and second magnetic members, the relative position of the first and second magnetic members, and the mass of the pendulum member can be adjusted to cancel out the nonlinear component of the gravity-based restoring force acting on the pendulum member and the nonlinear component of the magnetically restoring force based on the relationship between the first and second magnetic members.

[0013] Furthermore, a pendulum device is provided, wherein a first magnetic component is disposed on at least a portion of a pendulum component that experiences a gravity-based restoring force and performs pendulum motion around a fulcrum, and a second magnetic component is disposed at a position that provides a magnetically repulsive or attractive force to the first magnetic component as a magnetically restoring force. At least one of the magnetic flux density of the first and second magnetic components, the relative position of the first and second magnetic components, and the mass of the pendulum component can be adjusted to allow the restoring force characteristics of the sum of the gravity-based and magnetically restoring forces to possess soft-spring or hard-spring characteristics through the synergistic effect of the nonlinear component of the gravity-based restoring force acting on the pendulum component and the nonlinear component of the magnetically restoring force between the first and second magnetic components.

[0014] According to another aspect of the present invention, a pendulum device is provided, comprising: a first pendulum member acting with a restoring force based on gravity, pendulum motion about a fulcrum, and at least a portion thereof being composed of a first magnetic member; a first fixing member providing a magnetic repulsive force to the first pendulum member, and at least a portion thereof being composed of a second magnetic member, the repulsive force having a nonlinear component of the magnitude that cancels out the nonlinear component of the gravity-based restoring force acting on the first pendulum member; a second pendulum member acting with a gravity-based restoring force, pendulum motion about the fulcrum, and at least a portion thereof being composed of a third magnetic member; and a second fixing member providing a magnetic repulsive force to the second pendulum member. The magnetically repulsive force, at least partially composed of a fourth magnetic component, provides a nonlinear component that cancels out the nonlinear component of the gravity-based restoring force acting on the second pendulum component. The second pendulum component is provided as a pendulum component that is continuously rigidly connected to the first pendulum component along an extension of the first pendulum component. It is configured to perform a single pendulum motion in the vertical plane around the fulcrum, and thus, when at rest, is maintained in a horizontal state by the repulsive force based on the magnetic force between the first and second magnetic components and the attractive force based on the magnetic force between the third and fourth magnetic components.

[0015] Furthermore, according to another aspect of the present invention, a pendulum device is provided, comprising: a pendulum member acting with a gravity-based restoring force to perform pendulum motion around a fulcrum, and at least a portion thereof being composed of a first magnetic member; and a fixing member providing a magnetically repulsive or attractive force to the pendulum member as a magnetically based restoring force, and at least a portion thereof being composed of a second magnetic member, the pendulum device having a magnetically based restoring force that counteracts the nonlinear component of the gravity-based restoring force acting on the pendulum member.

[0016] Furthermore, according to another aspect of the present invention, a pendulum device is provided, which has a vertical Z-axis in an orthogonal XYZ coordinate system, and comprises: a pendulum member having rigidity, one end of which is rotatably mounted on a fulcrum, and which performs pendulum motion in the XY plane with the fulcrum as the center, at least a portion of which is composed of a first magnetic member; and a fixing member that provides a magnetically repulsive or attractive force to the pendulum member, at least a portion of which is composed of a second magnetic member.

[0017] Technical effect According to one aspect of the invention, in the pendulum device, the amplitude dependence of the restoring force can be adjusted to a desired characteristic, and by using the pendulum device, the reduction in the vibration damping performance of the damping device, which accompanies the amplitude dependence of the restoring force, can be suppressed. Attached Figure Description

[0018] Figure 1 This is an explanatory diagram illustrating an example of the vibration damping device of the present invention.

[0019] Figure 2 This is a structural diagram illustrating an example of the pendulum device of the present invention.

[0020] Figure 3 It is a graph showing the displacement of the pendulum body when it is allowed to vibrate freely without the restoring force based on the magnetic component being applied.

[0021] Figure 4 It is shown Figure 3 A chart of the backbone curve.

[0022] Figure 5 It is a graph showing the time history waveform obtained in the experiment when the pendulum component of the present invention is allowed to vibrate freely.

[0023] Figure 6 It is shown Figure 5 A chart of the spine's curve.

[0024] Figure 7 It is a graph showing the time history waveform obtained in the experiment when the pendulum component of the present invention is allowed to vibrate freely.

[0025] Figure 8 It is shown Figure 7 A chart of the spine's curve.

[0026] Figure 9 It is an explanatory diagram that schematically shows a horizontally moving magnet to illustrate the magnetic force acting on the magnetic component on the pendulum side.

[0027] Figure 10 It is a graph showing the relationship between the amount of magnet movement and the coefficients of the first and third terms in the mathematical formula representing the total magnetic force acting on a horizontally moving magnet.

[0028] Figure 11 schematically shown Figure 2 The diagram shows the pendulum device.

[0029] Figure 12 This is an explanatory diagram illustrating the pendulum device used in the calculation of the effect of the pendulum device of the present invention.

[0030] Figure 13 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 4.

[0031] Figure 14This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 4.

[0032] Figure 15 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 4.

[0033] Figure 16 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 5.

[0034] Figure 17 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 7.

[0035] Figure 18 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 7.

[0036] Figure 19 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 7.

[0037] Figure 20 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 7.

[0038] Figure 21 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 7.

[0039] Figure 22 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 7.

[0040] Figure 23 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 8.

[0041] Figure 24 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 8.

[0042] Figure 25 This is a schematic diagram illustrating the configuration of the pendulum device used in the trial calculation.

[0043] Figure 26 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 8.

[0044] Figure 27 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 9.

[0045] Figure 28 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 9.

[0046] Figure 29 This is an explanatory diagram that schematically shows the pendulum device for illustrating variation 9.

[0047] Figure 30 This is an explanatory diagram illustrating the installation position of the pendulum device in Modified Example 10.

[0048] Figure 31 This is an explanatory diagram illustrating the installation position of the pendulum device in Modified Example 10.

[0049] Figure 32 This is an explanatory diagram illustrating the installation position of the pendulum device in Modified Example 10.

[0050] Figure 33 It is a graph used to illustrate the relationship between the nonlinear component and the excitation frequency in variation 11.

[0051] Figure 34 It is a graph used to illustrate the relationship between the nonlinear component and the excitation frequency in variation 11.

[0052] Figure 35 This is an explanatory diagram of a pendulum device schematically illustrating a method for adjusting the motion characteristics of a pendulum component.

[0053] Figure 36 This is an explanatory diagram of a pendulum device schematically illustrating a method for adjusting the motion characteristics of a pendulum component.

[0054] Explanation of reference numerals in the attached figures 1, 101, 201, 301 Pendulum Mechanism 2, 102, 202 Pendulum Components 2' Disc-shaped pendulum component 21. Pendulum Body 22, 22a, 22b, 122, 222, 222a, 222b Magnetic components on the pendulum side 3. Pendulum support components 31 Support mechanism 32-axis Fixed magnetic components: 4a, 4b, 104, 104a, 204, 204a, 204b 5a, 5b Magnetic component support 51a, 51b First Component 52a, 52b Second Components 6 Support body 10 Vibration damping device 20 buildings 220 Vibration Reduction Object 320 piping 420 vehicles Detailed Implementation

[0055] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0056] It should be noted that in the following detailed description, several specific configurations are described in order to provide a comprehensive understanding of the embodiments of the present invention. However, it will be apparent that other embodiments can be implemented and that the invention is not limited to these specific configurations. Furthermore, the following embodiments do not limit the invention as defined in the claims. Additionally, the combinations of features described in the embodiments are not necessarily all necessary for the solution of the invention.

[0057] <Implementation Method> Here, we will describe the application of the pendulum device 1 of one embodiment of the present invention to the vibration damping device 10 of the building 20, but it is not limited to the vibration damping device 10 of the building 20.

[0058] Figure 1 (a) is a vibration model showing an example of the vibration damping device 10.

[0059] exist Figure 1 In (a), M, k, and c represent the mass, spring constant, and viscous decay coefficient of the main system, respectively. Additionally, m, θ, and L represent the mass of the pendulum component, the angle of the pendulum component relative to the vertical, and the distance of the pendulum component from the fulcrum to the other end, respectively.

[0060] Figure 1 (b) is a conceptual diagram of a case where the vibration damping device 10 is installed as a structure on the building 20. The vibration damping device 10 is installed on the roof of the building 20 to suppress the lateral sway of the building 20.

[0061] Figure 2 This is a front view showing an example of the pendulum device 1.

[0062] The pendulum device 1 comprises: a pendulum component that performs pendulum motion around a fulcrum, at least a portion of which is composed of a first magnetic component; and a fixing component that provides a magnetically repulsive or attractive force to the pendulum component, at least a portion of which is composed of a second magnetic component.

[0063] Specifically, the pendulum device 1 includes a pendulum component 2, a pendulum support component 3 that supports the pendulum component 2, a pair of fixed magnetic components (second magnetic components) 4a and 4b that are disposed on both sides of the pendulum component 2, magnetic component support portions 5a and 5b that support the fixed magnetic components 4a and 4b, and a support body 6 that supports the pendulum support component 3 and the magnetic component support portions 5a and 5b.

[0064] The pendulum component 2 is suspended from the pendulum support component 3, and performs pendulum motion in the vertical plane with the axis 32 of the pendulum support component 3 as the fulcrum.

[0065] The pendulum component 2 includes a pendulum body 21 and a pair of pendulum-side magnetic members 22a and 22b. The pendulum body 21 is formed from a thin, elongated rectangular plate, and the pendulum-side magnetic members 22a and 22b are respectively disposed on the front and back sides of the pendulum body 21. As will be described later, a repulsive force is generated between the fixed magnetic members 4a and 4b and the pendulum-side magnetic members 22a and 22b in the pendulum body 21. Therefore, the pendulum body 21 preferably has rigidity that will not deform even when a repulsive force is applied.

[0066] The pendulum-side magnetic components (first magnetic components) 22a and 22b are formed of plate-shaped magnets composed of thin, elongated rectangular permanent magnets, with one side of the front and the other side magnetized as the N pole and the other side magnetized as the S pole. The pendulum-side magnetic components 22a and 22b are fixed to the front and back of the pendulum body 21 such that one side of the pendulum body 21 is the N pole and the other side is the S pole. Here, pendulum-side magnetic components 22a and 22b are respectively provided on the front and back of the pendulum body 21, but for example, one of the pendulum-side magnetic components with one side magnetized as the N pole and the other side magnetized as the S pole can also be used as the pendulum body 21 itself.

[0067] It should be noted that the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b may not be permanent magnets. They can be electromagnets or the like that can generate a repulsive force between the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b. However, from the point of view of ease of use, permanent magnets are preferred.

[0068] Furthermore, from the viewpoint of adjusting the restoring force, it is preferable that the magnetic flux density and size of the pendulum-side magnetic component 22a and the pendulum-side magnetic component 22b are the same. Similarly, it is preferable that the magnetic flux density and size of the fixed magnetic component 4a and the fixed magnetic component 4b are the same.

[0069] One end of the pendulum body 21 is mounted on the shaft 32 of the pendulum support member 3. At this time, the pendulum body 21 moves in the vertical plane with the shaft 32 as the fulcrum. The magnetic members 22a and 22b on the pendulum side are mounted in the direction of increasing amplitude facing the pendulum body 21.

[0070] In the pendulum component 2, the pendulum body 21, to which the pendulum-side magnetic components 22a and 22b are fixed, functions as the hammer of the pendulum. Here, the pendulum body 21 itself is used as the hammer, but the invention is not limited thereto; a hammer may be separately provided on the pendulum body 21.

[0071] The pendulum support member 3 includes a support mechanism 31, and a support along the axis of the pendulum. Figure 2The axis 32 extends in a direction orthogonal to the plane of the paper. The support mechanism 31 connects the axis 32 to the pendulum member 2 via bearings, so that the pendulum member 2 can be freely supported about the axis 32 as a fulcrum and perform pendulum motion.

[0072] The fixed magnetic components 4a and 4b are formed, for example, by cylindrical ferrite magnets, with one side in the thickness direction magnetized as the N pole and the other side magnetized as the S pole.

[0073] The magnetic component support 5a is formed by connecting the first component 51a and the second component 52a in a roughly hiragana "く" shape. The end of the first component 51a is fixed to the support body 6 with the inner angle formed by the first component 51a and the second component 52a as the pendulum component 2 side and the second component 52a extending in the vertical direction. A fixed magnetic component 4a is fixed to the end of the magnetic component support 5a on the second component 52a side. The fixed magnetic component 4a is arranged such that its magnetized surface faces the magnetized surface of the pendulum-side magnetic component 22a fixed to the pendulum body 21 in a stationary (equilibrium) state. In addition, the fixed magnetic component 4a has the same magnetic polarity for the magnetized surfaces of the fixed magnetic component 4a and the pendulum-side magnetic component 22a.

[0074] The magnetic component support 5b is formed by connecting the first component 51b and the second component 52b in a roughly inverted "く" shape (like the character "く" in hiragana). The end of the first component 51b is fixed to the support body 6 with the inner angle formed by the first component 51b and the second component 52b forming the pendulum component 2 side, and the second component 52b extending vertically. A fixed magnetic component 4b is fixed to the end of the magnetic component support 5b on the second component 52b side. The fixed magnetic component 4b is arranged such that its magnetized surface faces the magnetized surface of the pendulum-side magnetic component 22b fixed to the stationary pendulum body 21. Furthermore, the fixed magnetic component 4b has the same magnetic polarity for the magnetized surfaces of the fixed magnetic component 4b and the pendulum-side magnetic component 22b.

[0075] Furthermore, the magnetic component support portion 5a and the magnetic component support portion 5b are configured to be linearly symmetrical about the stationary pendulum component 2 as the axis of symmetry. In addition, the magnetic component support portions 5a and 5b are arranged so as not to hinder the movement of the pendulum component 2 when it is performing pendulum motion.

[0076] Furthermore, the magnetic component supports 5a and 5b are mounted on the support body 6 in a manner that allows for variable positioning in the plumb direction. Additionally, the pendulum support member 3 is mounted on the support body 6 in a manner that allows for variable positioning in the plumb direction. Therefore, by adjusting the vertical positions of the magnetic component supports 5a and 5b and the vertical position of the shaft 32, the relative vertical positions of the fixed magnetic components 4a and 4b and the pendulum-side magnetic components 22a and 22b can be adjusted. That is, the repulsive force between the fixed magnetic components 4a and 4b and the pendulum-side magnetic components 22a and 22b can be adjusted. It should be noted that the configuration can also be configured such that not only the vertical positions of the magnetic component supports 5a and 5b can be adjusted, but also their horizontal positions.

