Pendulum device, vibration damping device, and method for designing vibration damping device

Abstract

The objective of the present invention is to provide a pendulum device in which the amplitude dependency of a restoring force of a pendulum due to gravity can be adjusted to a desired characteristic. To this end, a pendulum device (1) comprises a pendulum member (2) which is subjected to a restoring force due to gravity, performs a pendular movement around a shaft (32) serving as a fulcrum, and includes pendulum-side magnetic members (22a, 22b), and fixed magnetic members (4a, 4b) which impart a magnetic repulsive force or attractive force to the pendulum member (2) as a magnetic restoring force, wherein the pendulum device (1) is configured to provide a magnetic restoring force that cancels out a non-linear component of the restoring force due to gravity that acts on the pendulum member (2), by adjusting 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 positions of the pendulum-side magnetic members (22a, 22b) and the fixed magnetic members (4a, 4b), and the mass of the pendulum member (2).

Description

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

[0001] The present invention relates to a pendulum device, a vibration damping device, and a method for designing a vibration damping device.

[0002] Conventionally, vibration control devices that reduce vibration of structures caused by wind or earthquakes have been known, such as those that use a pendulum to control vibration (see, for example, Patent Document 1). For such vibration control devices that use a pendulum, a method is known in which a vibration control effect is achieved by using a pendulum in which the natural frequency of the object to be controlled and the natural frequency of the pendulum are in a 1:1 relationship. Another proposed method for a vibration control device that uses a pendulum is to construct a pendulum-type dynamic vibration absorber system that uses autoparametric excitation, and to achieve a vibration control effect by using a pendulum in which the natural frequency of the object to be controlled and the natural frequency of the pendulum are in a 1:1 / 2 relationship (see, for example, Non-Patent Document 1).

[0003] Japanese Patent Application Laid-Open No. 2021-125976

[0004] "Response of a dynamic vibration absorber system using parametric excitation of a pendulum", Transactions of the Japan Society of Mechanical Engineers (C), Vol. 67, No. 661 (September 2001), Paper No. 00-1494, pp. 15-21

[0005] When a pendulum is allowed to oscillate freely, in areas where the swing angle and amplitude are large, the restoring force due to gravity acting on the pendulum is not proportional to the swing angle but becomes nonlinear, causing the pendulum's natural frequency to change. Therefore, in vibration damping devices that use pendulums, in areas where the pendulum's amplitude is large and the restoring force is nonlinear, the natural frequency ratio with the object to be damped cannot be maintained at the required value (e.g., 1:1 or 1:1 / 2), resulting in a reduced damping effect or chaotic movement of the pendulum. Therefore, pendulums are typically used within a small amplitude range where the nonlinear effect can be ignored, and the vibration damping effect is achieved within this amplitude range.

[0006] In a pendulum-type dynamic vibration absorber system that utilizes autoparametric excitation, the natural frequency of the pendulum is set to half the natural frequency of the object to be damped, and the required restoring force can be obtained by reducing the mass of the pendulum weight and increasing the amplitude of the pendulum accordingly. However, in areas where the amplitude of the pendulum is large, the restoring force due to gravity acting on the pendulum is not proportional to the angle of the pendulum, and the natural frequency changes depending on the magnitude of the pendulum's amplitude. If the natural frequency changes, the condition "the natural frequency of the pendulum should be set to half the natural frequency of the object to be damped" is not met, and sufficient vibration damping effect cannot be obtained, resulting in a problem of reduced vibration damping performance of the vibration damping device.

[0007] Therefore, this invention has been made in light of the above-mentioned unresolved problems in the prior art, and aims to provide a pendulum device that makes it possible to adjust the amplitude dependency of the restoring force due to gravity of the pendulum to desired characteristics, as well as a vibration control device that uses this pendulum device and a method for designing a vibration control device.

[0008] According to one aspect of the present invention, there is provided a pendulum device comprising: a pendulum member, at least a part of which is constituted by a first magnetic member, which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum; and a fixed member, at least a part of which is constituted by a second magnetic member, which applies a magnetic repulsive or attractive force to the pendulum member as a magnetic restoring force; wherein 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, the pendulum device is able to provide the magnetic restoring force that cancels out the nonlinear component of the restoring force due to gravity acting on the pendulum member.

[0009] According to another aspect of the present invention, there is provided a vibration control device that controls vibration of an object to be vibration-controlled by using a pendulum device that performs pendulum motion, the pendulum device using the pendulum device of the above aspect as the pendulum device.

[0010] Furthermore, according to another aspect of the present invention, there is provided a method for designing a vibration control device that controls vibrations of an object to be vibration-controlled using a pendulum member that is subjected to a restoring force due to gravity and that moves in a pendulum motion around a fulcrum, the method comprising: arranging a first magnetic member on at least a part of the pendulum member; arranging a second magnetic member in a position that applies a magnetic repulsive or attractive force to the first magnetic member as a magnetic restoring force; and adjusting at least one of the magnetic flux densities of the first and second magnetic members, the relative positions of the first and second magnetic members, and the mass of the pendulum member so that the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first and second magnetic members are canceled out.

[0011] Furthermore, according to another aspect of the present invention, there is provided a pendulum device in which a first magnetic member is disposed in at least a part of a pendulum member that is subjected to a restoring force due to gravity and that moves in a pendulum motion around a fulcrum, and a second magnetic member is disposed in a position where it applies a magnetic repulsive or attractive force to the first magnetic member as a magnetic restoring force, and at least one of the magnetic flux densities of the first and second magnetic members, the relative positions of the first and second magnetic members, and the mass of the pendulum member is adjustable so that the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first and second magnetic members are canceled out.

[0012] Furthermore, there is provided a pendulum device in which a first magnetic member is disposed in at least a part of a pendulum member that is subjected to a restoring force due to gravity and that moves in a pendulum motion around a fulcrum, and a second magnetic member is disposed in a position where a magnetic repulsive or attractive force is applied to the first magnetic member as a restoring force due to magnetic force, and at least one of the magnetic flux densities of the first and second magnetic members, the relative positions of the first and second magnetic members, and the mass of the pendulum member can be adjusted so that the restoring force characteristics of the sum of the restoring force due to gravity and the restoring force due to magnetic force have soft spring characteristics or hard spring characteristics due to the synergistic effect of the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first and second magnetic members.

[0013] According to another aspect of the present invention, there is provided a first pendulum member, at least a portion of which is made up of a first magnetic member, on which a restoring force due to gravity acts and which performs pendulum motion around a fulcrum; a first fixed member, at least a portion of which is made up of a second magnetic member, which applies a repulsive force due to a magnetic force having a nonlinear component of a magnitude that cancels out the nonlinear component of the restoring force due to gravity acting on the first pendulum member; a second pendulum member, at least a portion of which is made up of a third magnetic member, on which a restoring force due to gravity acts and which performs pendulum motion around the fulcrum; and a second fixed member at least a portion of which is constituted by a fourth magnetic member, and which applies to the second pendulum member an attractive force due to a magnetic force having a nonlinear component of a magnitude such that the magnetic forces cancel each other out, wherein the second pendulum member is provided on an extension of the first pendulum member as a single pendulum member having rigidity continuous with the first pendulum member, and is capable of simple pendulum motion around the fulcrum in a vertical plane, and further wherein, when in a stationary state, the pendulum device is maintained in a horizontal state by the repulsive force due to the magnetic force between the first magnetic member and the second magnetic member and the attractive force due to the magnetic force between the third magnetic member and the fourth magnetic member.

[0014] Furthermore, according to another aspect of the present invention, there is provided a pendulum device comprising: a pendulum member, at least a part of which is constituted by a first magnetic member, which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum; and a fixed member, at least a part of which is constituted by a second magnetic member, which applies a magnetic repulsive or attractive force to the pendulum member as a magnetic restoring force, wherein the pendulum device provides a magnetic restoring force that cancels out the nonlinear component of the restoring force due to gravity acting on the pendulum member.

[0015] Furthermore, according to another aspect of the present invention, there is provided a pendulum device comprising: a pendulum member having a Z-axis in a mutually orthogonal XYZ coordinate system, having rigidity, one end rotatably attached to a fulcrum, which performs pendulum motion in the XY plane around said fulcrum, and at least a portion of which is constituted by a first magnetic member; and a fixed member which applies a magnetic repulsive or attractive force to said pendulum member, and at least a portion of which is constituted by a second magnetic member.

[0016] According to one aspect of the present invention, the amplitude dependency of the restoring force in a pendulum device can be adjusted to a desired characteristic, and by using this pendulum device, it is possible to suppress the deterioration of the vibration damping performance of the vibration damping device that is associated with the amplitude dependency of the restoring force.

[0017] FIG. 1 is an explanatory diagram showing an example of a vibration damping device according to the present invention. FIG. 2 is a configuration diagram showing an example of a pendulum device according to the present invention. FIG. 3 is a graph showing the displacement state when the pendulum main body is allowed to freely vibrate without the action of the restoring force of the magnetic member. FIG. 4 is a graph showing the spine curve of FIG. 3. FIG. 5 is a graph showing the time history waveform obtained in an experiment when the pendulum member according to the present invention is allowed to freely vibrate. FIG. 6 is a graph showing the spine curve of FIG. 7. FIG. 7 is an explanatory diagram showing a schematic diagram of a horizontally moving magnet to explain the magnetic force acting on the pendulum-side magnetic member. FIG. 8 is a graph showing the relationship between the amount of movement of the magnet and the ratio of the coefficient of the first-order term to the coefficient of the third-order term in the formula representing the total magnetic force acting on the horizontally moving magnet. FIG. 9 is a schematic diagram of the pendulum device shown in FIG. 2. FIG. 10 is an explanatory diagram showing a schematic diagram of a pendulum device used in trial calculations of the effects of the pendulum device according to the present invention. FIG. 11 is an explanatory diagram showing a schematic diagram of a pendulum device to explain Modification 4. FIG. 10 is an explanatory diagram schematically showing a pendulum device used to explain Modification 4. FIG. 11 is an explanatory diagram schematically showing a pendulum device used to explain Modification 4. FIG. 12 is an explanatory diagram schematically showing a pendulum device used to explain Modification 5. FIG. 13 is an explanatory diagram schematically showing a pendulum device used to explain Modification 7. FIG. 14 is an explanatory diagram schematically showing a pendulum device used to explain Modification 7. FIG. 15 is an explanatory diagram schematically showing a pendulum device used to explain Modification 7. FIG. 16 is an explanatory diagram schematically showing a pendulum device used to explain Modification 7. FIG. 17 is an explanatory diagram schematically showing a pendulum device used to explain Modification 7. FIG. 18 is an explanatory diagram schematically showing a pendulum device used to explain Modification 8. FIG. 19 is an explanatory diagram schematically showing a pendulum device used to explain Modification 8. FIG. 19 is an explanatory diagram schematically showing the configuration of a pendulum device used in trial calculations. Fig. 10 is an explanatory diagram showing a schematic view of a pendulum device used to explain Modification 9. Fig. 11 is an explanatory diagram showing a schematic view of a pendulum device used to explain Modification 9. Fig. 12 is an explanatory diagram showing a schematic view of a pendulum device used to explain Modification 9. Fig. 13 is an explanatory diagram showing an attachment position of a pendulum device used to explain Modification 10.FIG. 10 is an explanatory diagram of the mounting position of the pendulum device used to explain Modification 10. FIG. 11 is an explanatory diagram of the mounting position of the pendulum device used to explain Modification 10. FIG. 12 is a graph used to explain Modification 11, for explaining the relationship between nonlinear components and excitation frequency. FIG. 13 is a graph used to explain Modification 12, for explaining the relationship between nonlinear components and excitation frequency. FIG. 14 is an explanatory diagram schematically showing a pendulum device used to explain a method for adjusting the motion characteristics of a pendulum member. FIG. 15 is an explanatory diagram schematically showing a pendulum device used to explain a method for adjusting the motion characteristics of a pendulum member.