[0077] Furthermore, by fixing the main body 6 of the support portion, which is equipped with magnetic component support portions 5a and 5b and pendulum support component 3, to the building 20, which is the object to be damped, the pendulum component 2 is suspended in the vertical direction.

[0078] In the pendulum device 1 with this configuration, the pendulum member 2 performs pendulum motion with the axis 32 as the fulcrum. If the pendulum-side magnetic members 22a and 22b fixed to the pendulum body 21 approach the opposing fixed magnetic members 4a and 4b respectively as the pendulum moves, a repulsive force is generated between the pendulum-side magnetic members 22a and 22b and the fixed magnetic members 4a and 4b, and the repulsive force acts on the pendulum member 2. Therefore, compared with the case where there are no fixed magnetic members 4a and 4b and no pendulum-side magnetic members 22a and 22b, the restoring force is greater.

[0079] <Resilience Properties> Here, the restoring force characteristics of the pendulum component 2 will be explained.

[0080] The restoring force of the pendulum body 21 without the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b can be expanded by a Taylor series of sinθ as shown in equation (1). It should be noted that in equation (1), m is the mass of the pendulum component 2, g is the gravitational acceleration, and θ is the displacement angle from the resting state.

[0081]

Mathematical Formula 1

[0082] As shown in equation (1), since the coefficients of the terms proportional to the cube are negative, the restoring force based on gravity exhibits the nonlinear characteristics of a soft spring. Figure 3 The diagram shows the displacement of the pendulum body 21 in the direction of movement, taking into account the free vibration of the pendulum body 21. Figure 4The diagram shows a spine curve representing the relationship between the amplitude and natural frequency of the pendulum body 21, with a resting state as a reference. Figure 4 It can be seen that the natural frequency varies with the amplitude and has the characteristics of a soft spring.

[0083] On the other hand, such as Figure 2 As shown, the restoring force F of the magnetically-based pendulum is as follows: The pendulum has side magnetic components 22a and 22b and fixed magnetic components 4a and 4b. m It can be expressed by Taylor expansion as shown in equation (2).

[0084]

Mathematical Formula 2

[0085] Therefore, as Figure 2 As shown, the restoring force characteristics of the pendulum with pendulum-side magnetic components 22a and 22b and fixed magnetic components 4a and 4b can be approximated by the following equation (3) based on equations (1) and (2).

[0086]

Mathematical Expression 3

[0087] Equation (3) can be summarized as linear and nonlinear components as shown in equation (4).

[0088]

Mathematical Expression 4

[0089] Here, when the pendulum-side magnetic components 22a and 22b are respectively opposed to the fixed magnetic components 4a and 4b, and the magnetic poles of the opposing surfaces are set to be the same pole, i.e., when a repulsive force is generated, F1 in equation (4) is positive (linear restoring force characteristic) and F3 is positive (hard spring characteristic). When the magnetic poles of the opposing surfaces of the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b are set to be opposite poles, i.e., when an attractive force is generated, F1 is negative (not linear restoring force characteristic) and F3 is negative (soft spring characteristic).

[0090] As can be seen from equation (4), if F3 is adjusted to satisfy equation (5), the nonlinearity of the restoring force acting on the pendulum component 2 by gravity and magnetic force can be suppressed. That is, as long as the magnetic flux density, magnet shape, configuration position, and mass of the pendulum component 2 are selected for the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b, the magnetic force acting on the pendulum component 2 can be adjusted so that F3 satisfies equation (5). Specifically, the mass of the pendulum component 2 is the mass of the pendulum body 21 and the pendulum-side magnetic components 22a and 22b.

[0091]

Mathematical Expression 5

[0092] like Figure 2 As shown, in the pendulum device 1 equipped with pendulum-side magnetic components 22a and 22b and fixed magnetic components 4a and 4b, and adjusted to satisfy equation (5), in Figure 5 The figure shows the time history waveforms obtained in the experiment under the condition that the pendulum component 2 is allowed to vibrate freely. Figure 6 The diagram shows the spinal curve obtained experimentally, representing the relationship between the amplitude and natural frequency of pendulum component 2. Figure 6 It can be seen that the natural frequency hardly changes according to the amplitude of the pendulum component 2.

[0093] Figure 7 and Figure 8 This shows the adjustment to satisfy equation (5) as follows. Figure 2 In the pendulum device 1 shown, as fixed magnetic components 4a and 4b, the number of ferrite magnets is set to 2 respectively, increasing the magnetic force acting on the pendulum component 2, and the time history waveform obtained in the experiment under the condition that the pendulum component 2 vibrates freely ( Figure 7 ), and the spinal curve obtained in the experiment representing the relationship between the amplitude and natural frequency of pendulum component 2 (), Figure 8 ).Depend on Figure 8 It can be seen that by overlapping two ferrite magnets to form fixed magnetic components 4a and 4b respectively, the restoring force of the hard spring based on magnetic force is much greater than that of the soft spring based on gravity. Overall, it exhibits the characteristics of a hard spring with a higher natural frequency when the amplitude is larger.

[0094] That is, it can be seen that by changing the number of magnets used as magnetic components, the magnetic flux density of the magnetic components, and the arrangement position (relative position) of the magnetic components, the restoring force based on magnetic force can be adjusted. In this way, the synergistic effect of the nonlinear component of the gravity-based restoring force acting on the pendulum component 2 and the nonlinear component of the magnetic force based on the pendulum-side magnetic components 22a, 22b and the fixed magnetic components 4a, 4b can be utilized to adjust the restoring force characteristics of the pendulum component, which is composed of the sum of the gravity-based restoring force and the magnetic force based on the restoring force.

[0095] In equation (5), the restoring force based on magnetic force is adjusted to satisfy "(mg / 6) = F3", thus achieving the desired result. Figure 5 , Figure 6 As shown, a linear restoring force can be generated, maintaining the natural frequency approximately constant regardless of the amplitude. Furthermore, by adjusting the magnetically based restoring force to satisfy "(mg / 6) < F3", thus achieving... Figure 7 , Figure 8As shown, a restoring force with the characteristics of a hard spring can be generated. Conversely, by adjusting the magnetically based restoring force to satisfy "(mg / 6) > F3", a restoring force can be generated as shown. Figure 3 , Figure 4 As shown, compared to the case without a magnet, it can generate a restoring force with stronger soft spring characteristics.

[0096] It should be noted that the displacement of the pendulum body 21 and the pendulum component 2 was measured under the following conditions.

[0097] (a) When using, as Figure 2 The pendulum component 2 shown (corresponding to) Figure 5 , Figure 6 In the case of displacement measurement, the conditions are as follows.

[0098] Cylindrical ferrite magnets with a diameter d of 18 mm and a thickness t of 5 mm are used as fixed magnetic components 4a and 4b. The horizontal distance between the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b is set to 63 mm, and the vertical distance between the vertical center of the fixed magnetic components 4a and 4b and the center of the axis 32 is set to 50 mm.

[0099] For the measurement, a laser displacement meter (LK-G35A, manufactured by KEYENCE CORPORATION, Ltd.) was used. The laser displacement meter was fixed to the magnetic component support 5b, and the distance between it and the pendulum-side magnetic component 22b was measured. At this time, the horizontal distance to the pendulum-side magnetic component 22b was measured from the point 16 mm away vertically from the center of the axis 32 when the pendulum component 2 was in a stationary state. With the swing amplitude of the pendulum component 2 (the change amplitude of the measured value obtained by the laser displacement meter) being 5 mm, the rotation angle of the pendulum component 2 was approximately 17 degrees.

[0100] (b) The case where there are no fixed magnetic components 4a and 4b and pendulum-side magnetic components 22a and 22b (corresponding to) Figure 3 , Figure 4 The conditions for measuring the displacement of the pendulum body 21 are as follows.

[0101] That is, in using (a) above, such as Figure 2 In the case of the pendulum component 2 shown, the measurement was performed under the same conditions except that the fixed magnetic components 4a and 4b and the pendulum-side magnetic components 22a and 22b were not provided. That is, the horizontal distance to the pendulum body 21 was measured by taking the part of the pendulum body 21 in a stationary state that is 16 mm away from the center of the axis 32 in the vertical direction as the measurement point.

[0102] (c) In the case where a pendulum member 2 is used, each having two ferrite magnets as fixed magnetic components 4a and 4b respectively (corresponding to Figure 7 , Figure 8 The conditions for measuring displacement are as follows.

[0103] That is, in using (a) above, such as Figure 2 In the measurement conditions shown for the pendulum component 2, the measurements were performed under the same conditions, except that two ferrite magnets were used as fixed magnetic components 4a and 4b, respectively. Specifically, two cylindrical ferrite magnets with a diameter d of 18 mm and a thickness t of 5 mm were used overlappingly as fixed magnetic components 4a and 4b, effectively using ferrite magnets with a thickness of 10 mm for the fixed magnetic components 4a and 4b. Then, the horizontal distance to the pendulum-side magnetic component 22b was measured from a point 16 mm away from the center of the axis 32, where the pendulum component 2 was in a stationary state.

[0104] exist Figure 3 , Figure 5 , Figure 7 In the diagram, the horizontal axis represents time, and the vertical axis represents the displacement considering the direction of movement of the pendulum component 2 or the pendulum body 21. Figure 4 , Figure 6 , Figure 8 In the diagram, the horizontal axis represents frequency, and the vertical axis represents amplitude. Frequency is determined by... Figure 3 , Figure 5 , Figure 7 The calculation is based on the time interval between peaks. Figure 3 In the amplitude, the natural frequency changes from 1.398 Hz to 1.391 Hz, a change of approximately 0.5%. Figure 5 In the middle, based on the amplitude, the natural frequency changed from 1.446Hz to 1.448Hz, a change of about 0.1%. Figure 7 In the middle, based on the amplitude, the natural frequency changes from 1.511Hz to 1.518Hz, a change of about 0.5%.

[0105] <Adjustment of Restoration Properties> To make the pendulum device 1 have a linear restoring force, firstly, in Figure 2 In the pendulum device 1 shown, the number of magnets constituting each magnetic component, the magnetic force of the magnets, and the placement position (relative position) of the magnets are determined to satisfy equation (5). Specifically, the restoring force based on magnetic force is adjusted by adjusting the vertical positions of the magnetic component support portions 5a and 5b and the vertical position of the shaft 32, adjusting the number of fixed magnetic components 4a and 4b, the magnetic force of the magnets, the number of pendulum-side magnetic components 22a and 22b, the magnetic force of the magnets, and adjusting the mass of the pendulum component 2.

[0106] It should be noted that if the natural frequency of the building 20, which is the object of vibration reduction, is set as Ω, then the pendulum device 1 is constructed such that the natural frequency ω of the pendulum component 2 is ω=Ω.

[0107] (Properties of magnetism) Here, the characteristics of the magnetic force acting on the magnetic components 22a and 22b on the pendulum side will be explained.

[0108] (Magnetic properties during horizontal movement) First, such as Figure 9 As shown, the magnetic characteristics of magnets A to C are explained when they are arranged sequentially on a plane in a straight line and magnet B moves horizontally between magnets A and C.

[0109] Magnets A through C have the same shape, formed as thin plates, with one side magnetized as the N pole and the other as the S pole. Magnets A and B are arranged such that their S poles face each other, and magnets B and C are arranged such that their N poles face each other. It should be noted that the thickness of magnets A through C is denoted as d.

[0110] exist Figure 9 In the diagram, the initial state is defined as magnet B being positioned between magnets A and C. The gaps between magnets A and B in the initial state, and between magnets B and C in the initial state, are defined as r. The gap r between magnets A and B represents the horizontal distance from the center of the thickness of magnet A to the center of the thickness of magnet B. Similarly, the gap r between magnets B and C represents the horizontal distance from the center of the thickness of magnet B to the center of the thickness of magnet C. Furthermore, the displacement of magnet B from the initial state is defined as x. Displacement x represents the horizontal distance moved by the center of the thickness of magnet B.

[0111] exist Figure 9 In the middle, the force F exerted by magnet A on magnet B L It is represented by the following formula (6).

[0112]

Mathematical Expression 6

[0113] In addition, the force F exerted by magnet C on magnet B R It is represented by the following formula (7).

[0114]

Mathematical Expression 7

[0115] It should be noted that in equations (6) and (7), m is the magnetic charge of magnet B, m′ is the magnetic charge of magnets A and C, and μ is the permeability.

[0116] If we perform a Taylor expansion on equation (6), it is represented by equation (8).

[0117]

Mathematical Expression 8

[0118] If we perform a Taylor expansion on equation (7), it is represented by equation (9).

[0119]

Mathematical Expression 9

[0120] The total magnetic force F acting on magnet B can be approximated by equation (8) and equation (9) as shown in equation (10).

[0121]

Mathematical Formula 10

[0122] Here, in equation (10), the coefficient of the first-order term is defined as in equation (11).

[0123]

Mathematical Expression 11

[0124] In equation (10), the coefficient of the cubic term is defined as in equation (12).

[0125]

Mathematical Expression 12

[0126] According to equations (11) and (12), the ratio of the coefficient of the cubic term to the coefficient of the 1st term in equation (10) is expressed by equation (13).

[0127]

Mathematical Expression 13

[0128] Figure 10 This is a graph representing the relationship between "d / r" in equation (13) on the horizontal axis and "a3 / a1" on the vertical axis. Here, the larger the ratio of coefficients "a3 / a1", the greater the nonlinear effect of the magnetic force compared to the linear effect. Therefore, from... Figure 10 It can be seen that the smaller the "d / r" ratio, the easier it is to obtain the nonlinear effect of magnetic force.

[0129] (Magnetic properties of the pendulum during motion) Next, for example Figure 2 The magnetic characteristics of the pendulum device 1 during its pendulum motion will be explained.

[0130] Figure 11 schematically shown Figure 2 The pendulum device 1 shown.

[0131] When the fixed magnetic components 4a and 4b are in a position similar to the pendulum component 2 with pendulum-side magnetic components 22a and 22b, the pendulum component 2 is positioned as follows: Figure 11 Under the positional relationship shown, the force F exerted by the fixed magnetic component 4a on the pendulum component 2 l It is represented by the following formula (14).

[0132]

Mathematical Expression 14

[0133] In addition, the force F exerted by the fixed magnetic component 4b on the pendulum component 2 r It is represented by the following formula (15).

[0134]

Mathematical Expression 15

[0135] It should be noted that in equations (14) and (15), m1 is the magnetic charge of the magnets that serve as the magnetic components 22a and 22b mounted on the pendulum side of the pendulum, m2 is the magnetic charge of the fixed magnetic components 4a and 4b, μ is the permeability, and r is the gap between the magnetic poles when in a stationary state. Figure 11 In the context of considering the pendulum-side magnetic components 22a and 22b as a single magnetic component, the gap r is the horizontal distance from the center of the thickness of the fixed magnetic component 4a to the center of gravity of the pendulum-side magnetic component, and also the horizontal distance from the center of the thickness of the fixed magnetic component 4b to the center of gravity of the pendulum-side magnetic component. Furthermore, in... Figure 11 In the equation, x is the displacement of the pendulum component 2 from its rest state, and l is the equivalent length of the pendulum, which is the horizontal distance from the fulcrum Q to the center of gravity of the magnetic component on the pendulum side.

[0136] If we perform a Taylor expansion on equation (14), it is represented by equation (16).

[0137]

Mathematical Expression 16

[0138] If we perform a Taylor expansion on equation (15), it is represented by equation (17).

[0139]

Mathematical Expression 17

[0140] Here, equations (16) and (17) are defined as equation (18). k is a constant.

[0141]

Mathematical Expression 18

[0142] By combining the force F1 exerted by the fixed magnetic component 4a on the pendulum component 2 and the force F2 exerted by the fixed magnetic component 4b on the pendulum component 2... r Adding them together, the restoring force F based on the magnetic force can be approximated as shown in the following equation (19).

[0143]

Mathematical Expression 19

[0144] Furthermore, since x = lsinθ, we can obtain equation (20) from equation (19). It should be noted that θ is the displacement angle of the pendulum component 2 from its rest state.

[0145]

Mathematical Expression 20

[0146] On the other hand, the gravity-based restoring force of the pendulum component 2 can be approximated by the following equation (21). In equation (21), m is the mass of the pendulum component 2, and l is the equivalent length of the pendulum, which is the length from the fulcrum Q to the center of gravity of the magnetic component on the pendulum side. θ is the displacement angle of the pendulum component 2 from the resting state, θ″ is the angular acceleration of the displacement angle θ, and k is the value determined according to equation (18).

[0147]

Mathematical Expression 21

[0148] Here, it acts as Figure 11 The magnetic force of the pendulum component 2 shown can be considered as equivalent to the equivalent spring force F* shown in the following equation (22).

[0149]

Mathematical Expression 22

[0150] In equation (22), the term containing a1 is the linear component of the magnetic force, and the term containing a3 is the nonlinear component of the magnetic force.

[0151] The equivalent spring force F* has the following characteristics depending on the sign of the linear component containing a1 and the nonlinear component containing a3.

[0152] a1: When a1>0, it is positive rigidity; when a1<0, it is negative rigidity. a3: When a3>0, it is a hard spring; when a3<0, it is a soft spring. In equation (20), the coefficient of the first-order term can be regarded as the coefficient a1 in equation (22) as shown in equation (23).

[0153]

Mathematical Expression 23

[0154] Similarly, in equation (20), the coefficient of the cubic term can be regarded as the coefficient a3 in equation (22) as shown in equation (24).

[0155]

Mathematical Expression 24

[0156] Therefore, the restoring force of the magnetic force of the pendulum component 2 can be adjusted to have hard spring characteristics or soft spring characteristics by adjusting the components contained in the coefficient a3 of the cubic term represented by equation (24) to satisfy the following equation (25).

[0157]

Mathematical Expression 25

[0158] <Actions and Effects> With the restoring force adjusted in this way based on magnetic force, if vibration is input to the building 20, which is the object of vibration damping, the support body 6 fixed to the building 20 vibrates along with the vibration of the building 20, and the pendulum component 2 begins pendulum motion in the vertical plane with the axis 32 as the fulcrum. In the region where the amplitude of the pendulum component 2 is relatively small, since the restoring force based on magnetic force (i.e., the repulsive force) is relatively small, the restoring force based on gravity has a linear component, so the pendulum component 2 as a whole has a linear restoring force. In the region where the amplitude of the pendulum component 2 is relatively large, the restoring force based on gravity has a nonlinear component, but when a restoring force based on magnetic force is applied simultaneously with this restoring force based on gravity, this magnetic restoring force has a nonlinear component that cancels out the magnitude of the nonlinear component, so the nonlinear component is canceled out, and the pendulum component 2 has a linear restoring force. Therefore, regardless of the amplitude of the pendulum component 2, the restoring force is a linear restoring force.

[0159] Therefore, the restoring force of the pendulum component 2 is linear over a wider range of motion. As a result, regardless of the amplitude of the pendulum component 2, its natural frequency can be maintained at the same level as the natural frequency of the building 20. Thus, the reduction in vibration damping performance dependent on the amplitude of the pendulum device 1 can be suppressed.

[0160] Furthermore, since the pendulum component 2 maintains a linear restoring force within a wider range of amplitude, it can perform pendulum motion with a larger amplitude compared to pendulum devices where the linear restoring force is limited to a small amplitude range, thereby correspondingly improving vibration damping performance.

[0161] Assuming that the linear restoring force of the pendulum component 2 is limited to a small amplitude range, in order to achieve a vibration reduction effect over a wider amplitude range, it would be necessary to provide, for example, a vibration reduction device for small amplitudes and a vibration reduction device for large amplitudes. The vibration reduction device 10 of this embodiment, by simply providing fixed magnetic components 4a and 4b and pendulum-side magnetic components 22a and 22b, can achieve a vibration reduction effect over a wider amplitude range, from small amplitudes to relatively large amplitudes. Therefore, cost reduction and a larger-scale suppression device can be achieved.

[0162] Furthermore, since linear restoring force can be obtained over a wider range of motion in this way, even when a dynamic vibration absorber system utilizing self-parametric excitation is specifically constructed, for example, where the natural frequency of the object being damped and the natural frequency of the pendulum device 1 are configured as "1:1 / 2", a damping effect can still be achieved over a wider range of motion. Moreover, in the case of this dynamic vibration absorber system, the mass of the pendulum hammer can be reduced, that is, the mass of the pendulum component 2 can be reduced, thus enabling the pendulum device 1 and, consequently, the vibration damping device 10 to be lightweight.

[0163] Furthermore, while feedback control is theoretically known as a method for removing the nonlinear component of the restoring force, it requires actuators and sensors. Consequently, the construction of the vibration damping device becomes complex, leading to increased costs and power consumption. In the pendulum device 1 of this embodiment, a pendulum device 1 that generates a linear restoring force can be achieved simply by providing pendulum-side magnetic components 22a and 22b and fixed magnetic components 4a and 4b. Therefore, it can be implemented with a simple structure without increasing costs, and particularly without consuming power.

[0164] Furthermore, since the magnetic component supports 5a and 5b and / or the shaft 32 are mounted on the support body 6 in a vertically variable manner, the restoring force of the magnetically-based pendulum component 2 can be easily adjusted. Additionally, the pendulum-side magnetic components 22a and 22b are formed to be longer in the vertical direction than the fixed magnetic components 4a and 4b. Therefore, when the pendulum component 2 performs pendulum motion, a repulsive force can be generated between it and the fixed magnetic components 4a and 4b over a wider range, enabling efficient adjustment of the magnetically-based restoring force.

[0165] Here, the pendulum device of this embodiment is applied to a device having, for example... Figure 12 In the case of the pendulum device 1' with the disc-shaped pendulum 2' shown, the same effect as in the above embodiment can also be obtained. (The text abruptly ends here, likely due to an incomplete sentence or a formatting error.) Figure 12The calculations related to the vibration reduction performance of the disc-shaped pendulum 2' shown as a vibration reduction device for a building were performed. The results showed that the maximum amplitude of the disc-shaped pendulum 2' was [value missing] when it was excited with a maximum acceleration of 100 gal. Figure 12 θ) is 75°. Furthermore, the maximum displacement of the front end of the disc-shaped pendulum 2′ (i.e., the magnetic component 22′ on the pendulum side) is 1.57m. The building amplitude during vibration without the damping device is 0.16m, while the building amplitude during vibration with the damping device is 0.037m. That is, the building amplitude ratio is 22%, confirming that the use of the damping device can significantly suppress the building amplitude.

[0166] For example, a vibration damping device weighing 660t is installed inside the Taipei 101 skyscraper (509.2 meters high) in Xinyi District, Taipei City, Taiwan. In contrast, it can be seen that the pendulum device 1' can achieve the vibration damping effect of a 9-story building with a height of 30m by using a disc-shaped pendulum with a mass of 4800kg, and can significantly reduce the size.

[0167] exist Figure 12 And the configuration of the pendulum device 1′ used for the trial calculation is shown in Table 1.

[0168] The specifications of the buildings to be subjected to vibration reduction are as follows.

[0169] Mass: 800t, Height: 30m (9 floors), Natural Frequency: 1.24Hz, Attenuation Ratio: 0.05 Table 1

[0170] <Variation Example> (Variation Example 1) In the above embodiments, the case where the restoring force characteristic of the pendulum component 2 is linear was explained. However, in the above equation (5), by adjusting it to satisfy "(mg / 6) < F3", the restoring force characteristic of the pendulum device 1 can have a hard spring characteristic. Conversely, by adjusting it to satisfy "F3 < 0", it can have a stronger soft spring characteristic. For example, by configuring the pendulum device 1 with hard spring characteristics as a vibration damping device 10 in the piping of industrial equipment (plant) that performs self-excited vibration, good vibration damping performance can be achieved.

[0171] In enhancing the soft spring characteristics of the pendulum device 1, it is necessary to set the magnetic poles of the opposing surfaces of the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b to be opposite poles to generate an attractive force. In this case, since F1 in the above equation (2) is negative, a restoring force will not be generated by this alone, so a mg component (mg in the first term on the right side of equation (4)) that is the effect of gravity is necessarily required. For example, as described as a variation example below. Figure 20 As schematically shown in the pendulum device 201, when the pendulum component 202 vibrates in the horizontal plane, gravity does not affect the motion of the pendulum component 202. Therefore, in Figure 20 In the pendulum device 201 shown, if the magnetic poles of the opposing surfaces of the pendulum-side magnetic member and the fixed magnetic member are changed to opposite poles, the pendulum device cannot have restoring force and cannot realize a vibration reduction device.

[0172] (Variation Example 2) In the above embodiments, the natural frequency of the pendulum component 2 can also be obtained at a predetermined time, and the relative positions of the pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b can be adjusted so that the natural frequency is consistent with the natural frequency of the building 20, which is the object of vibration reduction.

[0173] For example, the natural frequency of the pendulum component 2 is obtained by measuring the distance between itself and the pendulum component 2 using a laser displacement meter and calculating the natural frequency based on the measurement result. An adjustment mechanism is provided that can adjust the relative position of the magnetic component supports 5a and 5b, which support and fix the magnetic components 4a and 4b, and the support body 6. Furthermore, the positions of the magnetic component supports 5a and 5b are adjusted in a direction that coincides with the natural frequency of the pendulum component 2 and the natural frequency of the building 20, which is the object of vibration reduction. By performing this operation at a pre-set time, such as a pre-set period, it is possible to eliminate deviations in the natural frequency caused by changes over time.

[0174] (Variation Example 3) In the above embodiment, a pendulum device 1 in which the pendulum member 2 performs pendulum motion in one vertical plane has been described, but it is not limited thereto. For example, it can also be configured to perform pendulum motion in two orthogonal vertical planes.

[0175] In this case, for example, in such Figure 2The support mechanism 31 shown is connected to the support body 6 by a separate mechanism that supports the support mechanism 31, with the axis of the support body 6 as the fulcrum, so that the pendulum motion occurs in a vertical plane orthogonal to the vertical plane in which the pendulum member 2 performs the pendulum motion. This allows the support mechanism 31 to perform the pendulum motion. Consequently, the pendulum member 2 performs the pendulum motion in a vertical plane orthogonal to the vertical plane in which it performs the pendulum motion with the axis 32 as the fulcrum. Furthermore, pendulum-side magnetic members 22a and 22b are provided on the pendulum member 2, and a pair of pendulum-side magnetic members, similarly formed to the pendulum-side magnetic members 22a and 22b, are provided on a surface orthogonal to these pendulum-side magnetic members 22a and 22b. Moreover, a pair of fixed magnetic members, similarly formed to the fixed magnetic members 4a and 4b, are provided opposite to these pair of pendulum-side magnetic members.

[0176] Therefore, since the pendulum member 2 performs pendulum motion in two mutually orthogonal vertical planes, a vibration damping device can be realized to reduce the vibration of the pendulum motion along the pendulum member. In this case, similarly to the above embodiment, since a magnetic restoring force can be generated along the two vertical planes, the same effect as the above embodiment can be obtained.

[0177] It should be noted that even when the pendulum component 2 performs pendulum motion in three or more vertical planes, the same effect as described above can be achieved by providing pendulum-side magnetic components 22a, 22b and fixed magnetic components 4a, 4b for each vertical plane.

[0178] (Variation Example 4) In a pendulum device that performs conical pendulum motion, the nonlinear component of the conical pendulum motion can also be removed.

[0179] In the case of a pendulum device 101 used to perform conical pendulum motion, such as Figure 13 As shown, the pendulum member 102 is supported by a pivot, for example, oscillating around a fulcrum Q. Furthermore, a pendulum-side magnetic member 122, including a permanent magnet, is disposed at the end of the pendulum member 102 opposite to the fulcrum Q. The permanent magnet of the pendulum-side magnetic member 122 is configured such that one end along its long side is magnetized as an N pole and the other end as an S pole, with one pole of the permanent magnet, for example, the N pole, being the fulcrum Q side, and the S pole being the side opposite to the fulcrum Q.

[0180] On the other hand, as the fixed magnetic member 104, for example, a sheet-like permanent magnet is used, and the fixed magnetic member 104 is horizontally arranged below the pendulum-side magnetic member 122. At this time, the side of the fixed magnetic member 104 that faces the pendulum-side magnetic member 122 is set as the S pole in a way that repels the pendulum-side magnetic member 122, and the other side is set as the N pole.

[0181] The magnetic force of the magnetic pole (fixed magnetic member 104) on the surface opposite to the pendulum-side magnetic member 122 can be expressed as follows.

[0182] (a) First, as Figure 14 As shown, the case where the magnetic pole face of the fixed magnetic member 104 is sufficiently large, i.e., the configuration in which the pendulum-side magnetic member 122 is always opposite to the fixed magnetic member 104 and is independent of the magnitude of the displacement angle θ of the pendulum member 102 from the rest state, will be explained.