[0018] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the following detailed description, many specific configurations are described to provide a complete understanding of the embodiments of the present invention. However, it is clear that other embodiments can be implemented without being limited to such specific configurations. Furthermore, the following embodiments do not limit the invention according to the claims. Furthermore, not all combinations of features described in the embodiments are necessarily essential to the solution of the invention.

[0019] <Embodiment> Here, a case will be described in which a pendulum device 1 according to one embodiment of the present invention is applied to a vibration control device 10 for a building 20, but the present invention is not limited to the vibration control device 10 for a building 20. FIG. 1( a) is a vibration model showing an example of the vibration control device 10. In FIG. 1( a), M, k, and c represent the mass, spring constant, and viscous damping coefficient of the main system, respectively. Furthermore, m, θ, and L represent the mass of the pendulum member, the angle of the pendulum member from the perpendicular line, and the distance from the fulcrum of the pendulum member to the other end, respectively. FIG. 1( b) is a conceptual diagram in which the vibration control device 10 is provided on a building 20 as a structure. The vibration control device 10 is provided on the roof of the building 20 to suppress lateral sway of the building 20.

[0020] 2 is a front view showing an example of a pendulum device 1. The pendulum device 1 comprises a pendulum member that moves in a pendulum motion around a fulcrum and is at least partially constituted by a first magnetic member, and a fixed member that applies a magnetic repulsive or attractive force to the pendulum member and is at least partially constituted by a second magnetic member. Specifically, the pendulum device 1 comprises a pendulum member 2, a pendulum support member 3 that supports the pendulum member 2, a pair of fixed magnetic members (second magnetic members) 4a, 4b provided on either side of the pendulum member 2, magnetic member support portions 5a, 5b that support the fixed magnetic members 4a, 4b, and a support main body 6 that supports the pendulum support member 3 and the magnetic member support portions 5a, 5b.

[0021] The pendulum member 2 is suspended from the pendulum support member 3 and performs pendulum motion in a vertical plane with the axis 32 of the pendulum support member 3 as a fulcrum. The pendulum member 2 comprises a pendulum main body 21 and a pair of pendulum-side magnetic members 22a, 22b. The pendulum main body 21 is formed from a thin, elongated rectangular plate, with the pendulum-side magnetic members 22a, 22b provided on the front and back surfaces of the pendulum main body 21. As will be described later, a repulsive force acts on the pendulum main body 21, which is generated between the fixed magnetic members 4a, 4b and the pendulum-side magnetic members 22a, 22b. Therefore, it is preferable that the pendulum main body 21 have sufficient rigidity to avoid deformation even when the repulsive force acts on it.

[0022] Pendulum-side magnetic members (first magnetic members) 22a, 22b are formed from plate-like magnets made of thin, elongated, rectangular permanent magnets, with one of the front and back surfaces magnetized to the north pole and the other magnetized to the south pole. Pendulum-side magnetic members 22a, 22b are fixed to the front and back surfaces of pendulum body 21 so that one surface of pendulum body 21 is the north pole and the other surface is the south pole. Here, pendulum-side magnetic members 22a and 22b are provided on each of the front and back surfaces of pendulum body 21, but it is also possible to use a single pendulum-side magnetic member itself, with one surface magnetized to the north pole and the other surface magnetized to the south pole, as pendulum body 21. The pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b do not have to be permanent magnets; electromagnets or the like can be used as long as they can generate a repulsive force between the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b. However, from the standpoint of ease of use, permanent magnets are preferable.

[0023] Furthermore, from the viewpoint of adjusting the restoring force, it is preferable that the pendulum-side magnetic members 22a and 22b have the same magnetic flux density and size, and similarly, it is preferable that the fixed magnetic members 4a and 4b have the same magnetic flux density and size.One end of the pendulum body 21 is attached to the shaft 32 of the pendulum support member 3, at which point the pendulum body 21 swings in a vertical plane with the shaft 32 as the fulcrum, and the pendulum-side magnetic members 22a and 22b are attached so that they each face in the direction in which the amplitude of the pendulum body 21 increases.

[0024] In the pendulum member 2, the entire pendulum body 21 to which the pendulum-side magnetic members 22a and 22b are fixed serves as the pendulum weight. Here, the pendulum body 21 itself is used as the weight, but this is not limited to this, and a separate weight may also be provided on the pendulum body 21. The pendulum support member 3 comprises a support mechanism 31 and a shaft 32 extending in a direction perpendicular to the plane of the paper in Figure 2. The support mechanism 31 connects the shaft 32 to the pendulum member 2 via a bearing, for example, so that the pendulum member 2 is supported movably around the shaft 32 as a fulcrum, allowing it to perform pendulum motion.

[0025] The fixed magnetic members 4a, 4b are formed, for example, from cylindrical ferrite magnets, with one surface in the thickness direction magnetized to the north pole and the other surface magnetized to the south pole. The magnetic member support portion 5a is formed by connecting a first member 51a and a second member 52a in a roughly V-shaped configuration, with the interior angle formed by the first member 51a and the second member 52a facing the pendulum member 2, and the end portion on the first member 51a side is fixed to the support portion main body 6 so that the second member 52a extends in the vertical direction. The fixed magnetic member 4a is fixed to the end portion on the second member 52a side of the magnetic member support portion 5a, and the fixed magnetic member 4a is positioned so that its magnetized surface faces the magnetized surface of the pendulum-side magnetic member 22a fixed to the pendulum main body 21 in a stationary state (equilibrium state). The fixed magnetic member 4a has magnetic polarity such that the magnetic polarity of the opposing magnetized surfaces of the fixed magnetic member 4a and the pendulum-side magnetic member 22a is the same polarity.

[0026] The magnetic member support portion 5b is formed by connecting a first member 51b and a second member 52b in a shape roughly resembling an inverted "L" character in hiragana. The inner angle formed by the first member 51b and the second member 52b faces the pendulum member 2, and the end of the first member 51b is fixed to the support portion main body 6 so that the second member 52b extends vertically. A fixed magnetic member 4b is fixed to the end of the magnetic member support portion 5b facing the second member 52b. The fixed magnetic member 4b is positioned so that its magnetized surface faces the magnetized surface of the pendulum-side magnetic member 22b fixed to the pendulum main body 21 in a stationary state. The fixed magnetic member 4b has magnetic polarity such that the magnetic polarities of the opposing magnetized surfaces of the fixed magnetic member 4b and the pendulum-side magnetic member 22b are the same. The magnetic member support portions 5a and 5b are configured to be symmetrical about the pendulum member 2 in a stationary state. Furthermore, the magnetic member support portions 5a and 5b are arranged so as not to hinder the movement of the pendulum member 2 when it makes a pendulum motion.

[0027] Furthermore, the magnetic member support portions 5a and 5b are attached to the support body 6 so that their vertical positions can be adjusted. The pendulum support member 3 is also attached to the support body 6 so that its vertical position can be adjusted. This allows the relative vertical positions of the fixed magnetic members 4a and 4b and the pendulum-side magnetic members 22a and 22b to be adjusted by adjusting the vertical positions of the magnetic member support portions 5a and 5b and the vertical position of the shaft 32. In other words, the repulsive force between the fixed magnetic members 4a and 4b and the pendulum-side magnetic members 22a and 22b can be adjusted. Note that the horizontal positions of the magnetic member support portions 5a and 5b may also be adjustable in addition to the vertical positions. The support body 6 to which the magnetic member support portions 5a and 5b and the pendulum support member 3 are attached is fixed to the building 20, which is the target of vibration control, so that the pendulum member 2 is suspended vertically.

[0028] In the pendulum device 1 having such a configuration, the pendulum member 2 performs pendulum motion with the axis 32 as the fulcrum. As the pendulum-side magnetic members 22a, 22b fixed to the pendulum main body 21 approach the opposing fixed magnetic members 4a, 4b, a repulsive force is generated between the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b, and this repulsive force acts on the pendulum member 2. Therefore, the restoring force is greater than when the fixed magnetic members 4a, 4b and the pendulum-side magnetic members 22a, 22b are not present.

[0029] <Restoring Force Characteristics> Here, we will explain the restoring force characteristics of the pendulum member 2. When the pendulum-side magnetic members 22a, 22b and fixed magnetic members 4a, 4b are not provided, the restoring force of the pendulum body 21 due to gravity can be expanded into a power series by Taylor expansion of sin θ, as shown in the following equation (1). In equation (1), m is the mass of the pendulum member 2, g is the gravitational acceleration, and θ is the displacement angle from the rest state.

[0030]

[0031] As shown in equation (1), the coefficient of the term proportional to the cube is negative, so the restoring force due to gravity has the nonlinear characteristics of a soft spring. Figure 3 shows the displacement of the pendulum body 21 when it is allowed to freely vibrate, taking into account its direction of movement, and Figure 4 shows the spine curve, which represents the relationship between the amplitude and natural frequency of the pendulum body 21 relative to its stationary state. From Figure 4, it can be seen that the natural frequency changes depending on the amplitude, exhibiting soft spring characteristics.

[0032] On the other hand, as shown in FIG. 2, when the pendulum side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b are provided, the restoring force F of the pendulum due to the magnetic force is ｍ can be expressed by Taylor expansion as shown in the following equation (2).

[0033]

[0034] Therefore, as shown in FIG. 2, when the pendulum includes pendulum-side magnetic members 22a, 22b and fixed magnetic members 4a, 4b, the restoring force characteristics of the pendulum can be approximated by the following equation (3) based on equations (1) and (2).

[0035]

[0036] Equation (3) can be summarized into a linear component and a nonlinear component as in the following equation (4).

[0037]

[0038] Here, when the pendulum-side magnetic members 22a and 22b and the fixed magnetic members 4a and 4b are opposed to each other and the magnetic poles of the opposing surfaces are the same, that is, when a repulsive force is generated, F in equation (4) is １ is positive (linear restoring force characteristic), and F ３ is positive (hard spring characteristic). When the magnetic poles of the opposing surfaces of the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b are opposite to each other, that is, when an attractive force is generated, F １ is negative (does not have linear restoring force characteristics), F ３ is negative (soft spring characteristic).