[0183] The magnetic restoring force F of the pendulum component 102 can be approximated by the following equation (26). In equation (26), k is a constant composed of magnetic permeability and magnetic flux density. In equation (26), l is the equivalent length of the pendulum, which is the distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic component 122. d is the distance from the center of gravity of the pendulum-side magnetic component 122 to the magnetized surface of the S pole of the fixed magnetic component 104 when in a stationary state. The distance from the fulcrum Q to the magnetized surface of the S pole of the fixed magnetic component 104 is "l+d".

[0184]

Mathematical Expression 26

[0185] On the other hand, the gravity-based restoring force of the pendulum component 102 can be approximated by the following equation (27). In equation (27), m is the mass of the pendulum component 102, l is the equivalent length of the pendulum, and l is the distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic component 122. θ is the displacement angle of the pendulum component 102 from its rest state, and θ″ is the angular acceleration of the displacement angle θ. Figure 14 In the configuration shown, the restoring force F based on the magnetic force is in the vertically upward direction.

[0186]

Mathematical Expression 27

[0187] In equation (27), the coefficient of the first-order term contains "-(k / d 2 ")" represents a linear component, where the coefficient of the cubic term contains "-(kl / d)". 3 ")" represents a nonlinear component. Here, if we define it as a linear component, a1 = -(k / d 2 ), nonlinear component a3=-(kl / d 3 Then, the ratio of the nonlinear component a3 to the linear component a1, a3 / a1, is expressed by the following equation (28).

[0188]

Mathematical Expression 28

[0189] Therefore, it can be seen that by making "l" larger than "d", it is easier to obtain the nonlinear effect of magnetic force.

[0190] (b) Next, as Figure 15 As shown, the case where the magnetic pole surface of the fixed magnetic member 104 is not large enough will be explained, that is, the following configuration: when the displacement angle θ of the pendulum member 102 from the rest state is small, the pendulum-side magnetic member 122 is opposite to the fixed magnetic member 104, but when the displacement angle θ is large, the pendulum-side magnetic member 122 is not opposite to the fixed magnetic member 104.

[0191] The gravity-based restoring force of the pendulum component 102 under this condition can be approximated by the following equation (29). In equation (29), m is the mass of the pendulum component 102, l is the equivalent length of the pendulum, θ is the displacement angle of the pendulum component 102 from the rest state, and θ″ is the angular acceleration of the displacement angle θ. k is a constant composed of magnetic permeability and magnetic flux density. d in equation (29) is the distance from the center of gravity of the pendulum-side magnetic component 122 to the center of the thickness of the fixed magnetic component 104 when in a rest state. The distance from the fulcrum Q to the center of the thickness of the fixed magnetic component 104 is “l+d”. Figure 15 In the configuration shown, the restoring force F based on magnetic force is in the upward direction as shown in the figure.

[0192]

Mathematical Expression 29

[0193] In equation (29), if we assume that the linear component is a1 = (kd + kl) / d 3 Nonlinear component a3 = (k(d+l)(d)) 2 +9dl+9l 2 )) / 6d 5 Then the ratio of the nonlinear component a3 to the linear component a1, a3 / a1, is expressed by the following equation (30).

[0194]

Mathematical Expression 30

[0195] Therefore, it can be seen that by making "l" larger than "d", it is easier to obtain the nonlinear effect of magnetic force.

[0196] It should be explained that Figure 13 An example of a pendulum device 101 that performs conical pendulum motion is schematically shown. Figures 13-15In this embodiment, the pendulum component 102 corresponds to the pendulum component 2 in the above embodiment, the fixed magnetic component 104 corresponds to the fixed magnetic components 4a and 4b, and the pendulum-side magnetic component 122 corresponds to the pendulum-side magnetic components 22a and 22b.

[0197] (Variation Example 5) In such Figure 13 In the pendulum device 101 shown, which performs conical pendulum motion, it is also possible to... Figure 16 As shown, a cylindrical radially anisotropic magnet is used as the fixed magnetic member 104a instead of the sheet-shaped fixed magnetic member 104.

[0198] and Figure 13 Similarly, the pendulum member 102 is supported, for example, by a pivot and pivotally centered on a fulcrum Q. A pendulum-side magnetic member 122, made of a permanent magnet or the like, is disposed at the end of the pendulum member 102 opposite to the fulcrum Q. The permanent magnet is configured such that one end in the long side direction is magnetized as the N pole and the other end is magnetized as the S pole, for example, the N pole is on the fulcrum Q side and the S pole is on the side opposite to the fulcrum Q.

[0199] A cylindrical radially anisotropic magnet is configured as a fixed magnetic component 104a. The magnetic poles on the inner surface of the cylindrical fixed magnetic component 104a are set as S poles that repel the pendulum-side magnetic component 122, and the outer surface is set as N poles.

[0200] The magnetization of the S pole is not strictly isotropic, so it cannot be guaranteed that the pendulum component 102 will stably face vertically downward. However, due to the effect of gravity, in a static state, the extension direction of the pendulum component 102 becomes the vertical direction.

[0201] In this case, similar to the case where the pendulum member 2 performs single pendulum motion in the vertical plane as described in the above embodiment, the nonlinear component of the restoring force of the pendulum member 102 in the conical pendulum motion can be removed by adjusting the restoring force based on the magnetic force and utilizing the nonlinear effect of the magnetic force.

[0202] In addition, in modified examples 4 and 5, the pendulum member 102 is supported oscillatingly by using a pivot, thereby enabling it to perform conical pendulum motion, but it can also perform spherical pendulum motion.

[0203] In addition, in modified examples 4 and 5, the pendulum member 102 side and the fixed magnetic members 104 and 104a are set to different polarities, but they can also be set to the same polarity.

[0204] (Variation Example 6) In the above embodiments, the pendulum-side magnetic component and the fixed magnetic component can each have an external shape that is cylindrical, prismatic, spherical, arc-shaped, annular, hollow cylindrical, curved, or planar. Furthermore, the pendulum-side magnetic component and the fixed magnetic component may not have the same external shape; preferably, they have shapes capable of generating the desired repulsive or attractive force.

[0205] Furthermore, in the above embodiments, the pendulum body 21 is not limited to a thin plate, and can be formed from any rigid component. For example, the pendulum body 21 may not be separately provided, and the pendulum-side magnetic components 22a and 22b may be used as the pendulum body 21 themselves.

[0206] In addition, the magnetic components 22a and 22b on the pendulum side do not necessarily have to be located at the front end of the pendulum body 21. They are preferably located at a position that can generate the required repulsive or attractive force.

[0207] Similarly, the fixed magnetic components 4a and 4b can be used as magnetic component supports 5a and 5b without the need for separate magnetic component supports 5a and 5b. The placement of the fixed magnetic components 4a and 4b is not limited to the front end of the magnetic component supports 5a and 5b.

[0208] The pendulum-side magnetic components 22a and 22b and the fixed magnetic components 4a and 4b can be located and sized (length) in any way that can generate the required repulsive or attractive force.

[0209] (Variation Example 7) In the above embodiments, the case of using the pendulum member 2 to make it perform pendulum motion as the vibration damping device 10 has been described, but it is not limited to this.

[0210] When the pendulum component 2 is suspended and subjected to pendulum motion, in a stationary state, the extension direction of the pendulum component 2 is vertical, but... Figure 17 As shown in (a), the following pendulum device can also be used as a vibration damping device: one end of the pendulum component is mounted on the wall of the object to be damped. In a static state, the pendulum component is horizontal about the fulcrum Q, and the pendulum moves in the vertical direction based on this state.

[0211] It should be explained that Figure 17 and the following Figures 18-29 This diagram schematically illustrates a pendulum device. Similar to the embodiment described above, one end of the pendulum member is mounted on the vibration-damping object in such a way that the pendulum member moves in sync with the vibration of the object being damped. The fixing magnetic member is configured to vibrate integrally with the vibration-damping object in sync with its vibration. Furthermore, Figures 17-29The X, Y, and Z axes in the figure represent the axes in the orthogonal XYZ coordinate system.

[0212] [A] Figure 17 (a) is a pendulum device 201, which is configured such that one end of the pendulum component 202 is mounted on the wall or other surface of the vibration damping object 220 in a manner that allows pendulum motion in the vertical plane. The movable end of the pendulum component 202 performs pendulum motion in the vertical plane due to the up-and-down vibration of the vibration damping object 220. Figure 17 In (a), the downward direction is the Z-axis, the leftward direction is the X-axis, the direction towards the paper is the Y-axis, and the Z-axis direction is the direction of gravity.

[0213] In the pendulum member 202, a pendulum-side magnetic member 222 is installed at the end opposite to the vibration damping object 220. Taking the point on the vibration damping object 220 where the pendulum member 202 is installed as the fulcrum Q, the pendulum member 202 has rigidity to maintain the horizontal state as a stable equilibrium state.

[0214] The configuration is as follows: as the vibration damping object 220 vibrates up and down, the pendulum component 202 performs pendulum motion with the fulcrum Q as the axis, and the magnetic component 222 on the pendulum side moves on a circular arc in the vertical plane.

[0215] It should be noted that the pendulum component 202 may not necessarily be in a horizontal state, such as... Figure 17 As shown in (a), the pendulum-side magnetic member 222 of the pendulum member 202 can also be in a state slightly lower than horizontal. Here, the longer the distance between the fixed magnetic member 204 and the pendulum-side magnetic member 222, the smaller the magnetic force exerted by the fixed magnetic member 204 on the pendulum-side magnetic member 222. Therefore, if the magnetic force acting on the pendulum-side magnetic member 222 is lower than the magnetic force required to maintain the pendulum member 202 in a horizontal state, the pendulum member 202 will descend about the fulcrum Q and the pendulum-side magnetic member 222 will descend below horizontal. At this time, as the pendulum-side magnetic member 222 descends below horizontal, the portion of the mass of the pendulum member 202 supported by the vibration-damping object becomes larger, so the magnetic force required to support the pendulum member 202 is actually a small magnetic force. Therefore, the state in which the pendulum-side magnetic member 222 is slightly lower than horizontal is achieved. Furthermore, if the distance between the fixed magnetic member 204 and the pendulum-side magnetic member 222 increases further, the magnetic force exerted by the fixed magnetic member 204 on the pendulum-side magnetic member 222 will not be able to completely attract the pendulum-side magnetic member 222, and the pendulum member 202 will become vertical. Thus, even when the pendulum-side magnetic member 222 of the pendulum member 202 is slightly lower than horizontal, the same effect as when the pendulum member 202 remains horizontal can be achieved.

[0216] Here, as Figure 17 As shown in (a), the case where the pendulum-side magnetic component 222 is in a state of equilibrium with its state slightly lower than horizontal is explained.

[0217] The fixed magnetic member 204 is positioned opposite the pendulum member 202, which is in a slightly lower equilibrium state than horizontal, located on the side of the pendulum-side magnetic member 222, and is configured to vibrate integrally with the vibration-damping object 220. The fixed magnetic member 204 and the pendulum-side magnetic member 222 are magnetized such that the magnetic poles of their opposing surfaces are opposite poles when the pendulum member 202 is in equilibrium. Thus, when the vibration-damping object 220 is not vibrating, the pendulum member 202 is maintained in a slightly lower equilibrium state than horizontal due to the attraction between the fixed magnetic member 204 and the pendulum-side magnetic member 222. With the amplitude of the oscillation from the equilibrium state of the pendulum member 202 within a certain range, the pendulum member 202 performs pendulum motion due to the attraction between the pendulum-side magnetic member 222 and the fixed magnetic member 204.

[0218] If the vibration damping object 220 starts from the equilibrium state of the pendulum component 202 at rest... Figure 17 When the object vibrates along the Z-axis, the vibration of the damping object 220 is accompanied by the vibration of the pendulum component 202, which performs pendulum motion in the ZX plane with the fulcrum Q as the axis.

[0219] In this case, the restoring force based on gravity and the restoring force based on magnetism act on the pendulum component 202, and the nonlinear components of the restoring force based on gravity and the nonlinear components of the restoring force based on magnetism cancel each other out. Therefore, the pendulum component 202 as a whole has a linear restoring force, regardless of the magnitude of the amplitude of the pendulum component 202.

[0220] Therefore, it is possible to suppress the nonlinear component of the force acting on the pendulum component 202 that is performing pendulum motion due to gravity.

[0221] It should be explained that, for example Figure 17 As shown in (b), it can also be configured as follows: Figure 17 In (a), for example, by making the magnet of the fixed magnetic member 204 larger or the magnetic flux density greater, the magnetic force acting between the fixed magnetic member 204 and the pendulum-side magnetic member 222 is increased, so that the pendulum member 202 in the equilibrium state is closer to the horizontal state.

[0222] In addition, such as Figure 17 As shown in (c), it can also be configured as follows: Figure 17In (a), for example, by further raising the position of the fulcrum Q of the pendulum member 202, or adjusting the arrangement position of the fixed magnetic member 204, the center of gravity of the fixed magnetic member 204 is positioned lower than the extension line of the pendulum member 202 in a horizontal state. That is, it can also be configured such that by configuring a magnetic force that pushes the pendulum-side magnetic member 222 of the pendulum member 202 upward to make the pendulum member 202 horizontal, the pendulum member 202 is closer to a horizontal state in equilibrium.

[0223] exist Figure 17 (b) and Figure 17 In any of the cases in (c), it is possible to obtain the same as Figure 17 (a) has the same effect.

[0224] It should be noted that, in Figure 17 In (a) to (c), the linearity of the pendulum motion can be ensured within the range where an attractive force is generated between the pendulum-side magnetic member 222 and the fixed magnetic member 204 provided on the pendulum member 202.

[0225] [B] Figure 18 Is Figure 17 The pendulum device 201 is equipped with two fixed magnetic components 204 as shown in the figure.

[0226] That is, in such Figure 18 In the pendulum device 201 shown in (a), with Figure 17 Similarly, in the pendulum device 201 of (a), the pendulum member 202 is configured to perform pendulum motion in the ZX plane about the fulcrum Q, accompanying the up-and-down vibration of the damping object 220. Furthermore, the pendulum member 202 has rigidity to maintain a stable equilibrium state where the movable end of the pendulum member 202 is slightly lower than the horizontal state. Fixed magnetic members 204a and 204b are arranged above and below the pendulum member 202 in this equilibrium state, clamping it between the pendulum member 202 and the damping object 220. It should be noted that in this case, the pendulum member 202 can be in a horizontal state in the equilibrium state, or it can be as follows: Figure 18 It is in a slightly declining state as shown in (a).

[0227] Fixed magnetic members 204a and 204b are configured to face the pendulum-side magnetic member 222, which is located at the movable end of the pendulum member 202 in a balanced state. The side of the pendulum-side magnetic member 222 facing the fixed magnetic member 204a and the side of the pendulum-side magnetic member 222 facing the fixed magnetic member 204b are magnetized to opposite poles, while the sides of the fixed magnetic member 204a and the pendulum-side magnetic member 222 are magnetized to be the same poles. Furthermore, the sides of the fixed magnetic member 204b and the pendulum-side magnetic member 222 are magnetized to be the same poles.

[0228] Therefore, when the vibration damping object 220 is not vibrating, the pendulum member 202 is maintained in equilibrium by the repulsive force between the fixed magnetic member 204a and the pendulum-side magnetic member 222, the repulsive force between the fixed magnetic member 204b and the pendulum-side magnetic member 222, and gravity. Furthermore, when the amplitude of the pendulum member 202 from the equilibrium state is within a certain range, the pendulum member 202 is configured to perform pendulum motion through the repulsive forces between the pendulum-side magnetic member 222 and the fixed magnetic members 204a and 204b.

[0229] If starting from the equilibrium state where the pendulum component 202 is at rest, the vibration damping object 220 is in Figure 18 If the vibration along the Z-axis occurs in (a), the vibration of the damping object 220 will be accompanied by the vibration of the pendulum component 202, which will perform pendulum motion in the ZX plane with the fulcrum Q as the axis.

[0230] In this case, both gravity-based and magnetic-based restoring forces act on the pendulum component 202, and the nonlinear components of the gravity-based and magnetic-based restoring forces cancel each other out. Therefore, as a whole, the restoring force of the pendulum component 202 has a linear component, and it remains linear regardless of the amplitude of the pendulum component 202. This allows the nonlinear component of the gravity-based restoring force of the pendulum component 202 undergoing pendulum motion to be suppressed.

[0231] It should be noted that in this case, such as Figure 18 As shown in (b), it can also be configured as follows: Figure 18 In (a), for example, by further increasing the magnet of the fixed magnetic member 204b, the magnetic force acting between the fixed magnetic member 204b and the pendulum-side magnetic member 222 is greater than the magnetic force acting between the fixed magnetic member 204a and the pendulum-side magnetic member 222. By configuring it to have a magnetic force that can suppress the situation where the pendulum-side magnetic member 222 of the pendulum member 202 is lower than the horizontal state, the pendulum member 202 in the equilibrium state is closer to the horizontal state.

[0232] In addition, such as Figure 18 As shown in (c), it can also be configured as follows: Figure 18 In (a), while maintaining the same magnetic force between the fixed magnetic member 204a and the pendulum-side magnetic member 222, the pendulum member 202 is brought closer to a horizontal state by raising the position of the fulcrum Q of the pendulum member 202 or adjusting the arrangement of the fixed magnetic members 204a and 204b. Specifically, the arrangement is as follows: the positional relationship between the pendulum-side magnetic member 222 and the fixed magnetic members 204a and 204b is adjusted so that the distance between the pendulum-side magnetic member 222 and the fixed magnetic member 204b in the horizontal state is shorter than the distance between the pendulum-side magnetic member 222 and the fixed magnetic member 204a, and a magnetic force required to push the pendulum member 202 upward is further applied between the pendulum-side magnetic member 222 and the fixed magnetic member 204b. Thus, the pendulum member 202 approaches a horizontal state in equilibrium.

[0233] exist Figure 18 (b) and Figure 18 In any of the cases (c), it is possible to obtain the same as Figure 18 (a) Equivalent effect.

[0234] It should be noted that, in Figure 17 , Figure 18 In this embodiment, the pendulum component 202 corresponds to the pendulum component 2 in the above embodiment, the fixed magnetic components 204, 204a, and 204b correspond to the fixed magnetic components 4a and 4b, and the pendulum-side magnetic component 222 corresponds to the pendulum-side magnetic components 22a and 22b.

[0235] [C] Figure 19 Is Figure 17 The diagram shows the vibration of the movable end of the pendulum component 202 in the XY plane when the vibration damping object 220, on which the pendulum component 202 is installed, vibrates along the Y-axis direction.

[0236] exist Figure 19 In this diagram, the leftward direction is designated as the X-axis, the upward direction as the Y-axis, and the direction towards the paper as the Z-axis. The Z-axis direction is then defined as the direction of gravity. That is, Figure 19 This is a view of the pendulum device 201 from above.

[0237] The magnetic poles of the surfaces opposite to the fixed magnetic component 204 and the pendulum-side magnetic component 222 are set as opposite poles.

[0238] The pendulum component 202 is configured to have rigidity that maintains a constant distance between the fulcrum Q and the pendulum-side magnetic component 222, accompanying the vibration damping object 220 in... Figure 19 The vibration along the Y-axis causes the pendulum component 202 to perform pendulum motion in the XY plane with the fulcrum Q as the axis, and the magnetic component 222 on the pendulum side moves on the arc in the XY plane.

[0239] The pendulum member 202 is mounted at one end to the wall or similar surface of the vibration damping object 220 in a horizontal manner, and is configured to perform pendulum motion in the XY plane. The fixed magnetic member 204 is configured such that, on the extension of the long side of the pendulum member 202 when the pendulum member 202 is in a state orthogonal to the YZ plane containing the fulcrum Q at one end, the end face of the fixed magnetic member 204 side of the pendulum-side magnetic member 222 faces the end face of the pendulum-side magnetic member 222 side of the fixed magnetic member 204, and is configured to vibrate integrally with the vibration damping object 220. The fixed magnetic member 204 and the pendulum-side magnetic member 222 are magnetized in a manner where they are opposite poles to each other.

[0240] Therefore, when the damping object 220 is stationary, the pendulum member 202 is in a roughly horizontal state. Furthermore, through the attraction between the fixed magnetic member 204 and the pendulum-side magnetic member 222, the pendulum member 202 is maintained in a state orthogonal to the YZ plane containing the fulcrum Q of the damping object 220. Moreover, the pendulum member 202 is configured such that, in conjunction with the vibration of the damping object 220 in the Y-axis direction, and with the amplitude of the pendulum member 202 in the XY plane within a certain range, it undergoes pendulum motion through the attraction between the pendulum-side magnetic member 222 and the fixed magnetic member 204.

[0241] If the object to be damped 220 vibrates along the Y-axis from a state where the pendulum member 202 is at rest and orthogonal to the YZ plane containing the fulcrum Q of the object to be damped 220, then due to the restoring force based on magnetic force acting on the pendulum member 202, the pendulum member 202 performs pendulum motion in the XY plane with the fulcrum Q as the axis. In this case, since gravity does not act on the vibration of the pendulum member 202, the restoring force characteristic of the pendulum device 201 is that of a soft spring.

[0242] [D] Figure 20 Is Figure 18 The pendulum device 201 has a vibration damping object 220 with a pendulum component 202 installed, which vibrates along the Y-axis direction, and thus the movable end of the pendulum component 202 vibrates in the XY plane.

[0243] That is, in Figure 20 In the pendulum device 201 shown, and Figure 19Similarly, in the pendulum device 201 shown, the pendulum component 202 is configured to perform pendulum motion in the XY plane with the fulcrum Q as the axis, accompanying the vibration of the damping object 220 along the Y-axis. Furthermore, the fixed magnetic components 204a and 204b are configured to be orthogonal to the ZX plane containing the fulcrum Q of the damping object 220 in a static state, sandwiching the horizontally positioned pendulum component 202 on both sides in the horizontal plane and opposing the pendulum-side magnetic component 222. These fixed magnetic components 204a and 204b are configured to vibrate integrally with the damping object 220. Furthermore, the side of the pendulum-side magnetic member 222 opposite to the fixed magnetic member 204a and the side of the pendulum-side magnetic member 222 opposite to the fixed magnetic member 204b are magnetized to be opposite poles. The sides of the fixed magnetic member 204a and the pendulum-side magnetic member 222 opposite to each other are magnetized to be the same poles, and the sides of the fixed magnetic member 204b and the pendulum-side magnetic member 222 opposite to each other are magnetized to be the same poles.

[0244] Therefore, when the vibration damping object 220 is not vibrating, the pendulum member 202 is maintained in a horizontal state orthogonal to the ZX plane containing the fulcrum Q by the repulsive force between the fixed magnetic member 204a and the pendulum-side magnetic member 222, and the repulsive force between the fixed magnetic member 204b and the pendulum-side magnetic member 222. Furthermore, the pendulum member 202 is configured such that, when the amplitude of the pendulum member 202 from its state of orthogonality to the ZX plane containing the fulcrum Q is within a certain range, pendulum motion occurs due to the repulsive force between the pendulum-side magnetic member 222 and the fixed magnetic members 204a and 204b.

[0245] If the vibration damping object 220 starts from the state where the pendulum component 202 is at rest... Figure 20 When the object 220 vibrates along the Y-axis, the pendulum component 202 vibrates along the same direction, and the pendulum motion of the pendulum component 202 around the fulcrum Q in the XY plane is also accompanied by the vibration of the object 220. In this case, since gravity does not act on the vibration of the pendulum component 202, the pendulum device 201 has the characteristics of a stiff spring.

[0246] With Figure 2 Compared to the suspended pendulum device 1 shown above, such as Figure 19 and Figure 20 The pendulum device 201 shown, in which the pendulum component 202 vibrates in the XY plane in sync with the vibration of the damping object 220, can be installed in a space with a shorter vertical dimension at the installation location. For example, when using... Figure 19 and Figure 20 When the pendulum device 201 shown is used to constitute the vibration damping device 10, the dimension in the height direction of the location where the vibration damping device 10 is installed is greater than that of the location where the device is used. Figure 2In the case of the suspension-type pendulum device 1 vibration damping device shown, this size is short. Therefore, the vibration damping device can be installed relatively easily. When using the suspension-type pendulum device 1 vibration damping device, the installation location needs to be relatively high. Especially when installing a new vibration damping device in an existing building, there is a possibility that it is necessary to penetrate multiple layers to install it, making installation difficult, and there is also a possibility that it cannot be installed at all. In contrast, using Figure 19 and Figure 20 The vibration damping device of the pendulum device 201 shown does not require such a high height, so it can be installed relatively easily even when installed in an existing building. In addition, it can be installed even in spaces with a relatively short vertical dimension.

[0247] In addition, for such Figure 19 and Figure 20 As shown in the pendulum device 201, since the pendulum component 202 vibrates in the XY plane and is not subject to gravity, it is possible to obtain a result similar to... Figure 2 While maintaining the same vibration damping capacity as the suspended pendulum device 1, the mass of the pendulum component 202 can be reduced. That is, further miniaturization can be achieved.

[0248] It should be noted that, in Figure 19 , Figure 20 In this embodiment, the pendulum component 202 corresponds to the pendulum component 2 in the above embodiment, the fixed magnetic components 204, 204a, and 204b correspond to the fixed magnetic components 4a and 4b, and the pendulum-side magnetic component 222 corresponds to the pendulum-side magnetic components 22a and 22b.

[0249] [E] Figure 21 Is Figure 17 In the pendulum device 201, the vibration damping object 220, on which the pendulum component 202 is installed, is... Figure 21 The image shows the vibration along the X-axis, resulting in the movable end of the pendulum component 202 vibrating in the ZX plane. Figure 21 In this diagram, the leftward direction is defined as the Z-axis, the upward direction as the X-axis, the direction towards the paper as the Y-axis, and the Z-axis direction as the direction of gravity. That is, as shown... Figure 21 The pendulum device 201 shown is a pendulum device in which the pendulum component 202 is suspended relative to the vibration damping object 220.

[0250] In this case, the magnetic poles of the surfaces opposite to the fixed magnetic component 204 and the pendulum-side magnetic component 222 can be set as opposite poles, or they can be set as the same poles.

[0251] The pendulum component 202 is configured to maintain a constant distance between the fulcrum Q and the pendulum-side magnetic component 222. As the vibration damping object 220 vibrates along the X-axis, the pendulum component 202 performs pendulum motion with the fulcrum Q as the axis, and the pendulum-side magnetic component 222 moves on an arc in the vertical ZX plane.

[0252] A fixed magnetic member 204 is positioned on the extension line of the pendulum member 202, which is in a stationary state and is mounted at one end and suspended from the fulcrum Q of the damping object 220. It is configured to vibrate integrally with the damping object 220. The fixed magnetic member 204 and the pendulum-side magnetic member 222 are magnetized, for example, in a manner where they are opposite poles. Thus, when the damping object 220 is not vibrating, the pendulum member 202 is maintained in a vertical state by gravity and the attractive force between the fixed magnetic member 204 and the pendulum-side magnetic member 222.

[0253] If the vibration damping object 220 starts from a state where the pendulum component 202 is stationary and in a vertical position... Figure 21 When the middle vibrates along the X-axis, the pendulum component 202 will perform pendulum motion in the ZX plane with the fulcrum Q as the axis.

[0254] When the opposing surfaces of the fixed magnetic component 204 and the pendulum-side magnetic component 222 are opposite poles, the pendulum component 202 is subjected to a restoring force based on magnetic force. As a result, the nonlinear components based on gravity and magnetic force cannot cancel each other out. As a whole, the pendulum component 202 has a linear restoring force, but the resultant force of gravity and magnetic force acting on the pendulum is proportional to the angle of the pendulum, and the soft spring characteristics of nonlinearity increase.

[0255] It should be noted that when the magnetic poles of the opposing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 are set to be the same, the pendulum member 202 is configured such that, when the vibration damping object 220 is not vibrating, and the linear component of the force acting on the pendulum based on gravity is greater than the linear component of the repulsive force based on magnetic force, the pendulum member 202 is maintained in a stationary state facing vertically downwards. The pendulum member 202 performs pendulum motion when the amplitude of its oscillation from the vertically downwards position is within a certain range. Therefore, when the opposing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 are the same pole, since there is a restoring force consisting of the sum of the restoring force based on gravity and the restoring force based on magnetic force, the nonlinear components contained in each restoring force can be canceled out. As a whole, the pendulum member 202 can possess a nonlinear linear restoring force characteristic.

[0256] [F] Figure 22 Is Figure 18In the pendulum device 201, the vibration damping object 220, on which the pendulum component 202 is installed, is... Figure 22 The figure shows the vibration along the X-axis, resulting in the movable end of the pendulum component 202 vibrating in the ZX plane.