[0039] From equation (4), F ３It can be seen that if F is adjusted to satisfy the following equation (5), the nonlinearity of the restoring force acting on the pendulum member 2 due to gravity and magnetic force can be suppressed. ３ The magnetic flux density, magnet shape, and arrangement of the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b, as well as the mass of the pendulum member 2 (specifically, the mass of the pendulum main body 21 and the pendulum-side magnetic members 22a, 22b), can be selected so as to satisfy equation (5), and the magnetic force acting on the pendulum member 2 can be adjusted.

[0040]

[0041] As shown in Figure 2, in a pendulum device 1 equipped with pendulum-side magnetic members 22a, 22b and fixed magnetic members 4a, 4b and adjusted to satisfy equation (5), the pendulum member 2 is allowed to freely oscillate. The time history waveform obtained in an experiment is shown in Figure 5, and the spine curve obtained in the experiment, which shows the relationship between the amplitude and natural frequency of the pendulum member 2, is shown in Figure 6. It can be seen from Figure 6 that there is almost no change in the natural frequency depending on the amplitude of the pendulum member 2.

[0042] Figures 7 and 8 show the time history waveform (Figure 7) and the spine curve (Figure 8) obtained from an experiment showing the relationship between the amplitude and natural frequency of the pendulum member 2 when the pendulum device 1 shown in Figure 2, which has been adjusted to satisfy equation (5), uses two ferrite magnets as each of the fixed magnetic members 4a and 4b, increases the magnetic force acting on the pendulum member 2, and causes the pendulum member 2 to oscillate freely. Figure 8 shows that by forming the fixed magnetic members 4a and 4b each using two overlapping ferrite magnets, the restoring force of the hard spring characteristics due to magnetic force greatly exceeds the restoring force of the soft spring characteristics due to gravity, and as a whole, the device exhibits hard spring characteristics in which the natural frequency increases as the amplitude increases.

[0043] In other words, by adjusting the restoring force due to magnetic force by changing the number of magnets used as the magnetic members, the magnetic flux density of the magnetic members, or the arrangement position (relative position) of the magnetic members, it is possible to adjust the restoring force characteristics of the pendulum member, which is the sum of the restoring force due to gravity and the restoring force due to magnetic force, due to the synergistic effect of the nonlinear component of the restoring force due to gravity acting on the pendulum member 2 and the nonlinear component of the restoring force due to magnetic force from the pendulum-side magnetic members 22a, 22b and fixed magnetic members 4a, 4b.

[0044] In the formula (5), "(mg / 6) = F ３ By adjusting the restoring force due to the magnetic force so as to satisfy the condition "(mg / 6)<F", a linear restoring force can be generated as shown in FIGS. 5 and 6, and the natural frequency can be maintained substantially constant regardless of the amplitude. ３ By adjusting the restoring force due to the magnetic force so as to satisfy "(mg / 6) > F", it is possible to generate a restoring force having hard spring characteristics, as shown in Figures 7 and 8. ３ By adjusting the restoring force due to magnetic force so as to satisfy the condition "a restoring force with soft spring characteristics that is stronger than when there is no magnet," it is possible to generate a restoring force with soft spring characteristics as shown in Figures 3 and 4.

[0045] The displacement of the pendulum main body 21 and pendulum member 2 was measured under the following conditions. (a) When the pendulum member 2 shown in FIG. 2 was used (corresponding to FIGS. 5 and 6 ), the conditions for measuring the displacement were as follows: Cylindrical ferrite magnets with a diameter d of 18 mm and a thickness t of 5 mm were used as the fixed magnetic members 4a and 4b. The horizontal distance between the pendulum-side magnetic members 22a and 22b and the fixed magnetic members 4a and 4b was 63 mm, and the vertical distance between the vertical centers of the fixed magnetic members 4a and 4b and the center of the shaft 32 was 50 mm. Measurements were performed using a laser displacement meter (LK-G35A, manufactured by Keyence Corporation) fixed to the magnetic member support portion 5b to measure the distance from the pendulum-side magnetic member 22b. The horizontal distance to the pendulum-side magnetic member 22b was measured at a point 16 mm vertically away from the center of the shaft 32 of the stationary pendulum member 2. When the swing amplitude of the pendulum member 2 (the variation amplitude of the measured value by the laser displacement meter) was 5 mm, the rotation angle of the pendulum member 2 was approximately 17 degrees.

[0046] (b) When the fixed magnetic members 4a, 4b and the pendulum-side magnetic members 22a, 22b are not provided (corresponding to Figures 3 and 4), that is, the conditions for measuring the displacement of the pendulum body 21 are as follows. That is, the measurement conditions were the same as those for the case where the pendulum member 2 shown in (a) Figure 2 is used, except that the fixed magnetic members 4a, 4b and the pendulum-side magnetic members 22a, 22b were not provided. In other words, the horizontal distance to the pendulum body 21, which is stationary, was measured at a point 16 mm vertically away from the center of the axis 32.

[0047] (c) When a pendulum member 2 having two ferrite magnets as the fixed magnetic members 4a and 4b was used (corresponding to Figures 7 and 8), the displacement was measured under the following conditions. The measurement conditions were the same as those for the pendulum member 2 shown in Figure 2 (a) above, except that two ferrite magnets were used as the fixed magnetic members 4a and 4b. Specifically, two cylindrical ferrite magnets with a diameter d of 18 mm and a thickness t of 5 mm were stacked on top of each other as the fixed magnetic members 4a and 4b, so that the thickness of the fixed magnetic members 4a and 4b was essentially 10 mm. The horizontal distance to the pendulum-side magnetic member 22b was measured from a point 16 mm away from the center of the axis 32 of the stationary pendulum member 2.

[0048] In Figures 3, 5, and 7, the horizontal axis represents elapsed time, and the vertical axis represents displacement taking into account the direction of movement of the pendulum member 2 or the pendulum body 21. In Figures 4, 6, and 8, the horizontal axis represents frequency, and the vertical axis represents amplitude. The frequency was calculated from the time interval between peaks in Figures 3, 5, and 7. In Figure 3, the natural frequency changes from 1.398 Hz to 1.391 Hz depending on the amplitude, a change of approximately 0.5%. In Figure 5, the natural frequency changes from 1.446 Hz to 1.448 Hz depending on the amplitude, a change of approximately 0.1%, and in Figure 7, the natural frequency changes from 1.511 Hz to 1.518 Hz depending on the amplitude, a change of approximately 0.5%.

[0049] <Adjusting Restoring Force Characteristics> To provide the pendulum device 1 with a linear restoring force, first, in the pendulum device 1 shown in Fig. 2, the number of magnets constituting each magnetic member, the magnetic force of the magnets, the installation positions (relative positions) of the magnets, etc. are determined so as to satisfy equation (5). Specifically, the restoring force due to magnetic force is adjusted by adjusting the vertical positions of the magnetic member support parts 5a, 5b and the vertical position of the shaft 32, adjusting the number and magnetic force of the fixed magnetic members 4a, 4b, the number and magnetic force of the pendulum-side magnetic members 22a, 22b, adjusting the mass of the pendulum member 2, etc. Note that if the natural frequency of the building 20, which is the object to be damped, is Ω, the pendulum device 1 is constructed so that the natural frequency ω of the pendulum member 2 satisfies the equation ω = Ω.

[0050] (Magnetic force characteristics) Here, we will explain the characteristics of the magnetic force acting on the pendulum-side magnetic members 22a, 22b. (Magnetic force characteristics during horizontal movement) First, as shown in Figure 9, we will explain the magnetic force characteristics when magnets A to C are arranged in this order on a plane in a straight line, and magnet B moves horizontally between magnets A and C. Magnets A to C have the same shape, are formed like thin plates, and are magnetized with a north pole on one of their front and back sides, and a south pole on the other. Magnets A and B are arranged so that their south poles face each other, and magnets B and C are arranged so that their north poles face each other. The thickness of magnets A to C is d.

[0051] In Figure 9, the initial state is when magnet B is in the middle position between magnet A and magnet C, and the gap between magnet A and magnet B in the initial state and the gap between magnet B and magnet C in the initial state are denoted as r. The gap r between magnet A and magnet B represents the horizontal distance from the center of magnet A's thickness to the center of magnet B's thickness. Similarly, the gap r between magnet B and magnet C represents the horizontal distance from the center of magnet B's thickness to the center of magnet C's thickness. Also, the displacement of magnet B from the initial state is denoted as x. The displacement x represents the horizontal movement distance of the center of magnet B's thickness. In Figure 9, the force F acting on magnet B by magnet A is Ｌ is expressed by the following equation (6).

[0052]

[0053] Also, the force F acting on magnet B by magnet C is Ｒ is expressed by the following equation (7).

[0054]

[0055] In equations (6) and (7), m is the magnetic charge of magnet B, m' is the magnetic charge of magnet A and magnet C, and μ is the magnetic permeability. Taylor expansion of equation (6) gives the following equation (8).

[0056]

[0057] When formula (7) is expanded by Taylor, it is expressed as formula (9) below.

[0058]

[0059] The total magnetic force F acting on the magnet B can be approximated from equations (8) and (9) as shown in the following equation (10).

[0060]

[0061] Here, in equation (10), the coefficient of the first-order term is defined as in the following equation (11).

[0062]

[0063] In equation (10), the coefficient of the third-order term is defined as in the following equation (12).

[0064]

[0065] From equations (11) and (12), the ratio of the coefficient of the first-order term to the coefficient of the third-order term in equation (10) is expressed by the following equation (13).

[0066]

[0067] In FIG. 10, the horizontal axis represents "d / r" in equation (13), and the vertical axis represents "a ３ / a １ This graph shows these relationships as the coefficient ratio "a ３ / a １ As "d / r" increases, the nonlinear effect of the magnetic force becomes greater than the linear effect. Therefore, it can be seen from FIG. 10 that the smaller "d / r" is, the easier it is to obtain the nonlinear effect of the magnetic force.

[0068] (Magnetic Force Characteristics During Pendulum Motion) Next, the magnetic force characteristics during pendulum motion in the pendulum device 1 shown in Fig. 2 will be described. Fig. 11 is a schematic representation of the pendulum device 1 shown in Fig. 2. When the fixed magnetic members 4a and 4b and the pendulum member 2 having the pendulum-side magnetic members 22a and 22b are in the positional relationship shown in Fig. 11, the force F acting on the pendulum member 2 by the fixed magnetic member 4a is ｌ is expressed by the following equation (14).

[0069]

[0070] In addition, the force F acting on the pendulum member 2 by the fixed magnetic member 4b is ｒ is expressed by the following equation (15).

[0071]

[0072] In equations (14) and (15), m1 is the magnetic charge of the magnets serving as the pendulum-side magnetic members 22a and 22b attached to the pendulum, m2 is the magnetic charge of the fixed magnetic members 4a and 4b, μ is the magnetic permeability, and r is the gap between the magnetic poles when the pendulum is stationary. In FIG. 11, when the pendulum-side magnetic members 22a and 22b are considered as a single magnetic member, the gap r is the horizontal distance from the center of the thickness of the fixed magnetic member 4a to the center of gravity of the pendulum-side magnetic members, and the horizontal distance from the center of the thickness of the fixed magnetic member 4b to the center of gravity of the pendulum-side magnetic members. Also in FIG. 11, x is the displacement of the pendulum member 2 from its stationary 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 pendulum-side magnetic members. Taylor expansion of equation (14) yields the following equation (16).