[0257] In this case, the magnetic poles of the surfaces of the fixed magnetic components 204a and 204b opposite to the pendulum-side magnetic component 222 can be either the same pole or opposite poles. An example of the case where they are the same pole is... Figure 2 The pendulum device 1 shown.

[0258] The pendulum component 202 is configured to have rigidity that maintains a constant distance between the fulcrum Q and the pendulum-side magnetic component 222, as the vibration damping object 220... Figure 22 The pendulum vibrates in the X-axis direction, and the pendulum component 202 moves in the ZX plane with the fulcrum Q as the axis. The magnetic component 222 on the pendulum side moves on the arc in the vertical plane.

[0259] Fixed magnetic components 204a and 204b are positioned along the extension of the pendulum component 202 in a stationary state, with one end mounted and suspended from the fulcrum Q of the damping object 220, and are configured to vibrate integrally with the damping object 220. The surfaces of the pendulum-side magnetic component 222 opposite to the fixed magnetic component 204a and the pendulum-side magnetic component 222 opposite to the fixed magnetic component 204b are magnetized in a manner that makes them opposite poles. For example, the fixed magnetic component 204a and the pendulum-side magnetic component 222 are magnetized in a manner that makes them the same pole, and similarly, the fixed magnetic component 204b and the pendulum-side magnetic component 222 are magnetized in a manner that makes them the same pole. Thus, when the damping object 220 is not vibrating, the pendulum component 202 is maintained in a vertical state by the gravitational and repulsive forces between the fixed magnetic components 204a and 204b and the pendulum-side magnetic component 222.

[0260] If the vibration damping object 220 starts from a state where the pendulum component 202 is stationary and in a vertical position... Figure 22 When the middle vibrates along the X-axis, the pendulum component 202 will perform pendulum motion in the ZX plane with the fulcrum Q as the axis.

[0261] When the magnetic poles of the surfaces opposite to the fixed magnetic components 204a and 204b and the pendulum-side magnetic component 222 are the same, a restoring force based on magnetic force acts on the pendulum component 202. Thus, by adjusting parameters such as the distance between magnets and / or the thickness of magnets in a static state facing vertically downward, the nonlinear component based on gravity cancels out the nonlinear component based on magnetic force. Therefore, the pendulum component 202 as a whole has a linear restoring force, and the restoring force is linear regardless of the amplitude of the pendulum component 202.

[0262] On the other hand, when the magnetic poles of the opposing surfaces of the fixed magnetic components 204a and 204b and the pendulum-side magnetic component 222 are respectively set to opposite poles, the configuration is such that, when the damping object 220 is not vibrating, the pendulum component 202 maintains a static state in the vertically downward direction by making the restoring force based on gravity greater than the linear component of the attraction force based on magnetic force. When the opposing surfaces of the fixed magnetic components 204a and 204b and the pendulum-side magnetic component 222 are opposite poles, there exists a restoring force consisting of the sum of the restoring force based on gravity and the linear component based on magnetic force, which can cause the pendulum component 202 to perform pendulum motion along with the vibration of the damping object 220. However, in this case, the nonlinear component cannot be canceled out, resulting in increased soft spring characteristics.

[0263] Here, the restoring force characteristics of the pendulum device 201 differ depending on whether the magnetic poles of the surfaces opposite to the fixed magnetic components 204a and 204b and the pendulum-side magnetic component 222 are set to opposite poles or the same poles. When the poles are the same poles, it exhibits soft spring characteristics, while when the poles are opposite poles, it exhibits hard spring characteristics. Therefore, it is sufficient to determine whether the magnetic poles of the surfaces opposite to the fixed magnetic components 204a and 204b and the pendulum-side magnetic component 222 are set to opposite poles or the same poles based on the desired characteristics.

[0264] (Variation Example 8) [A] can be combined as follows: Figure 17 The pendulum device 201 shown and as Figure 18 The pendulum device 201 shown is as follows: Figures 23-26 As shown, pendulum-side magnetic components 222a and 222b are provided at both ends of the pendulum component 202, forming a pendulum device 301 with a fulcrum Q in the middle part of the long side direction of the pendulum component 202.

[0265] like Figure 23 As shown, a pendulum-side magnetic member (first magnetic member) 222a is provided at one end of the pendulum member 202. Additionally, a fixed magnetic member (second magnetic member, first fixed member) 204 is provided on the extension line of the pendulum member 202 in its equilibrium state (stationary state), opposite to the pendulum-side magnetic member 222a. The magnetic poles of the surfaces of the pendulum-side magnetic member 222a and the fixed magnetic member 204 are opposite poles to generate an attractive force. Furthermore, the configuration is such that the pendulum member 202 is supported approximately horizontally at a fulcrum Q located in its middle portion, and the pendulum member 202 performs pendulum motion in the ZX plane about the fulcrum Q as an axis. Figure 23 In the diagram, the downward direction is the Z-axis, the leftward direction is the X-axis, the direction towards the paper is the Y-axis, and the Z-axis direction is the direction of gravity.

[0266] A pendulum-side magnetic component (third magnetic component) 222b is provided at the other end of the pendulum component 202. Fixed magnetic components (fourth magnetic component, second fixed component) 204a and 204b are provided on both sides of the pendulum-side magnetic component 202 in a manner that clamps the pendulum-side magnetic component 222b. The magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204b are set to opposite poles, while the magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204a are set to the same pole, so that they repel each other.

[0267] Thus, the pendulum A on the left end and the pendulum B on the right end of the pendulum member 202 operate in conjunction, and the magnetic components are configured differently; for example, pendulum A is configured to have soft spring characteristics, and pendulum B is configured to have hard spring characteristics. Furthermore, the configuration allows for independent adjustment of the magnetic force acting on pendulum A and pendulum B. Moreover, by adjusting either or both of the magnetic forces acting on pendulum A and pendulum B according to desired characteristics, the linear restoring force and the nonlinear restoring force can be set independently.

[0268] Furthermore, in this case, the magnetic components 222a and 222b on the pendulum side are also subject to gravity and magnetic force between themselves and their respective opposing fixed magnetic components. Therefore, sometimes the pendulum component 202, even in a static equilibrium state, is not horizontal and may tilt to one side. In this case, either pendulum A or pendulum B, or both, may also be tilted as follows: Figure 17 (b) Figure 17 (c) Figure 18 (b) Figure 18 As shown in (c), by adjusting the positional relationship between the pendulum-side magnetic component 222a and the fixed magnetic component 204, the positional relationship between the pendulum-side magnetic component 222b and the fixed magnetic component 204b, or by adjusting the size of the magnets of the fixed magnetic components 204 and 204b, the magnetic force acting on one or both of the pendulum-side magnetic components 222a and 222b is adjusted, thereby adjusting the pendulum component 202 to a near-horizontal state when it is in a stationary state.

[0269] [B] can also be combined as follows: Figure 19 The pendulum device 201 shown and as Figure 20 The pendulum device 201 shown is, for example, as Figure 24 As shown, pendulum-side magnetic components 222a and 222b are provided at both ends of the pendulum component 202, forming a pendulum device 301 with a fulcrum Q in the middle part of the long side direction of the pendulum component 202.

[0270] like Figure 24 As shown, a pendulum-side magnetic member (first magnetic member) 222a is provided at one end of the pendulum member 202. Additionally, a fixed magnetic member (second magnetic member, first fixed member) 204 is provided on the extension line of the pendulum member 202 in its equilibrium state (stationary state), opposite to the pendulum-side magnetic member 222a. The magnetic poles of the surfaces of the pendulum-side magnetic member 222a and the fixed magnetic member 204 are set as opposite poles to generate an attractive force. Furthermore, the pendulum member 202 is configured such that it is supported approximately horizontally at a fulcrum Q located in its middle portion, and the pendulum member 202 performs pendulum motion in the XY plane. Figure 24 In this diagram, the leftward direction is designated as the X-axis, the upward direction as the Y-axis, and the direction towards the paper as the Z-axis. The Z-axis direction is then defined as the direction of gravity. That is, Figure 24 This is a view of the pendulum device 301 from above.

[0271] A pendulum-side magnetic component (third magnetic component) 222b is provided at the other end of the pendulum component 202. Fixed magnetic components (fourth magnetic component, second fixed component) 204a and 204b are provided on both sides of the pendulum-side magnetic component 222b in a manner that clamps the pendulum-side magnetic component 222b. The magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204b are set to be opposite poles. The magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204a are set to be the same poles. The magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204b are set to be the same poles, so that they repel each other.

[0272] Thus, the pendulum A on the left end and the pendulum B on the right end of the pendulum component 202 are configured to operate in tandem, and the magnetic components are configured differently; for example, pendulum A is configured to have soft spring characteristics, and pendulum B is configured to have hard spring characteristics. Furthermore, by configuring the magnetic force acting on pendulum A and pendulum B to be individually adjustable, either or both of the magnetic forces acting on pendulum A and pendulum B can be adjusted according to the desired characteristics, thereby enabling independent setting of the linear restoring force and the nonlinear restoring force.

[0273] In such a case Figure 24 In the case of the pendulum device 301 shown, it is also possible to obtain the same result as described above. Figure 19 and Figure 20 The pendulum component 202 shown has the same effect as the pendulum device 201 that vibrates in the XY plane in sync with the vibration of the damping object 220. For example, it is similar to... Figure 23 The following Figure 26Compared to the case where the pendulum component 202 performs pendulum motion in the ZX plane, the height of the space required to install the pendulum device 301 can be lower. Therefore, even if the pendulum device 301 is subsequently installed in an existing building or similar structure, it can be installed more easily.

[0274] Incidentally, a meeting was held with the general Figure 24 The calculations related to the vibration reduction performance of the pendulum device 301, in which the pendulum component 202 vibrates in the XY plane, are performed when it is used as a vibration reduction device for a building. The results show that, under the condition of excitation with a maximum acceleration of 50 gal, the maximum amplitude of the pendulum component 202 of the vibration reduction device is ( Figure 25 θ) is 12°. In addition, the building amplitude when the building vibrates without the vibration damping device is 0.082m, while the building amplitude when the vibration damping device is used is 0.023m, and the amplitude ratio is 28%, confirming that the use of the vibration damping device can significantly suppress the building amplitude.

[0275] exist Figure 25 And the configuration of the pendulum device 301 used for the trial calculation is shown in Table 2.

[0276] The specifications of the buildings to be subjected to vibration reduction are as follows.

[0277] Mass: 800t, Height: 30m, Natural Frequency: 1.24Hz, Attenuation Ratio: 0.05 Table 2

[0278] [C] can also be combined as follows: Figure 21 The pendulum device 201 shown and as Figure 22 The pendulum device 201 shown is, for example, as Figure 26 As shown, pendulum-side magnetic components 222a and 222b are provided at both ends of the pendulum component 202, forming a pendulum device 301 with a fulcrum Q in the middle part of the long side direction of the pendulum component 202.

[0279] like Figure 26As shown, a pendulum-side magnetic member (first magnetic member) 222a is provided at one end of the pendulum member 202. Additionally, a fixed magnetic member (second magnetic member, first fixed member) 204 is provided on the extension line of the pendulum member 202 in its equilibrium state (stationary state), opposite to the pendulum-side magnetic member 222a. The magnetic poles of the surfaces of the pendulum-side magnetic member 222a and the fixed magnetic member 204 are set as opposite poles to generate an attractive force. Furthermore, the configuration is such that the pendulum member 202 is supported vertically at a fulcrum Q located in its middle portion, and the pendulum member 202 performs pendulum motion in the ZX plane about the fulcrum Q as an axis. Figure 26 In the diagram, the leftward direction is set as the X-axis, the downward direction as the Z-axis, the direction towards the paper as the Y-axis, and the Z-axis direction is set as the direction of gravity.

[0280] A pendulum-side magnetic component (third magnetic component) 222b is provided at the other end of the pendulum component 202. Fixed magnetic components (fourth magnetic component, second fixed component) 204a and 204b are provided on both sides of the pendulum-side magnetic component 202 in a manner that clamps the pendulum-side magnetic component 222b. The magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204b are set to opposite poles, while the magnetic poles of the surfaces of the pendulum-side magnetic component 222b and the fixed magnetic component 204a are set to the same pole, so that they repel each other.

[0281] Thus, the upper pendulum A and the lower pendulum B of the pendulum member 202 move in tandem, and the magnetic components are configured differently; for example, pendulum A is configured to have soft spring characteristics, and pendulum B is configured to have hard spring characteristics. Furthermore, by configuring the magnetic force acting on pendulum A and pendulum B to be individually adjustable, either or both of the magnetic forces acting on pendulum A and pendulum B can be adjusted according to desired characteristics, thereby enabling independent setting of linear and nonlinear restoring forces.

[0282] It should be noted that, in Figure 26 In this case, the upper side is designated as pendulum A and the lower side as pendulum B. However, the configuration can also be reversed, with the upper side designated as pendulum B and the lower side as pendulum A.

[0283] (Variation Example 9) In such Figure 19 , Figure 20 , Figure 24In the pendulum devices 201 and 301 shown, which are configured such that the pendulum member 202 performs pendulum motion in a horizontal plane, a spring member may be further provided. This spring member is used to position the pendulum member 202 in a balanced state that is perpendicular to the mounting surface of the vibration damping object 220, such as the wall of the building.

[0284] [A] Figure 27 Is Figure 19 The diagram shows a pendulum device 201 with a spring member for positioning the pendulum member 202. A pair of spring members 210a and 210b are provided in the middle part along the long side of the pendulum member 202. Specifically, one spring member 210a is installed between the pendulum member 202 and a component that vibrates integrally with the vibration damping object 220 (such as the wall surface of the vibration damping object 220), arranged parallel to the Y-axis and perpendicular to the pendulum member 202. Another spring member 210b is arranged parallel to the Y-axis and perpendicular to the pendulum member 202 between the location where the spring member 210a is installed on the pendulum member 202 and the vibration damping object 220 or a component that vibrates integrally with the vibration damping object 220.

[0285] By arranging the spring members 210a and 210b in this way, the pendulum member 202 is subjected to a restoring force to achieve a balanced state (a state perpendicular to the damping object 220), and can be easily positioned in a balanced state. In addition, the pendulum member 202 can be supported by the spring members 210a and 210b, which improves durability.

[0286] Furthermore, by providing spring members 210a and 210b, the restoring force based on the spring members has a nonlinear component. However, since a magnetically based restoring force is applied simultaneously with the restoring force based on the spring members, and this magnetically based restoring force has a nonlinear component that cancels out the magnitude of the nonlinear component, the nonlinear component is canceled out, and the pendulum member 202 has a linear restoring force. Therefore, regardless of the amplitude of the pendulum member 202, it is a linear restoring force.

[0287] [B] Figure 28 In such Figure 20 The diagram shows a spring member for positioning the pendulum component 202 within the pendulum device 201. (Compared to...) Figure 27 Similarly, in the pendulum device 201 shown, the spring members 210a and 210b only need to be arranged parallel to the Y-axis between the vibration damping object 220 or a component vibrating integrally with the vibration damping object 220 and the pendulum member 202. In this case, it is also possible to achieve the same result as... Figure 27 The pendulum device 201 shown has the same effect.

[0288] [C] Figure 29 Is Figure 23 The diagram shows a spring member for positioning the pendulum component 202 within the pendulum device 301. (Compared to...) Figure 27 Similarly, in the pendulum device 201 shown, the spring members 210a and 210b only need to be arranged parallel to the Y-axis between the vibration damping object 220 or a component vibrating integrally with the vibration damping object 220 and the pendulum member 202. In this case, it is also possible to achieve the same result as... Figure 27 The pendulum device 201 shown has the same effect. Figure 29 In this configuration, spring components 210a and 210b are positioned between the fulcrum Q and the pendulum-side magnetic component 222a, but they can also be positioned between the fulcrum Q and the pendulum-side magnetic component 222b.

[0289] (Variation Example 10) Vibration reduction can be applied to objects other than buildings 20, such as moving bodies like trains, bridges, trestle bridges, and piping.

[0290] [A] When the pendulum device of this embodiment is installed in the piping as a vibration absorber, for example, as Figure 30 As shown in (a) and (b), when piping 320 vibrates in the vertical direction, the following method is used: Figure 17 or Figure 18 The pendulum device 201 is shown. Furthermore, the pendulum member 202 in its stationary state... Figure 30 A pendulum device 201 is arranged on the side of the pipe 320, extending along the X-axis direction. The pendulum device 201 is configured to perform pendulum motion in the ZX plane by the vibration of the pendulum component 202 relative to the vertical direction of the pipe 320. Figure 30 In (a), the leftward direction is set as the Y-axis, the direction from the paper towards the front is set as the X-axis, the downward direction is set as the Z-axis, and the Z-axis direction is set as the direction of gravity. Figure 30 (b) is viewed from the Y-axis direction. Figure 30 (a) Diagram of piping 320.

[0291] In addition, such as Figure 31 As shown in (a) and (b), when piping 320 vibrates in the horizontal direction, using Figure 19 or Figure 20 The pendulum device 201 is shown. Furthermore, the pendulum member 202 in its stationary state... Figure 31 A pendulum device 201 is arranged at the lower part of the pipe 320, extending along the Z-axis direction. The pendulum device 201 is configured to perform pendulum motion in the ZX plane by the horizontal vibration of the pendulum component 202 relative to the pipe 320. Figure 31In (a), the leftward direction is set as the Y-axis, the upward direction is set as the X-axis, the direction toward the paper is set as the Z-axis, and the Z-axis direction is set as the direction of gravity. Figure 31 (b) is viewed from the Y-axis direction. Figure 31 The diagram of piping 320 is shown in (a).

[0292] [B] In the case where the pendulum device of this embodiment is installed as a vibration absorber in a tram vehicle, such as Figure 32 As shown in (a) and (b), when vibrating in the left-right direction in the direction of travel of vehicle 420, the suppression is as follows: Figure 31 Similarly, the horizontal vibration of the piping 320 shown is also observed using... Figure 19 or Figure 20 The pendulum device 201 is shown. Furthermore, the pendulum member 202 in its stationary state... Figure 32 The pendulum device 201 is disposed in the roof or other interior space of the vehicle, extending along the lower part of the vehicle. The pendulum device 201 is configured such that the movable part of the pendulum member 202 vibrates in the left-right direction in the vertical plane relative to the vehicle 420 in the direction of travel of the vehicle. By configuring it in this way, the vibration in the left-right direction relative to the direction of travel of the vehicle 420 can be stabilized.

[0293] Additionally, for example, when the pendulum device of this embodiment is installed on a bridge as a vibration damping device to suppress the vertical vibration of the bridge, using, for example, Figure 17 or Figure 18 The pendulum device 201 shown is configured such that the pendulum member 202 moves in a pendulum motion in the vertical plane relative to the vertical vibration of the bridge. In this case, it is preferable to set the natural frequency ω of the pendulum member 2 to ω=Ω / 2 when the natural frequency of the bridge is set to Ω.

[0294] In addition, in suppressing the vertical vibration of bridges, etc., the following methods are used: Figure 23 The pendulum device 301 shown is also effective; in this case, it is preferably located near the center of the bridge or similar structure along its length. Figure 23 The pendulum device 301 shown and as shown Figure 24 The pendulum device 301 shown is also effective when applied to elevated roads.

[0295] (Variation Example 11) It can also enhance the nonlinearity of the pendulum device in this embodiment and be applied to energy harvesters.

[0296] Typically, the collector resonates and extracts energy only when the excitation frequency γ is close to the natural frequency ω of the collector (oscillator, in this case, the pendulum component). That is, as Figure 33As shown, energy can be extracted only when the excitation frequency γ is within a limited range.

[0297] By using the pendulum device of this embodiment, the characteristics of the pendulum component are adjusted to give it either soft spring or hard spring characteristics, thereby achieving... Figure 34 As shown, it can achieve a resonant state over a wider range of excitation frequencies γ, enabling efficient energy harvesting.

[0298] In order to have Figure 34 The characteristics shown require a pendulum device that possesses both hard spring and soft spring characteristics. For example, the one described in Modification 8 can be used. Figure 23 The pendulum device 301 shown is described. Figure 23 In this design, pendulum A has the characteristics of a soft spring, while pendulum B has the characteristics of a hard spring. By independently adjusting the distance between the magnets in pendulum A and pendulum B respectively, the nonlinear characteristics of the pendulums can be set more freely.

[0299] For example, when the excitation frequency γ is less than the linear natural frequency ω of the pendulum device 301, the electromagnet of pendulum A, which has soft spring characteristics, is activated, while the electromagnet of pendulum B is stopped. Conversely, when the excitation frequency γ is greater than the linear natural frequency ω of the pendulum device 301, the electromagnet of pendulum A is stopped, while the electromagnet of pendulum B, which has hard spring characteristics, is activated. Thus, as... Figure 34 As shown, energy harvesting is possible over a wider range of excitation frequencies γ.

[0300] like Figure 23 The pendulum device 301 shown is configured to vibrate in the same direction as the vibration direction of the object being damped.

[0301] In addition, not limited to, Figure 23 The pendulum device 301 shown can be used in energy harvesters, but other pendulum devices can also be applied. For example, it can be configured as follows: Figure 32 As shown, a pendulum device is installed on a vehicle, and the pendulum component performs a pendulum motion as the vehicle swings left and right relative to the direction of travel, converting its vibration into electrical energy. Alternatively, the pendulum device can be configured to be placed on a bridge, and the pendulum component performs a pendulum motion as the bridge swings up and down, converting its vibration into electrical energy. Another configuration is to arrange the pendulum device so that the pendulum component performs a pendulum motion due to waves, converting the vibration of the pendulum component caused by the waves into electrical energy.

[0302] As a generator that converts vibration into electrical energy, piezoelectric, electromagnetic induction, and electrostatic generators can be used, for example.

[0303] For example, when the pendulum device is installed in a vehicle, it can also be like... Figure 32As shown in (b), a generator 420a that converts vibration into electrical energy is set near the fulcrum Q of the pendulum component, thereby extracting electrical energy.

[0304] <Methods for configuring magnetic components and adjusting the motion characteristics of the pendulum component> In such Figure 14 In the pendulum component 102 shown for performing conical pendulum motion (assuming the magnetic pole face of the fixed magnetic component 104 is sufficiently large), as... Figure 35 As shown, when the extension direction of the pendulum member 102 is vertical, the distance from the surface of the fixed magnetic member 104 to the center of gravity of the pendulum-side magnetic member 122 is set as r. The difference between the height of the center of gravity of the pendulum-side magnetic member 122 from the surface of the fixed magnetic member 104 and the displacement angle of the pendulum member 102 relative to the vertical direction is θ is set as x. The distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic member 122 is set as the equivalent length l of the pendulum. x is expressed by the following formula (31).

[0305]

Mathematical Expression 31

[0306] Furthermore, the magnetic restoring force F of the pendulum component 102 can be approximated by equation (31) as shown in equation (32). In equation (32), k is a constant composed of magnetic permeability and magnetic flux density.

[0307]

Mathematical Expression 32

[0308] On the other hand, the gravity-based restoring force of the pendulum component 102 can be approximated by the following equation (33). In equation (33), m is the mass of the pendulum component 102, and θ″ is the angular acceleration of the displacement angle θ. Figure 35 In the configuration shown, the restoring force F based on magnetic force is in the vertically upward direction.

[0309]

Mathematical Expression 33

[0310] In equation (32), the coefficient of the first-order term contains "(k / r) 2 ")" represents a linear component, where the coefficient of the cubic term contains "-(kl / r"). 3 ")" represents a nonlinear component. Here, if we define it as a linear component a1 = (k / r 2 ), nonlinear component a3=-(kl / r 3 Then, the ratio of the nonlinear component a3 to the linear component a1, a3 / a1, is expressed by the following equation (34).

[0311]

Mathematical Expression 34

[0312] Therefore, it can be seen that by making "l" larger than "r", it is easier to obtain nonlinear effects.

[0313] Here, when the surfaces of the pendulum-side magnetic member 122 and the fixed magnetic member 104 are opposite poles and attract each other, a1 is a1>0, exhibiting positive linear stiffness, and a3 is a3<0, exhibiting nonlinear stiffness and soft spring characteristics. Since a1>0, a restoring force can be generated.

[0314] When the surfaces of the pendulum-side magnetic component 122 and the fixed magnetic component 104 are opposite each other and repel each other, a1 is a1 < 0, exhibiting negative linear stiffness, and a3 is a3 > 0, exhibiting nonlinear stiffness and the characteristics of a hard spring. Since a1 < 0, the linear stiffness is negative, therefore the pendulum device cannot have restoring force.

[0315] It should be noted that, in situations where the restoring force of gravity can be utilized, such as in... Figure 21 In the case of the pendulum device 201 shown, even when a1 < 0 and has negative linear stiffness, it can be offset by the effect of gravity, resulting in positive linear stiffness overall. In this case, while a restoring force exists, it also possesses the characteristics of a hard spring with a magnetic component.

[0316] In addition, in such Figure 15 The pendulum component 102 that performs conical pendulum motion (in the case where the magnetic pole surface of the fixed magnetic component 104 is not large enough) also has the same characteristics. In this case, the coefficient a1 representing the linear component and the coefficient a3 representing the nonlinear component can be obtained by the following steps.

[0317] In such Figure 15 In the pendulum component 102 shown, as Figure 36 As shown, when the extension direction of the pendulum member 102 is vertical, the vertical distance from the center of gravity of the fixed magnetic member 104 to the center of gravity of the pendulum-side magnetic member 122 is defined as r; when the displacement angle of the pendulum member 102 relative to the vertical direction is θ, the distance from the center of gravity of the fixed magnetic member 104 to the center of gravity of the pendulum-side magnetic member 122 is defined as x; and the distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic member 122 is defined as the equivalent length l of the pendulum. Figure 36In the configuration shown, the restoring force F based on magnetic force is a force in a vector direction extending from the center of gravity of the fixed magnetic member 104 toward the center of gravity of the pendulum-side magnetic member 122, and also in a vector direction extending from the center of gravity of the pendulum-side magnetic member 122. Let α be the angle between the tangent at the position of the center of gravity of the pendulum-side magnetic member 122 at a displacement angle θ on the trajectory of the center of gravity of the pendulum member 102 during pendulum motion, and the vector representing the restoring force F based on magnetic force.

[0318] The magnetic restoring force F of the pendulum component 102 can be expressed by the following equation (35). In equation (35), k is a constant composed of magnetic permeability and magnetic flux density.

[0319]

Mathematical Expression 35

[0320] Furthermore, based on equation (35), the approximate equation shown in equation (36) can be derived.

[0321]

Mathematical Expression 36

[0322] On the other hand, the gravity-based restoring force of the pendulum component 102 can be approximated by the following equation (37). In equation (37), m is the mass of the pendulum component 102, and θ″ is the angular acceleration of the displacement angle θ.

[0323]

Mathematical Expression 37

[0324] In equation (36), the coefficient of the first-order term contains "(kl+kr)θ / r". 3 "" represents the linear component, where the coefficient of the cubic term contains "-k(r+l)(r 2 +9rl+9l 2 )θ 3 / 6r 3 "" indicates a nonlinear component. Here, if we take it as a linear component, a1 = (kl + kr) / r 3 The nonlinear component a3 = -k(r+l)(r 2 +9rl+9l 2 ) / 6r 3 Then the ratio of the nonlinear component a3 to the linear component a1, a3 / a1, is expressed by the following equation (38).

[0325]

Mathematical Expression 38

[0326] Therefore, it can be seen that by making "l" larger than "r", it is easier to obtain the nonlinear effect of magnetic force.

[0327] It should be noted that the scope of this invention is not limited to the exemplary embodiments illustrated and described, but also includes all embodiments that achieve the same effects as the objectives to be achieved by this invention. Furthermore, the scope of this invention can be described by any desired combination of specific features among all the disclosed features.