[0073]

[0074] When equation (15) is expanded by Taylor expansion, it is expressed as the following equation (17).

[0075]

[0076] Here, in equations (16) and (17), the following equation (18) is defined: k is a constant.

[0077]

[0078] The force F acting on the pendulum member 2 by the fixed magnetic member 4a ｌ and the force F acting on the pendulum member 2 by the fixed magnetic member 4b. ｒ By adding these together, the restoring force F due to the magnetic force can be approximated as shown in the following equation (19).

[0079]

[0080] Furthermore, since x = l sin θ, the following equation (20) can be obtained from equation (19): where θ is the displacement angle of the pendulum member 2 from its resting state.

[0081]

[0082] On the other hand, the restoring force of the pendulum member 2 due to gravity can be approximated as shown in the following equation (21). In equation (21), m is the mass of the pendulum member 2, l is the equivalent length of the pendulum, which is the length from the fulcrum Q to the center of gravity of the pendulum-side magnetic member, θ is the displacement angle of the pendulum member 2 from its rest state, θ" is the angular acceleration of the displacement angle θ, and k is a value determined from equation (18).

[0083]

[0084] Here, the magnetic force acting on the pendulum member 2 shown in FIG. 11 is an equivalent spring force F expressed by the following equation (22): ＊ can be considered equivalent to

[0085]

[0086] In formula (22), a １ The term containing the linear component of the magnetic force, a ３ The term containing is the nonlinear component of the magnetic force. ＊ is a １ and a linear component including ３ Depending on the sign of the nonlinear component including １ :a １ > 0 is positive stiffness, a １ < 0, negative stiffness a ３ :a ３ >0 is hard spring, a ３ <0: Soft spring In equation (20), the coefficient of the first-order term is the coefficient a in equation (22), as shown in the following equation (23). １ It can be considered as follows.

[0087]

[0088] Similarly, in equation (20), the coefficient of the third-order term is the coefficient a in equation (22), as shown in the following equation (24). ３ It can be considered as follows.

[0089]

[0090] Therefore, the coefficient a of the third-order term expressed by equation (24) is set to satisfy the following equation (25). ３By adjusting each component contained in the magnetic material, the restoring force of the magnetic force of the pendulum member 2 can be adjusted to have hard spring characteristics or soft spring characteristics.

[0091]

[0092] <Operation and Effects> When vibrations are input to the building 20, which is the vibration-damping target, with the restoring force due to the magnetic force adjusted in this manner, the support body 6 fixed to the building 20 vibrates in conjunction with the vibration of the building 20, and the pendulum member 2 begins to swing in a vertical plane around the axis 32 as a fulcrum. In a region where the amplitude of the pendulum member 2 is relatively small, the restoring force due to the magnetic force, i.e., the repulsive force, is relatively small, and the restoring force due to gravity has a linear component, so that the pendulum member 2 as a whole has a linear restoring force. In a region where the amplitude of the pendulum member 2 is relatively large, the restoring force due to gravity has a nonlinear component, but since this restoring force due to gravity is simultaneously supplemented by the restoring force due to the magnetic force, which has a nonlinear component large enough to cancel out the nonlinear component, the nonlinear component is canceled out, and the pendulum member 2 as a whole has a linear restoring force. Therefore, the restoring force is linear regardless of the magnitude of the amplitude of the pendulum member 2.

[0093] For this reason, the restoring force of the pendulum member 2 is linear over a wider operating range, and as a result, the natural frequency of the pendulum member 2 can be maintained at approximately the same as the natural frequency of the building 20, regardless of the magnitude of the amplitude of the pendulum member 2. This makes it possible to suppress a decrease in vibration control performance that depends on the amplitude of the pendulum device 1. Furthermore, because the pendulum member 2 maintains a linear restoring force over a wider operating range of the amplitude of the pendulum member 2, the pendulum member 2 can be made to pendulum with a larger amplitude than in pendulum devices whose linear restoring force is limited to a small amplitude range, thereby improving vibration control performance accordingly.

[0094] If the linear restoring force of the pendulum member 2 is limited to a small amplitude range, in order to obtain a vibration-damping effect over a wider amplitude range, it would be necessary to provide, for example, a vibration-damping device for small amplitudes and a vibration-damping device for large amplitudes. The vibration-damping device 10 according to this embodiment can exert a vibration-damping effect over a wider amplitude range, from small amplitudes to relatively large amplitudes, simply by providing the fixed magnetic members 4a, 4b and the pendulum-side magnetic members 22a, 22b, thereby reducing costs and preventing the device from becoming larger.

[0095] Furthermore, because a linear restoring force can be obtained over a wider operating range, a dynamic vibration absorber system utilizing autoparametric excitation can be constructed, and vibration damping effects can be exerted over a wider operating range, even when, for example, the natural frequency of the object to be damped and the natural frequency of the pendulum device 1 are constructed at a ratio of 1:1 / 2. Furthermore, with this dynamic vibration absorber system, the mass of the pendulum weight can be reduced, i.e., the mass of the pendulum member 2 can be reduced, making it possible to reduce the weight of the pendulum device 1 and, in turn, the vibration damping device 10.

[0096] Furthermore, while feedback control is generally known theoretically as a method for removing nonlinear components of the restoring force, it is necessary to provide actuators and sensors to perform feedback control. This means that the structure of the vibration control device becomes more complex, resulting in increased costs and power consumption. With the pendulum device 1 according to this embodiment, a pendulum device 1 that generates a linear restoring force can be realized simply by providing the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b. This allows for a simple structure without increased costs, and in particular, without consuming much power.

[0097] Furthermore, because the magnetic member support parts 5a and 5b and the shaft 32 are attached to the support part main body 6 so that their vertical positions can be changed, it is possible to easily adjust the restoring force of the pendulum member 2 due to the magnetic force. Furthermore, because the pendulum-side magnetic members 22a, 22b are formed to be longer in the vertical direction than the fixed magnetic members 4a, 4b, when the pendulum member 2 performs pendulum motion, a repulsive force can be generated between them and the fixed magnetic members 4a, 4b over a wider range, making it possible to efficiently adjust the restoring force due to the magnetic force.

[0098] The pendulum device according to this embodiment can achieve the same effects as the above embodiment when applied to a pendulum device 1' having a disk-shaped pendulum 2' shown in Figure 12. A trial calculation was conducted on the vibration control performance when the pendulum device 1' having the disk-shaped pendulum 2' shown in Figure 12 was used as a vibration control device for a building. When the pendulum device 1' having the disk-shaped pendulum 2' shown in Figure 12 was used as a vibration control device for a building, the maximum amplitude (θ in Figure 12) of the disk-shaped pendulum 2' was 75° when vibrated at a maximum acceleration of 100 gal. Furthermore, the maximum displacement of the tip of the disk-shaped pendulum 2' (i.e., the pendulum-side magnetic member 22') was 1.57 m. When the building vibrated without the vibration control device, the amplitude of the building was 0.16 m, while when the building vibrated with the vibration control device, the amplitude of the building was 0.037 m. In other words, the amplitude ratio of the building was 22%, confirming that the use of the vibration control device significantly reduced the amplitude of the building.

[0099] Furthermore, for example, a vibration control device weighing 660 t is installed in the Taipei 101 skyscraper (509.2 m high) in the Xinyi District of Taipei, Taiwan. In contrast, the pendulum device 1' can obtain vibration control effects by using a disk-shaped pendulum with a mass of 4,800 kg for a 30 m high, 9-story building, and it can be seen that it can be made significantly smaller. The configuration of the pendulum device 1' used in the calculations is shown in Figure 12 and Table 1. The various specifications of the building to be vibration controlled are as follows: Mass: 800 t, Height: 30 m (9 stories), Natural frequency: 1.24 Hz, Damping ratio: 0.05

[0100]

[0101] <Modifications> (Modification 1) In the above embodiment, the case where the restoring force characteristic of the pendulum member 2 is linear has been described. However, in the above formula (5), "(mg / 6)<F ３ ", the restoring force characteristic of the pendulum device 1 can be made to have a hard spring characteristic. ３ < 0", it is possible to provide a stronger soft spring characteristic. For example, by using the pendulum device 1 having hard spring characteristics as the vibration damping device 10 and arranging it on a self-excited vibrating pipe or a plant pipe, it is possible to provide good vibration damping performance.

[0102] To strengthen the soft spring characteristics of the pendulum device 1, it is necessary to make the magnetic poles of the opposing surfaces of the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b opposite to each other to generate an attractive force. １ is negative and does not generate a restoring force by itself, so the component mg ​​(mg in the first term on the right-hand side of equation (4)) which represents the effect of gravity is always required. For example, as in the pendulum device 201 shown schematically in FIG. 20, which will be described as a modified example later, when the pendulum member 202 oscillates in a horizontal plane, gravity does not affect the movement of the pendulum member 202. Therefore, in the pendulum device 201 shown in FIG. 20, if the magnetic poles on the opposing surfaces of the pendulum-side magnetic member and the fixed magnetic member are changed to opposite poles, the pendulum device will not have a restoring force and will not be able to achieve a vibration damping device.

[0103] (Variation 2) In the above embodiment, the natural frequency of the pendulum member 2 may be acquired at a predetermined timing, and the relative positions of the pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b may be adjusted so that this natural frequency coincides with the natural frequency of the building 20 serving as the object to be vibration-controlled. For example, the natural frequency of the pendulum member 2 is determined by measuring the distance between the pendulum member 2 and the fixed magnetic members 4a, 4b using a laser displacement meter, and calculating the natural frequency from the measurement results. An adjustment mechanism is provided that can adjust the relative positions of the magnetic member supports 5a and 5b that support the fixed magnetic members 4a, 4b and the support body 6. The positions of the magnetic member supports 5a, 5b are then adjusted in a direction such that the natural frequency of the pendulum member 2 coincides with the natural frequency of the building 20 serving as the object to be vibration-controlled. By performing this operation at a predetermined timing, such as at a predetermined fixed interval, it is possible to eliminate deviations in the natural frequency due to changes over time.

[0104] (Variation 3) In the above embodiment, the pendulum device 1 has been described in which the pendulum member 2 performs pendulum motion within a single vertical plane, but this is not limiting. For example, it is also possible to configure the pendulum member 2 to perform pendulum motion within two perpendicular vertical planes. In this case, for example, a separate mechanism for supporting the support mechanism 31 is provided between the support mechanism 31 and the support main body 6 shown in FIG. 2 so that the pendulum member 2 performs pendulum motion within a vertical plane perpendicular to the vertical plane in which the pendulum member 2 performs pendulum motion, with an axis provided on the support main body 6 as the fulcrum. This causes the pendulum member 2 to perform pendulum motion within a vertical plane perpendicular to the vertical plane in which the pendulum member 2 performs pendulum motion with the axis 32 as the fulcrum. Pendulum-side magnetic members 22a and 22b are provided on the pendulum member 2, and a pair of pendulum-side magnetic members formed similarly to the pendulum-side magnetic members 22a and 22b are provided on a plane perpendicular to the pendulum-side magnetic members 22a and 22b. Furthermore, a pair of fixed magnetic members formed in the same manner as the fixed magnetic members 4a and 4b are provided at positions facing the pair of pendulum-side magnetic members.

[0105] As a result, the pendulum member 2 performs pendulum motion in two mutually perpendicular vertical planes, making it possible to realize a vibration damping device that damps vibrations caused by the pendulum motion of the pendulum member. In this case, as in the above embodiment, a restoring force due to magnetic force can be generated along two vertical planes, thereby achieving the same effects as in the above embodiment. Note that even if the pendulum member 2 performs pendulum motion in three or more vertical planes, the same effects as above can be achieved by providing pendulum-side magnetic members 22a, 22b and fixed magnetic members 4a, 4b for each vertical plane.

[0106] (Variation 4) In a pendulum device that performs conical pendulum motion, it is also possible to remove the nonlinear component of the conical pendulum motion. When applied to a pendulum device 101 that performs conical pendulum motion, as shown in Figure 13, a pendulum member 102 is supported so that it can swing around a fulcrum Q, for example, using a pivot. A pendulum-side magnetic member 122, for example, a permanent magnet, is disposed at the end of the pendulum member 102 on the side opposite the fulcrum Q. The permanent magnet serving as the pendulum-side magnetic member 122 is magnetized with a north pole on one end in the longitudinal direction and a south pole on the other end, and is disposed so that one pole of the permanent magnet, for example, the north pole, is on the fulcrum Q side and the south pole is on the opposite side from the fulcrum Q.

[0107] On the other hand, a sheet-like permanent magnet is used as the fixed magnetic member 104, and this fixed magnetic member 104 is placed horizontally below the pendulum-side magnetic member 122. At this time, the surface of the fixed magnetic member 104 facing the pendulum-side magnetic member 122 is set as an S pole so as to repel the pendulum-side magnetic member 122, and the other surface is set as an N pole.

[0108] The magnetic force considering only the magnetic pole (fixed magnetic member 104) on the surface facing the pendulum-side magnetic member 122 can be expressed as follows: (a) First, as shown in Figure 14, we will explain the case where the magnetic pole surface of the fixed magnetic member 104 is sufficiently wide, that is, the case where the pendulum-side magnetic member 122 always faces the fixed magnetic member 104 regardless of the magnitude of the displacement angle θ from the stationary state of the pendulum member 102. The restoring force F due to the magnetic force of the pendulum member 102 can be approximated as shown in the following equation (26). In equation (26), k is a constant consisting 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 member 122. d is the distance from the center of gravity of the pendulum-side magnetic member 122 to the magnetized surface of the south pole of the fixed magnetic member 104 when the pendulum member is stationary. The distance from the fulcrum Q to the magnetized surface of the south pole of the fixed magnetic member 104 is "l+d".

[0109]

[0110] On the other hand, the restoring force due to gravity of the pendulum member 102 can be approximated as shown in the following equation (27). In equation (27), m is the mass of the pendulum member 102, l is the equivalent length of the pendulum, and is the distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic member 122. θ is the displacement angle of the pendulum member 102 from its resting state, and θ" is the angular acceleration of the displacement angle θ. In the configuration shown in FIG. 14, the restoring force F due to the magnetic force is directed vertically upward.

[0111]

[0112] In equation (27), the coefficient of the first-order term is "-(k / d ２ ) represents the linear component, and "-(kl / d ３ ) represents the nonlinear component. Here, the linear component a １ = -(k / d ２ ), nonlinear component a ３ = -(kl / d ３ ), then the linear component a １ and the nonlinear component a ３ Ratio a ３ / a １ is expressed by the following equation (28).

[0113]

[0114] Therefore, it can be seen that by making "l" larger than "d", it is easier to obtain a nonlinear effect of the magnetic force.

[0115] (b) Next, as shown in FIG. 15 , we will explain the case where the magnetic pole face of the fixed magnetic member 104 is not sufficiently wide. In other words, when the displacement angle θ of the pendulum member 102 from its rest state is small, the pendulum-side magnetic member 122 and the fixed magnetic member 104 face each other, but when the displacement angle θ is large, the pendulum-side magnetic member 122 and the fixed magnetic member 104 do not face each other. In this case, the restoring force due to gravity of the pendulum member 102 can be approximated as shown in the following equation (29). In equation (29), m is the mass of the pendulum member 102, l is the equivalent length of the pendulum, θ is the displacement angle of the pendulum member 102 from its rest state, and θ" is the angular acceleration of the displacement angle θ. k is a constant consisting of magnetic permeability and magnetic flux density. In equation (29), d is the distance from the center of gravity of the pendulum-side magnetic member 122 to the center of the thickness of the fixed magnetic member 104 when it is resting. The distance from the fulcrum Q to the center of the thickness of the fixed magnetic member 104 is "l + d". In the configuration shown in FIG. 15, the restoring force F due to the magnetic force is directed obliquely upward as shown in the drawing.

[0116]

[0117] In equation (29), the linear component a １ =(kd+kl) / d ３ , nonlinear component a ３ =(k(d+l)(d ２ +9dl+9l ２ )) / 6d ５ Then, the linear component a １ and the nonlinear component a ３ Ratio a ３ / a １ is expressed by the following equation (30).

[0118]

[0119] Therefore, it can be seen that a nonlinear effect of magnetic force can be easily obtained by making "l" larger than "d." Note that Fig. 13 is a schematic diagram showing an example of a pendulum device 101 that performs conical pendulum motion. In Figs. 13 to 15, pendulum member 102 corresponds to pendulum member 2 in the above embodiment, fixed magnetic member 104 corresponds to fixed magnetic members 4a and 4b, and pendulum-side magnetic member 122 corresponds to pendulum-side magnetic members 22a and 22b.

[0120] (Variation 5) In the pendulum device 101 performing conical pendulum motion shown in Fig. 13, instead of the sheet-like fixed magnetic member 104, a cylindrical radially anisotropic magnet can be used as the fixed magnetic member 104a, as shown in Fig. 16. As in Fig. 13, the pendulum member 102 is supported so as to be swingable about a fulcrum Q, for example, using a pivot, and a pendulum-side magnetic member 122, such as a permanent magnet, is disposed at the end of the pendulum member 102 opposite the fulcrum Q. The permanent magnet is magnetized with a north pole at one end in the longitudinal direction and a south pole at the other end, with the north pole facing the fulcrum Q and the south pole facing away from the fulcrum Q, for example. A cylindrical radially anisotropic magnet is disposed as the fixed magnetic member 104a. The magnetic pole on the inner cylindrical surface of the fixed magnetic member 104a is the south pole that repels the pendulum-side magnetic member 122, and the magnetic pole on the outer surface is the north pole.

[0121] Because the magnetization of the south pole is not strictly isotropic, it is not guaranteed that the pendulum member 102 will stably point vertically downward, but due to the effect of gravity, the extension direction of the pendulum member 102 will be vertical when it is stationary. In this case, as in the case where the pendulum member 2 described in the above embodiment moves in a simple pendulum motion within a vertical plane, the nonlinear component of the restoring force of the pendulum member 102 in conical pendulum motion can be removed by adjusting the restoring force due to magnetic force and utilizing the nonlinear effect of magnetic force.

[0122] In addition, in Modifications 4 and 5, the pendulum member 102 is supported oscillatably using a pivot, thereby causing a conical pendulum motion, but it may also be made to cause a spherical pendulum motion. In addition, in Modifications 4 and 5, the pendulum member 102 and the fixed magnetic members 104, 104a have different polarities, but they may also have the same polarity.

[0123] (Variation 6) In the above embodiment, the external shapes of the pendulum-side magnetic member and the fixed magnetic member may be any of cylindrical, columnar, spherical, arc-shaped, ring-shaped, hollow cylindrical, curved, and flat. The pendulum-side magnetic member and the fixed magnetic member do not need to have the same external shape; they are preferably shaped to generate the required repulsive or attractive force. Furthermore, in the above embodiment, the pendulum body 21 is not limited to a thin plate, but may be made of any rigid material. For example, the pendulum-side magnetic members 22a and 22b themselves may be used as the pendulum body 21, without providing a separate pendulum body 21.

[0124] Furthermore, the pendulum-side magnetic members 22a, 22b do not necessarily have to be provided at the tip of the pendulum body 21; they are preferably provided in a position where they can generate the required repulsive or attractive force. The same applies to the fixed magnetic members 4a, 4b; the fixed magnetic members 4a, 4b themselves may be used as the magnetic member supports 5a, 5b without providing separate magnetic member supports, and the locations of the fixed magnetic members 4a, 4b are not limited to the tips of the magnetic member supports 5a, 5b. The pendulum-side magnetic members 22a, 22b and the fixed magnetic members 4a, 4b may be located in any position and have any size (length) that allows them to generate the required repulsive or attractive force.

[0125] (Variation 7) In the above embodiment, the vibration damping device 10 is described as being a pendulum device 1 in which the pendulum member 2 is suspended and causes pendulum motion, but the present invention is not limited to this. When the pendulum member 2 is suspended and causes pendulum motion, the direction in which the pendulum member 2 extends is vertical when stationary. However, as shown in Figure 17(a) , a pendulum device in which one end of the pendulum member is attached to a wall surface or the like of an object to be damped and the pendulum member is horizontal when stationary with fulcrum Q as the axis and causes pendulum motion in the vertical direction based on this state may also be used as a vibration damping device.

[0126] 17 and Figures 18 to 29 described below are schematic diagrams of a pendulum device, and as in the above embodiment, one end of the pendulum member is attached to the object to be damped so that the pendulum member performs pendulum motion as the object vibrates, and the fixed magnetic member is arranged to vibrate integrally with the object to be damped as the object vibrates. Also, the X-axis, Y-axis, and Z-axis in Figures 17 to 29 represent the respective axes in an XYZ coordinate system that are orthogonal to each other.

[0127] [A] Figure 17(a) shows a pendulum device 201 in which one end of a pendulum member 202 is attached to a wall surface or the like of an object 220 to be damped so that it can swing in a vertical plane, and the movable end of the pendulum member 202 swings in a vertical plane as the object 220 vibrates up and down. In Figure 17(a), the downward direction is the Z-axis, the leftward direction is the X-axis, the direction into the paper is the Y-axis, and the Z-axis direction is the direction of gravity. A pendulum-side magnetic member 222 is attached to the end of the pendulum member 202 opposite the object 220 to be damped. The point on the object 220 to which one end of the pendulum member 202 is attached serves as fulcrum Q, and the pendulum member 202 has the rigidity to maintain a horizontal state as a stable equilibrium state. As the object 220 to be damped vibrates up and down, the pendulum member 202 performs pendulum motion around the fulcrum Q as an axis, and the pendulum-side magnetic member 222 moves along an arc within a vertical plane.