[0328] The present invention may, for example, take the following configuration. (1) A pendulum device, characterized in that it comprises: The pendulum component, which functions to exert a restoring force based on gravity and to propel the pendulum motion around a fulcrum, is at least partially composed of a first magnetic component; and A fixing member, which provides a magnetically repulsive or attractive force to the pendulum member as a magnetically restoring force, is at least partially composed of a second magnetic member. The pendulum device has a magnetic restoring force that counteracts the nonlinear component of the gravity-based restoring force acting on the pendulum component by adjusting at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component. (2) According to the pendulum device described in (1) above, the pendulum component is suspended from the fulcrum in a rotatable manner. (3) According to the pendulum device described in (1) or (2) above, the pendulum motion is characterized in that the pendulum motion is any one of single pendulum motion, spherical pendulum motion, and conical pendulum motion. (4) According to the pendulum device described in (1) above, the pendulum component is characterized in that the pendulum component is rigid and is configured to perform a single pendulum motion in a vertical plane with the fulcrum as the center, and when in a stationary state, it is maintained in a horizontal state by a restoring force based on the magnetic force, which is a repulsive force or attractive force between the first magnetic component and the second magnetic component. (5) According to the pendulum device described in (1) above, the characteristic is that, The fixing member is configured such that, when in a stationary state, the end of the fixing member and the end of the pendulum member are opposite each other on the extension line of the pendulum member on the side opposite to the fulcrum. When at rest, it is maintained in a horizontal state by a restoring force based on the magnetic force, which is the attraction between the first magnetic component and the second magnetic component. (6) The pendulum device according to any one of (1) to (4) above is characterized in that, The pendulum motion is a single pendulum motion, and it has a pair of second magnetic members, which are arranged facing each other, sandwiching the pendulum member in the direction of the single pendulum motion. The first magnetic member is configured to face each of the second magnetic members. (7) The pendulum device according to any one of (1) to (3) above is characterized in that, The second magnetic component is configured to surround the pendulum component. The first magnetic component and the second magnetic component are configured such that the magnetic poles on their opposite sides are either the same pole or opposite poles. (8) The pendulum device according to any one of (1) to (7) above is characterized in that the first magnetic component and the second magnetic component are respectively composed of a permanent magnet or an electromagnet. (9) The pendulum device according to any one of (1) to (8) above is characterized in that the external shapes of the first magnetic component and the second magnetic component are any one of cylindrical, prismatic, spherical, arc-shaped, annular, hollow cylindrical, curved and planar. (10) The pendulum device according to any one of (1) to (4) and (6) to (8) above is characterized in that, The second magnetic component has a planar or curved shape. The first magnetic component and the second magnetic component are configured such that the magnetic poles facing each other are like poles or opposite poles. (11) According to any one of (1) to (10) above, the pendulum device is characterized in that the fulcrum is directly disposed on the vibration damping object, or disposed on a structural part fixed to the vibration damping object. (12) A vibration damping device, characterized in that it uses a pendulum device that performs pendulum motion to dampen the vibration of the object to be damped. The vibration damping device uses the pendulum device described in any one of (1) to (11) above as the pendulum device. (13) A method for designing a vibration damping device, characterized in that it uses a pendulum component that experiences a restoring force based on gravity and moves like a pendulum around a fulcrum to dampen the vibration of an object, comprising: A first magnetic component is disposed on at least a portion of the pendulum component. A second magnetic component is positioned at a location that provides a magnetically repulsive or attractive force as a magnetically restoring force to the first magnetic component. At least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component is adjusted so that the nonlinear component of the gravity-based restoring force acting on the pendulum component and the nonlinear component of the restoring force based on the magnetic force between the first magnetic component and the second magnetic component cancel each other out. (14) A pendulum device, characterized in that, A first magnetic component is disposed on at least a portion of a pendulum component that is subjected to a restoring force based on gravity and moves about a fulcrum. A second magnetic component is positioned at a location that provides a magnetically repulsive or attractive force as a magnetically restoring force to the first magnetic component. It is possible to adjust at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component, so that the nonlinear component of the gravity-based restoring force acting on the pendulum component and the nonlinear component of the restoring force based on the magnetic force between the first magnetic component and the second magnetic component cancel each other out. (15) A pendulum device, characterized in that, A first magnetic component is disposed on at least a portion of a pendulum component that is subjected to a restoring force based on gravity and moves about a fulcrum. A second magnetic component is positioned at a location that provides a magnetically repulsive or attractive force as a magnetically restoring force to the first magnetic component. It is possible to adjust at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component, so that the restoring force characteristics of the sum of the restoring force based on gravity and the restoring force based on the magnetic force acting on the pendulum component have soft spring characteristics or hard spring characteristics through the synergistic effect of the nonlinear component of the restoring force based on gravity and the nonlinear component of the restoring force based on the magnetic force between the first magnetic component and the second magnetic component. (16) A pendulum device, characterized in that it comprises: The first pendulum component has the function of restoring force based on gravity, and performs pendulum motion around the fulcrum, and at least part of it is composed of the first magnetic component. A first fixing member provides a magnetically repulsive force to the first pendulum member and is at least partially composed of a second magnetic member, the repulsive force having a nonlinear component of magnitude that cancels out the nonlinear component of the gravity-based restoring force acting on the first pendulum member. The second pendulum component, which functions based on the restoring force of gravity, performs pendulum motion around the fulcrum, and is at least partially composed of a third magnetic component; and The second fixing member provides a magnetically repulsive force to the second pendulum member, and is at least partially composed of a fourth magnetic member. This repulsive force has a nonlinear component that cancels out the nonlinear component of the gravity-based restoring force acting on the second pendulum member. The second pendulum member is provided as a pendulum member that is rigidly continuous with the first pendulum member on the extension line of the first pendulum member, and is configured to perform single pendulum motion in the vertical plane around the fulcrum, and thus, when in a stationary state, is maintained in a horizontal state by the repulsive force based on the magnetic force between the first magnetic member and the second magnetic member and the attractive force based on the magnetic force between the third magnetic member and the fourth magnetic member. (17) According to the pendulum device described in (16) above, the characteristic is that, At least one of the first magnetic component, the second magnetic component, the third magnetic component, and the fourth magnetic component is composed of an electromagnet. The ability to change at least one of the hard spring characteristics of the first pendulum member, which varies based on the repulsive force of the magnetic force, and the soft spring characteristics of the second pendulum member, which vary based on the attractive force of the magnetic force, by changing the magnitude of the magnetic force of the electromagnet and stopping the operation of the electromagnet, is possible. (18) According to the pendulum device described above (17), the first magnetic component and the second magnetic component are respectively composed of permanent magnets or electromagnets, and the third magnetic component and the fourth magnetic component are respectively composed of permanent magnets or electromagnets. (19) The pendulum device according to any one of (16) to (18) above is characterized in that it includes a generator that converts the vibration of the first pendulum member or the second pendulum member into electrical energy. (20) A pendulum device, characterized in that it comprises: A pendulum component, whose function is to restore the balance force based on gravity, to perform pendulum motion around a fulcrum, and which is at least partially composed of a first magnetic component; and A fixing member provides a magnetically repulsive or attractive force to the pendulum member as a magnetically restoring force, and at least a portion of it is composed of a second magnetic member. The pendulum device has a magnetic restoring force that counteracts the nonlinear component of the gravity-based restoring force acting on the pendulum component. (twenty one) A pendulum device, characterized in that it has the vertical direction as the Z-axis in a mutually orthogonal XYZ coordinate system, and includes: A pendulum component, rigidly mounted, is rotatably mounted at one end to a fulcrum, and performs pendulum motion in the XY plane around the fulcrum. At least a portion of the pendulum component is composed of a first magnetic component; and A fixing member that provides a magnetically repulsive or attractive force to the pendulum member, at least a portion of which is composed of a second magnetic member.

Claims

1. A pendulum device, characterized in that, have: The pendulum component, which functions to exert a restoring force based on gravity and to propel the pendulum motion around a fulcrum, is at least partially composed of a first magnetic component; and A fixing member, which provides a magnetically repulsive or attractive force to the pendulum member as a magnetically restoring force, is at least partially composed of a second magnetic member. The pendulum device has a magnetic restoring force that counteracts the nonlinear component of the gravity-based restoring force acting on the pendulum component by adjusting at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component.

2. The pendulum device according to claim 1, characterized in that, The pendulum component is suspended from the fulcrum in a rotatable manner.

3. The pendulum device according to claim 1, characterized in that, The pendulum motion is any one of simple pendulum motion, spherical pendulum motion, and conical pendulum motion.

4. The pendulum device according to claim 1, characterized in that, The pendulum component is rigid and configured to perform a single pendulum motion in a vertical plane with the fulcrum as the center, and when in a stationary state, it is maintained in a horizontal state by a restoring force based on the magnetic force, which is a repulsive or attractive force between the first magnetic component and the second magnetic component.

5. The pendulum device according to claim 1, characterized in that, The fixing member is configured such that, when in a stationary state, the end of the fixing member and the end of the pendulum member are opposite each other on the extension line of the pendulum member on the side opposite to the fulcrum. When at rest, it is maintained in a horizontal state by a restoring force based on the magnetic force, which is the attraction between the first magnetic component and the second magnetic component.

6. The pendulum device according to any one of claims 1 to 4, characterized in that, The pendulum motion is a single pendulum motion, and it has a pair of second magnetic members, which are arranged facing each other, sandwiching the pendulum member in the direction of the single pendulum motion. The first magnetic member is configured to face each of the second magnetic members.

7. The pendulum device according to any one of claims 1 to 3, characterized in that, The second magnetic component is configured to surround the pendulum component. The first magnetic component and the second magnetic component are configured such that the magnetic poles on their opposite sides are either the same pole or opposite poles.

8. The pendulum device according to any one of claims 1 to 5, characterized in that, The first magnetic component and the second magnetic component are respectively composed of permanent magnets or electromagnets.

9. The pendulum device according to any one of claims 1 to 5, characterized in that, The first magnetic component and the second magnetic component have external shapes that are any one of cylindrical, prismatic, spherical, arc-shaped, ring-shaped, hollow cylindrical, curved, and planar.

10. The pendulum device according to any one of claims 1 to 5, characterized in that, The second magnetic component has a planar or curved shape. The first magnetic component and the second magnetic component are configured such that the magnetic poles facing each other are like poles or opposite poles.

11. The pendulum device according to any one of claims 1 to 5, characterized in that, The fulcrum is either directly set on the vibration-damping object or set on a structural part fixed to the vibration-damping object.

12. A vibration damping device, characterized in that, It is a vibration damping device that uses a pendulum device to reduce the vibration of the object being damped. The vibration damping device uses the pendulum device as described in any one of claims 1 to 5.

13. A design method for a vibration damping device, characterized in that, It is a design method for a vibration damping device that uses a pendulum component with a restoring force based on gravity and a pendulum motion centered on a fulcrum to dampen the vibration of an object, including: A first magnetic component is disposed on at least a portion of the pendulum component. A second magnetic component is positioned at a location that provides a magnetically repulsive or attractive force as a magnetically restoring force to the first magnetic component. At least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component is adjusted so that the nonlinear component of the gravity-based restoring force acting on the pendulum component and the nonlinear component of the restoring force based on the magnetic force between the first magnetic component and the second magnetic component cancel each other out.

14. A pendulum device, characterized in that, A first magnetic component is disposed on at least a portion of a pendulum component that is subjected to a restoring force based on gravity and moves about a fulcrum. A second magnetic component is positioned at a location that provides a magnetically repulsive or attractive force as a magnetically restoring force to the first magnetic component. It is possible to adjust at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component, so that the nonlinear component of the gravity-based restoring force acting on the pendulum component and the nonlinear component of the restoring force based on the magnetic force between the first magnetic component and the second magnetic component cancel each other out.

15. A pendulum device, characterized in that, A first magnetic component is disposed on at least a portion of a pendulum component that is subjected to a restoring force based on gravity and moves about a fulcrum. A second magnetic component is positioned at a location that provides a magnetically repulsive or attractive force as a magnetically restoring force to the first magnetic component. It is possible to adjust at least one of the magnetic flux density of the first magnetic component and the second magnetic component, the relative position of the first magnetic component and the second magnetic component, and the mass of the pendulum component, so that the restoring force characteristics of the sum of the restoring force based on gravity and the restoring force based on the magnetic force acting on the pendulum component have soft spring characteristics or hard spring characteristics through the synergistic effect of the nonlinear component of the restoring force based on gravity and the nonlinear component of the restoring force based on the magnetic force between the first magnetic component and the second magnetic component.

16. A pendulum device, characterized in that, have: The first pendulum component has the function of restoring force based on gravity, and performs pendulum motion around the fulcrum, and at least part of it is composed of the first magnetic component. A first fixing member provides a magnetically repulsive force to the first pendulum member and is at least partially composed of a second magnetic member, the repulsive force having a nonlinear component of magnitude that cancels out the nonlinear component of the gravity-based restoring force acting on the first pendulum member. The second pendulum component, which functions based on the restoring force of gravity, performs pendulum motion around the fulcrum, and is at least partially composed of a third magnetic component; and The second fixing member provides a magnetically repulsive force to the second pendulum member, and is at least partially composed of a fourth magnetic member. This repulsive force has a nonlinear component that cancels out the nonlinear component of the gravity-based restoring force acting on the second pendulum member. The second pendulum member is provided as a pendulum member that is rigidly continuous with the first pendulum member on the extension line of the first pendulum member, and is configured to perform single pendulum motion in the vertical plane around the fulcrum, and thus, when in a stationary state, is maintained in a horizontal state by the repulsive force based on the magnetic force between the first magnetic member and the second magnetic member and the attractive force based on the magnetic force between the third magnetic member and the fourth magnetic member.

17. The pendulum device according to claim 16, characterized in that, At least one of the first magnetic component, the second magnetic component, the third magnetic component, and the fourth magnetic component is composed of an electromagnet. The ability to change at least one of the hard spring characteristics of the first pendulum member, which varies based on the repulsive force of the magnetic force, and the soft spring characteristics of the second pendulum member, which vary based on the attractive force of the magnetic force, by changing the magnitude of the magnetic force of the electromagnet and stopping the operation of the electromagnet, is possible.

18. The pendulum device according to claim 17, characterized in that, The first magnetic component and the second magnetic component are respectively composed of permanent magnets or electromagnets, and the third magnetic component and the fourth magnetic component are respectively composed of permanent magnets or electromagnets.

19. The pendulum device according to any one of claims 16 to 18, characterized in that, It is equipped with a generator that converts the vibration of the first pendulum component or the second pendulum component into electrical energy.

20. A pendulum device, characterized in that, have: A pendulum component, whose function is to restore the balance force based on gravity, to perform pendulum motion around a fulcrum, and which is at least partially composed of a first magnetic component; and A fixing member provides a magnetically repulsive or attractive force to the pendulum member as a magnetically restoring force, and at least a portion of it is composed of a second magnetic member. The pendulum device has a magnetic restoring force that counteracts the nonlinear component of the gravity-based restoring force acting on the pendulum component.

21. A pendulum device, characterized in that, In a mutually orthogonal XYZ coordinate system, with the vertical direction as the Z-axis, it possesses the following properties: A pendulum component, rigidly mounted, is rotatably mounted at one end to a fulcrum, and performs pendulum motion in the XY plane around the fulcrum. At least a portion of the pendulum component is composed of a first magnetic component; and A fixing member that provides a magnetically repulsive or attractive force to the pendulum member, at least a portion of which is composed of a second magnetic member.

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