[0128] The pendulum member 202 does not necessarily have to be horizontal; as shown in FIG. 17( a), the pendulum-side magnetic member 222 side of the pendulum member 202 may be slightly lower than horizontal. Here, the magnetic force acting on the pendulum-side magnetic member 222 by the fixed magnetic member 204 decreases as the distance between the fixed magnetic member 204 and the pendulum-side magnetic member 222 increases. Therefore, when the magnetic force acting on the pendulum-side magnetic member 222 falls below the magnetic force required to maintain the pendulum member 202 in a horizontal position, the pendulum-side magnetic member 222 side of the pendulum member 202 will descend below horizontal around the fulcrum Q. As the pendulum-side magnetic member 222 side descends below horizontal, a larger portion of the pendulum member 202's mass is supported by the object to be damped, and therefore, less magnetic force is required to support the pendulum member 202. Therefore, the equilibrium state is achieved with the pendulum-side magnetic member 222 side slightly lower than horizontal. If the distance between the fixed magnetic member 204 and the pendulum-side magnetic member 222 becomes even longer, the magnetic force acting on the pendulum-side magnetic member 222 by the fixed magnetic member 204 is not enough to attract the pendulum-side magnetic member 222, and the pendulum member 202 becomes vertical. Even if the pendulum-side magnetic member 222 side of the pendulum member 202 is thus slightly lower than horizontal, the same effects can be obtained as when the pendulum member 202 is maintained horizontally. Here, we will explain the case where the equilibrium state is one in which the pendulum-side magnetic member 222 side is slightly lower than horizontal, as shown in Figure 17(a).

[0129] The fixed magnetic member 204 is disposed in a position facing the pendulum member 202, which is in an equilibrium state with the pendulum-side magnetic member 222 side slightly below horizontal, and is disposed so as to vibrate integrally with the object of vibration damping 220. The fixed magnetic member 204 and the pendulum-side magnetic member 222 are magnetized so that the magnetic poles of the opposing surfaces are opposite when the pendulum member 202 is in an equilibrium state. As a result, when the object of vibration damping 220 is not vibrating, the attractive force between the fixed magnetic member 204 and the pendulum-side magnetic member 222 maintains the pendulum member 202 in an equilibrium state slightly below horizontal, and when the amplitude of the pendulum member 202 from the equilibrium state is within a certain range, the attractive force between the pendulum-side magnetic member 222 and the fixed magnetic member 204 causes the pendulum member 202 to perform pendulum motion. When the object to be damped 220 vibrates in the Z-axis direction in FIG. 17 from an equilibrium state in which the pendulum member 202 is stationary, the pendulum member 202 performs pendulum motion in the ZX plane with the fulcrum Q as its axis as the object to be damped 220 vibrates.

[0130] In this case, the restoring force due to gravity and the restoring force due to magnetic force act on the pendulum member 202, and the nonlinear components of the restoring force due to gravity and the restoring force due to magnetic force cancel each other out. Therefore, the pendulum member 202 as a whole has a linear restoring force, regardless of the amplitude of the pendulum member 202. This suppresses the nonlinear component of the force due to gravity acting on the pendulum member 202 during pendulum motion. As shown in FIG. 17( b ), the pendulum member 202 in the equilibrium state may be configured to approach a more horizontal position by increasing the magnetic force acting between the fixed magnetic member 204 and the pendulum-side magnetic member 222 in FIG. 17( a ), for example, by increasing the size of the magnet of the fixed magnetic member 204 or by increasing the magnetic flux density.

[0131] 17(c), the pendulum member 202 in FIG. 17(a) may be positioned such that the center of gravity of the fixed magnetic member 204 is located below the extension of the horizontal pendulum member 202, for example, by raising the position of the fulcrum Q of the pendulum member 202 or adjusting the position of the fixed magnetic member 204. In other words, the pendulum member 202 may be configured so that the pendulum-side magnetic member 222 side of the pendulum member 202 is positioned so that a magnetic force acts on the pendulum member 202 to push it toward a horizontal position, thereby making the pendulum member 202 closer to a horizontal position in the balanced state. Both of the cases shown in FIG. 17(b) and FIG. 17(c) can achieve the same effect as the case shown in FIG. 17(a). In FIGS. 17(a) to 17(c), the linearity of the pendulum motion can be ensured within the range in which an attractive force is generated between the pendulum-side magnetic member 222 provided on the pendulum member 202 and the fixed magnetic member 204.

[0132] [B] Figure 18 shows a pendulum device 201 shown in Figure 17 with two fixed magnetic members 204. That is, in the pendulum device 201 shown in Figure 18(a), the pendulum member 202 is arranged so as to perform pendulum motion in the Z-X plane around fulcrum Q as an axis in response to the up and down vibration of the vibration-damping target 220, similar to the pendulum device 201 shown in Figure 17(a). The pendulum member 202 also has sufficient rigidity to maintain a stable equilibrium state in which the movable end of the pendulum member 202 is slightly lower than the horizontal position. Fixed magnetic members 204a and 204b are arranged above and below the pendulum member 202 in this equilibrium state, and these fixed magnetic members 204a and 204b are arranged so as to vibrate integrally with the vibration-damping target 220. Note that in this case, the pendulum member 202 may be horizontal in equilibrium, or may be slightly lowered as shown in Figure 18(a).

[0133] The fixed magnetic members 204a and 204b are positioned to face the pendulum-side magnetic member 222, which is positioned at the movable end of the pendulum member 202 in a balanced state. The surface of the pendulum-side magnetic member 222 facing the fixed magnetic member 204a and the surface facing the fixed magnetic member 204b are magnetized with opposite polarities, and the surfaces of the fixed magnetic member 204a and the pendulum-side magnetic member 222 facing each other are magnetized with the same polarity. Furthermore, the surfaces of the fixed magnetic member 204b and the pendulum-side magnetic member 222 facing each other are magnetized with the same polarity.

[0134] As a result, when the object 220 to be damped is not vibrating, the pendulum member 202 is maintained in an equilibrium state 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. When the amplitude of the pendulum member 202 from the equilibrium state is within a certain range, the pendulum member 202 performs pendulum motion by the repulsive forces between the pendulum-side magnetic member 222 and each of the fixed magnetic members 204a and 204b. When the object 220 to be damped vibrates in the Z-axis direction in Figure 18(a) from the equilibrium state in which the pendulum member 202 is stationary, the vibration of the object 220 to be damped causes the pendulum member 202 to perform pendulum motion in the Z-X plane with the fulcrum Q as the axis.

[0135] In this case, the restoring force due to gravity and the restoring force due to magnetic force act on the pendulum member 202, and the nonlinear components of the restoring force due to gravity and the restoring force due to magnetic force cancel each other out. Therefore, the restoring force of the pendulum member 202 as a whole has a linear component, and the restoring force is linear regardless of the amplitude of the pendulum member 202. This suppresses the nonlinear component contained in the restoring force due to gravity of the pendulum member 202 performing pendulum motion. Note that, in this case, as shown in FIG. 18( b ), the magnetic force acting between the fixed magnetic member 204 b and the pendulum-side magnetic member 222 in FIG. 18( a ) may be made larger than the magnetic force acting between the fixed magnetic member 204 a and the pendulum-side magnetic member 222, for example, by increasing the size of the magnet of the fixed magnetic member 204 b. This configuration may provide a magnetic force that can prevent the pendulum-side magnetic member 222 side of the pendulum member 202 from descending below the horizontal, thereby allowing the pendulum member 202 to approach the horizontal in the balanced state.

[0136] 18(c), the magnetic force acting between the fixed magnetic member 204a and the pendulum-side magnetic member 222 and the magnetic force acting between the fixed magnetic member 204b and the pendulum-side magnetic member 222 in FIG. 18(a) may be kept the same, but the position of the fulcrum Q of the pendulum member 202 may be raised or the positions of the fixed magnetic members 204a and 204b may be adjusted to bring the pendulum member 202 closer to the horizontal state. Specifically, 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 204a and 204b is shorter than the distance between the pendulum-side magnetic member 222 and the fixed magnetic member 204a in the horizontal state, and the position is arranged so that the magnetic force required to push up the pendulum member 202 acts more strongly between the pendulum-side magnetic member 222 and the fixed magnetic member 204b. As a result, the pendulum member 202 approaches the horizontal state in the equilibrium state.

[0137] In both cases of Figure 18(b) and Figure 18(c), the same effects as those of Figure 18(a) can be obtained. In Figures 17 and 18, pendulum member 202 corresponds to pendulum member 2 in the above embodiment, fixed magnetic members 204, 204a, and 204b correspond to fixed magnetic members 4a and 4b, and pendulum-side magnetic member 222 corresponds to pendulum-side magnetic members 22a and 22b.

[0138] [C] Figure 19 shows the pendulum device 201 in Figure 17, where the movable end of the pendulum member 202 vibrates within the X-Y plane when the object 220 to be damped, to which the pendulum member 202 is attached, vibrates in the Y-axis direction. In Figure 19, the left direction is the X-axis, the upward direction is the Y-axis, the direction into the paper is the Z-axis, and the Z-axis direction is the direction of gravity. In other words, Figure 19 is a view of the pendulum device 201 as seen from above. The magnetic poles of the facing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 are opposite.

[0139] The pendulum member 202 has rigidity that maintains a constant distance between the fulcrum Q and the pendulum-side magnetic member 222, and is configured so that as the object to be damped 220 vibrates in the Y-axis direction in Figure 19, the pendulum member 202 performs pendulum motion in the X-Y plane around the fulcrum Q as its axis, and the pendulum-side magnetic member 222 moves on an arc in the X-Y plane. One end of the pendulum member 202 is attached to a wall surface or the like of the object to be damped 220 so that it is maintained horizontally, and the pendulum member 202 is provided so as to be able to perform pendulum motion in the X-Y plane. The fixed magnetic member 204 is arranged so that the end face of the pendulum-side magnetic member 222 facing the fixed magnetic member 204 faces the end face of the fixed magnetic member 204 facing the pendulum-side magnetic member 222 on the extension of the longitudinal direction of the pendulum member 202 when the pendulum member 202 is in a state perpendicular to the YZ plane including the fulcrum Q to which one end of the pendulum member 202 is attached, and so that the fixed magnetic member 204 vibrates integrally with the vibration damping object 220. The fixed magnetic member 204 and the pendulum-side magnetic member 222 are magnetized to have opposite polarities.

[0140] As a result, when the vibration-damping object 220 is stationary, the pendulum member 202 is in a substantially horizontal state, and furthermore, the attractive force between the fixed magnetic member 204 and the pendulum-side magnetic member 222 maintains the pendulum member 202 in a state perpendicular to the Y-Z plane including the fulcrum Q of the vibration-damping object 220. Then, when the amplitude of the pendulum member 202 in the X-Y plane is within a certain range as the vibration-damping object 220 vibrates in the Y-axis direction, the pendulum member 202 performs pendulum motion due to the attractive force between the pendulum-side magnetic member 222 and the fixed magnetic member 204. When the vibration-damping object 220 vibrates in the Y-axis direction from a state in which the pendulum member 202 is stationary and perpendicular to the Y-Z plane including the fulcrum Q of the vibration-damping object 220, a restoring force due to the magnetic force acts on the pendulum member 202, and the pendulum member 202 performs pendulum motion in the X-Y plane around the fulcrum Q. In this case, gravity does not act on the vibration of the pendulum member 202, so the restoring force characteristics of the pendulum device 201 are soft spring characteristics.

[0141] [D] Figure 20 shows a pendulum device 201 in Figure 18 in which the object 220 to be damped, to which the pendulum member 202 is attached, vibrates in the Y-axis direction, causing the movable end of the pendulum member 202 to vibrate in the X-Y plane. That is, in the pendulum device 201 shown in Figure 20, similar to the pendulum device 201 in Figure 19, the pendulum member 202 is arranged to perform pendulum motion in the X-Y plane around fulcrum Q as the object 220 to be damped vibrates in the Y-axis direction. Furthermore, in a stationary state, fixed magnetic members 204a and 204b are arranged on both sides of the pendulum member 202, which is in a horizontal position and perpendicular to the Z-X plane containing fulcrum Q of the object 220 to be damped, so as to face the pendulum-side magnetic member 222. These fixed magnetic members 204a and 204b are arranged to vibrate integrally with the object 220 to be damped. The surface of the pendulum-side magnetic member 222 facing the fixed magnetic member 204a and the surface of the pendulum-side magnetic member 222 facing the fixed magnetic member 204b are magnetized with opposite polarities, the surfaces of the fixed magnetic member 204a and the pendulum-side magnetic member 222 facing each other are magnetized with the same polarity, and the surfaces of the fixed magnetic member 204b and the pendulum-side magnetic member 222 facing each other are magnetized with the same polarity.

[0142] As a result, when the object 220 to be damped is not vibrating, 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 maintain the pendulum member 202 in a horizontal state perpendicular to the Z-X plane including the fulcrum Q. When the amplitude of the pendulum member 202 from a state perpendicular to the Z-X plane including the fulcrum Q is within a certain range, the pendulum member 202 performs pendulum motion due to the repulsive force between the pendulum-side magnetic member 222 and the fixed magnetic members 204a and 204b. When the object 220 to be damped vibrates in the Y-axis direction in Figure 20 from a state in which the pendulum member 202 is stationary, the pendulum member 202 performs pendulum motion in the X-Y plane around the fulcrum Q as the object 220 vibrates. In this case, gravity does not act on the oscillation of the pendulum member 202, so the pendulum device 201 has hard spring characteristics.

[0143] The pendulum device 201 shown in Figures 19 and 20, in which the pendulum member 202 vibrates in the X-Y plane in response to vibration of the vibration-damping target 220, can be installed in a space with a shorter height dimension than the hanging-type pendulum device 1 shown in Figure 2, etc. For example, when the vibration damping device 10 is configured using the pendulum device 201 shown in Figures 19 and 20, the height dimension of the installation location for the vibration damping device 10 can be shorter than when installing a vibration damping device using the hanging-type pendulum device 1 shown in Figure 2, etc. Therefore, the vibration damping device can be installed relatively easily. A vibration damping device using the hanging-type pendulum device 1 requires a relatively high installation location. In particular, when installing a new vibration damping device in an existing building, a vibration damping device using the hanging-type pendulum device 1 may have to be installed by punching holes across multiple floors, making installation difficult or even impossible. In contrast, the vibration control device using the pendulum device 201 shown in Figures 19 and 20 does not require much height, so it can be installed relatively easily even when retrofitting an existing building, and can also be installed in a space with a relatively short vertical dimension.

[0144] 19 and 20, the pendulum member 202 vibrates within the XY plane and is not affected by gravity, so the mass of the pendulum member 202 can be smaller to achieve the same vibration damping capacity as the hanging-type pendulum device 1 of FIG. 2 etc. In other words, it is possible to achieve a smaller size. In addition, in Figures 19 and 20, the pendulum member 202 corresponds to the pendulum member 2 in the above embodiment, the fixed magnetic members 204, 204a, 204b correspond to the fixed magnetic members 4a, 4b, and the pendulum-side magnetic member 222 corresponds to the pendulum-side magnetic members 22a, 22b.

[0145] [E] Figure 21 shows the pendulum device 201 in Figure 17, where the object 220 to be damped, to which the pendulum member 202 is attached, vibrates in the X-axis direction in Figure 21, causing the movable end of the pendulum member 202 to vibrate within the Z-X plane. In Figure 21, the left direction is the Z-axis, the upward direction is the X-axis, the direction into the paper is the Y-axis, and the Z-axis direction is the direction of gravity. In other words, the pendulum device 201 shown in Figure 21 is a pendulum device in which the pendulum member 202 is suspended from the object 220 to be damped. In this case, the magnetic poles on the opposing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 may be opposite or the same polarity.

[0146] The pendulum member 202 has rigidity that maintains a constant distance between the fulcrum Q and the pendulum-side magnetic member 222. As the object to be vibration-damped 220 vibrates in the X-axis direction, the pendulum member 202 performs pendulum motion around the fulcrum Q, causing the pendulum-side magnetic member 222 to move along an arc within the vertical Z-X plane. The fixed magnetic member 204 is disposed on an extension of the pendulum member 202, which is suspended and in a stationary state with one end attached to the fulcrum Q of the object to be vibration-damped 220, so as to vibrate integrally with the object to be vibration-damped 220. The fixed magnetic member 204 and the pendulum-side magnetic member 222 are magnetized, for example, to have opposite polarities. As a result, when the object to be vibration-damped 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.

[0147] 21 from a state in which the pendulum member 202 is stationary and vertical, and the vibration-damping target 220 vibrates in the X-axis direction in Fig. 21, the pendulum member 202 will then perform pendulum motion in the Z-X plane, with fulcrum Q as its axis. If the opposing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 have opposite polarities, the restoring force due to the magnetic force will act on the pendulum member 202, and the nonlinear component due to gravity and the nonlinear component due to the magnetic force will not be able to cancel each other out, and although the pendulum member 202 as a whole will have a linear restoring force, the resultant force acting on the pendulum due to gravity and magnetic force will increase in nonlinear soft spring characteristics in proportion to the angle of the pendulum.

[0148] If the magnetic poles of the opposing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 are the same, when the object to be vibration-damped 220 is not vibrating, if the magnitude of the linear component of the force due to gravity acting on the pendulum is greater than the linear component of the repulsive force due to the magnetic force, the pendulum member 202 is maintained in a stationary state facing vertically downward, and when the amplitude of the pendulum member 202 from its state facing vertically downward is within a certain range, the pendulum member 202 is configured to perform pendulum motion. As a result, when the opposing surfaces of the fixed magnetic member 204 and the pendulum-side magnetic member 222 have the same polarity, a restoring force exists that is the sum of the restoring force due to gravity and the restoring force due to the magnetic force, and the nonlinear components contained in each restoring force can be canceled out, allowing the pendulum member 202 as a whole to have linear restoring force characteristics without nonlinearity.

[0149] [F] Figure 22 shows a configuration in which the pendulum device 201 in Figure 18, to which the object 220 to be damped is attached, vibrates in the X-axis direction in Figure 22, causing the movable end of the pendulum member 202 to vibrate in the Z-X plane. In this case, the magnetic poles on the opposing surfaces of the fixed magnetic members 204a, 204b and the pendulum-side magnetic member 222 may be the same or different. An example of a configuration in which the magnetic poles are the same is the pendulum device 1 shown in Figure 2. The pendulum member 202 has rigidity that maintains a constant distance between the fulcrum Q and the pendulum-side magnetic member 222. As the object 220 to be damped vibrates in the X-axis direction in Figure 22, the pendulum member 202 performs pendulum motion in the Z-X plane around the fulcrum Q as its axis, and the pendulum-side magnetic member 222 moves along an arc in a vertical plane.

[0150] Fixed magnetic members 204a, 204b are arranged on the extension of the direction of extension of pendulum member 202, which is suspended at a stationary state with one end attached to fulcrum Q of vibration-damping object 220, and are arranged so as to vibrate integrally with vibration-damping object 220. The surface of pendulum-side magnetic member 222 facing fixed magnetic member 204a and the surface of pendulum-side magnetic member 222 facing fixed magnetic member 204b are magnetized to have opposite polarities, and fixed magnetic member 204a and pendulum-side magnetic member 222 are magnetized to have the same polarity, for example, and similarly fixed magnetic member 204b and pendulum-side magnetic member 222 are magnetized to have the same polarity. As a result, when vibration-damping object 220 is not vibrating, gravity and the repulsive force between fixed magnetic members 204a, 204b and pendulum-side magnetic member 222 keep pendulum member 202 in a vertical position.

[0151] 22 from a state in which the pendulum member 202 is stationary and vertical, and the vibration-damping target 220 vibrates in the X-axis direction in Figure 22, the pendulum member 202 accordingly performs pendulum motion in the Z-X plane around the fulcrum Q. When the magnetic poles of the opposing surfaces of the fixed magnetic members 204a, 204b and the pendulum-side magnetic member 222 are the same, a restoring force due to magnetic force acts on the pendulum member 202, and by adjusting parameters such as the distance between the magnets and the thickness of the magnets when the pendulum member 202 is stationary facing vertically downward, the nonlinear component of the restoring force due to gravity and the nonlinear component of the magnetic force cancel each other out, so that the pendulum member 202 as a whole has a linear restoring force, and the restoring force is linear regardless of the magnitude of the amplitude of the pendulum member 202.

[0152] On the other hand, if the magnetic poles of the opposing surfaces of the fixed magnetic members 204a, 204b and the pendulum-side magnetic member 222 are opposite, the restoring force due to gravity is made greater than the linear component of the attractive force due to the magnetic force when the object to be damped 220 is not vibrating, thereby maintaining the pendulum member 202 facing vertically downward and in a stationary state. When the opposing surfaces of the fixed magnetic members 204a, 204b and the pendulum-side magnetic member 222 are opposite in polarity, a restoring force consisting of the sum of the restoring force of gravity and the linear component of the magnetic force exists, and the pendulum member 202 can swing in response to the vibration of the object to be damped 220. However, in this case, the nonlinear component cannot be offset, resulting in an increased soft spring characteristic. Here, the restoring force characteristics of the pendulum device 201 differ depending on whether the magnetic poles on the opposing surfaces of the fixed magnetic members 204a, 204b and the pendulum-side magnetic member 222 are opposite or the same polarity: if they are the same polarity, a soft spring characteristic results, and if they are opposite polarity, a hard spring characteristic results. Therefore, depending on the desired characteristics, it is sufficient to determine whether the magnetic poles on the opposing surfaces of the fixed magnetic members 204a, 204b and the pendulum-side magnetic member 222 are opposite or the same polarity.

[0153] (Variation 8) [A] A pendulum device 301 may be constructed by combining the pendulum device 201 shown in Fig. 17 with the pendulum device 201 shown in Fig. 18, as shown in Figs. 23 to 26, with pendulum-side magnetic members 222a, 222b provided at both ends of the pendulum member 202 and with a fulcrum Q located midway in the longitudinal direction of the pendulum member 202. As shown in Fig. 23, a pendulum-side magnetic member (first magnetic member) 222a is provided at one end of the pendulum member 202. In addition, a fixed magnetic member (second magnetic member, first fixed member) 204 is provided at a position facing the pendulum-side magnetic member 222a, on an extension of the pendulum member 202 in a balanced state (stationary state). The magnetic poles of the opposing surfaces of the pendulum-side magnetic member 222a and the fixed magnetic member 204 are opposite to each other, so that an attractive force is generated. The pendulum member 202 is supported so as to be approximately horizontal at the position of fulcrum Q provided in the middle part of the pendulum member 202, and is configured so that the pendulum member 202 performs pendulum motion in the Z-X plane with fulcrum Q as its axis. In Figure 23, the downward direction is the Z axis, the left direction is the X axis, the direction into the paper is the Y axis, and the Z axis direction is the direction of gravity.

[0154] A pendulum-side magnetic member (third magnetic member) 222b is provided at the other end of the pendulum member 202, and fixed magnetic members (fourth magnetic member, second fixed member) 204a and 204b are provided on either side of the pendulum-side magnetic member 222b. The magnetic pole of the surface of the pendulum-side magnetic member 222b facing the fixed magnetic member 204a is different from the magnetic pole of the surface facing the fixed magnetic member 204b, the magnetic pole of the surface where the pendulum-side magnetic member 222b and the fixed magnetic member 204a face each other is the same, and the magnetic pole of the surface where the pendulum-side magnetic member 222b and the fixed magnetic member 204b face each other is the same, so that they repel each other.

[0155] In this way, pendulum A on the left end of pendulum member 202 and pendulum B on the right end are configured to operate in conjunction with each other, and the magnetic members are arranged differently; for example, pendulum A is configured to have soft spring characteristics, and pendulum B is configured to have hard spring characteristics. Furthermore, the magnetic forces acting on pendulums A and B can be adjusted separately. By adjusting either or both of the magnetic forces acting on pendulums A and B according to the desired characteristics, the linear restoring force and the nonlinear restoring force can be set independently.

[0156] In this case, gravity and the magnetic force between the pendulum-side magnetic members 222a and 222b act on each of the pendulum-side magnetic members 222a and 222b and the fixed magnetic member 204. Therefore, when the pendulum member 202 is stationary and in equilibrium, it may not be horizontal, but may be tilted to one side. In this case, as shown in Figures 17(b), 17(c), 18(b), and 18(c), for either or both of pendulums A and B, the positional relationship between the pendulum-side magnetic member 222a and the fixed magnetic member 204, or the positional relationship between the pendulum-side magnetic member 222b and the fixed magnetic member 204b may be adjusted, or the size of the magnets in the fixed magnetic members 204 and 204b may be adjusted. This may adjust the magnetic force acting on either or both of the pendulum-side magnetic members 222a and 222b, so that the stationary pendulum member 202 approaches the horizontal state.

[0157] [B] The pendulum device 201 shown in FIG. 19 and the pendulum device 201 shown in FIG. 20 may be combined to form a pendulum device 301, as shown in FIG. 24, in which pendulum-side magnetic members 222a, 222b are provided at both ends of the pendulum member 202 and a fulcrum Q is located at the longitudinal midpoint of the pendulum member 202.

[0158] As shown in FIG. 24 , a pendulum-side magnetic member (first magnetic member) 222a is provided at one end of the pendulum member 202. A fixed magnetic member (second magnetic member, first fixed member) 204 is provided at a position facing the pendulum-side magnetic member 222a, along an extension of the pendulum member 202 in a balanced (stationary) state. The magnetic poles of the opposing surfaces of the pendulum-side magnetic member 222a and the fixed magnetic member 204 are opposite to each other, generating an attractive force. The pendulum member 202 is supported at a fulcrum Q located at its midpoint so that the pendulum member 202 is approximately horizontal, and is configured to perform pendulum motion within the X-Y plane. In FIG. 24 , the left direction is the X-axis, the upward direction is the Y-axis, the direction toward the page is the Z-axis, and the Z-axis direction is the direction of gravity. In other words, FIG. 24 is a top view of the pendulum device 301.

[0159] A pendulum-side magnetic member (third magnetic member) 222b is provided at the other end of the pendulum member 202, and fixed magnetic members (fourth magnetic member, second fixed member) 204a and 204b are provided on either side of the pendulum-side magnetic member 222b. The magnetic pole of the surface of the pendulum-side magnetic member 222b facing the fixed magnetic member 204a is different from the magnetic pole of the surface facing the fixed magnetic member 204b, the magnetic pole of the surface where the pendulum-side magnetic member 222b and the fixed magnetic member 204a face each other is the same, and the magnetic pole of the surface where the pendulum-side magnetic member 222b and the fixed magnetic member 204b face each other is the same, so that they repel each other.

[0160] In this way, pendulum A on the left end of pendulum member 202 and pendulum B on the right end are configured to operate in conjunction with each other, and the magnetic members are arranged differently, for example, pendulum A is configured to have soft spring characteristics, and pendulum B is configured to have hard spring characteristics. Furthermore, the magnetic forces acting on pendulums A and B can be configured to be individually adjustable, and by adjusting either or both of the magnetic forces acting on pendulums A and B according to the desired characteristics, the linear restoring force and the nonlinear restoring force can be set independently.

[0161] The pendulum device 301 shown in Fig. 24 can also provide the same effects as the pendulum device 201 shown in Fig. 19 and Fig. 20, in which the pendulum member 202 vibrates in the X-Y plane in response to vibration of the vibration-damping target 220. For example, the height of the space required to install the pendulum device 301 is lower than in the case in which the pendulum member 202 performs pendulum motion in the Z-X plane, as shown in Fig. 23 and Fig. 26 described below, and therefore the pendulum device 301 can be installed relatively easily even when being installed later in an existing building, etc.

[0162] Incidentally, when a trial calculation was made on the vibration control performance when a pendulum device 301 shown in Figure 24, in which the pendulum member 202 oscillates in the XY plane, was used as a vibration control device for a building, the maximum amplitude (θ in Figure 25) of the pendulum member 202 of the vibration control device was 12° when vibrated at a maximum acceleration of 50 gal. Furthermore, the amplitude of the building when the building vibrated without the vibration control device was 0.082 m, whereas the amplitude of the building when the building vibrated with the vibration control device was 0.023 m, a building amplitude ratio of 28%, confirming that using a vibration control device can significantly reduce the amplitude of the building.

[0163] The configuration of the pendulum device 301 used in the calculations is shown in Figure 25 and Table 2. The various specifications of the building to be vibration-controlled are as follows: Mass: 800 t, height: 30 m, natural frequency: 1.24 Hz, damping ratio: 0.05

[0164]

[0165] [C] The pendulum device 201 shown in Fig. 21 and the pendulum device 201 shown in Fig. 22 may be combined to form a pendulum device 301, for example as shown in Fig. 26, in which pendulum-side magnetic members 222a, 222b are provided at both ends of the pendulum member 202, with a fulcrum Q located midway along the length of the pendulum member 202. As shown in Fig. 26, a pendulum-side magnetic member (first magnetic member) 222a is provided at one end of the pendulum member 202. In addition, a fixed magnetic member (second magnetic member, first fixed member) 204 is provided at a position facing the pendulum-side magnetic member 222a, on an extension of the pendulum member 202 in a balanced state (stationary state). The magnetic poles of the opposing surfaces of the pendulum-side magnetic member 222a and the fixed magnetic member 204 are opposite to each other, so that an attractive force is generated. The pendulum member 202 is supported vertically at the position of fulcrum Q provided in the middle of the pendulum member 202, and is configured to perform pendulum motion in the Z-X plane with fulcrum Q as its axis. In Figure 26, the left direction is the X-axis, the downward direction is the Z-axis, the direction into the paper is the Y-axis, and the Z-axis direction is the direction of gravity.

[0166] A pendulum-side magnetic member (third magnetic member) 222b is provided at the other end of the pendulum member 202, and fixed magnetic members (fourth magnetic member, second fixed member) 204a and 204b are provided on either side of the pendulum-side magnetic member 222b. The magnetic pole of the surface of the pendulum-side magnetic member 222b facing the fixed magnetic member 204a is different from the magnetic pole of the surface facing the fixed magnetic member 204b, the magnetic pole of the surface where the pendulum-side magnetic member 222b and the fixed magnetic member 204a face each other is the same, and the magnetic pole of the surface where the pendulum-side magnetic member 222b and the fixed magnetic member 204b face each other is the same, so that they repel each other.

[0167] In this way, the upper pendulum A and the lower pendulum B of the pendulum member 202 are configured to operate in conjunction with each other, and the magnetic members are arranged differently; for example, pendulum A is configured to have soft spring characteristics and pendulum B is configured to have hard spring characteristics. Furthermore, the magnetic forces acting on pendulums A and B can be configured to be individually adjustable, and by adjusting either or both of the magnetic forces acting on pendulums A and B according to the desired characteristics, it is possible to set the linear restoring force and the nonlinear restoring force independently. While Fig. 26 shows pendulum A on the upper side and pendulum B on the lower side, they may also be installed upside down, with pendulum B on the upper side and pendulum A on the lower side.

[0168] (Variation 9) In the pendulum devices 201 and 301 shown in Figs. 19, 20 and 24, in which the pendulum member 202 is configured to perform pendulum motion in a horizontal plane, a spring member may be further provided to position the pendulum member 202 in an equilibrium state perpendicular to the installation surface of the vibration-damping object 220, such as the wall of a building.

[0169] [A] Figure 27 shows the pendulum device 201 shown in Figure 19, with spring members provided for positioning the pendulum member 202, and a pair of spring members 210a, 210b provided in the longitudinal middle portion of the pendulum member 202. Specifically, one of the spring members 210a is attached so as to be perpendicular to the pendulum member 202 and disposed parallel to the Y axis between the pendulum member 202 and a member that vibrates integrally with the object of vibration damping 220, such as a wall surface of the object of vibration damping 220. Furthermore, the other spring member 210b is placed parallel to the Y axis on the pendulum member 202 between the position where the spring member 210a is attached and the object of vibration damping 220 or a member that vibrates integrally with the object of vibration damping 220 and disposed so as to be perpendicular to the pendulum member 202.

[0170] By providing the spring members 210a and 210b in this manner, a force acts on the pendulum member 202 to return it to a balanced state (a state perpendicular to the vibration-damping target 220), making it easy to position it in the balanced state. Furthermore, the pendulum member 202 can be supported by the spring members 210a and 210b, improving durability. Furthermore, by providing the spring members 210a and 210b, the restoring force of the spring members has a nonlinear component. However, since the restoring force of the spring members is simultaneously supplemented by a restoring force of the magnetic force, which has a nonlinear component large enough to cancel out the nonlinear component, the nonlinear component is canceled out, and the pendulum member 202 has a linear restoring force. Therefore, the restoring force is linear regardless of the amplitude of the pendulum member 202.

[0171] [B] Figure 28 shows the pendulum device 201 shown in Figure 20, with spring members provided to position the pendulum member 202. As with the pendulum device 201 shown in Figure 27, spring members 210a and 210b may be provided parallel to the Y-axis between the pendulum member 202 and the object 220 to be damped or a member that vibrates integrally with the object 220 to be damped, and in this case too, the same effects as those of the pendulum device 201 shown in Figure 27 can be obtained.

[0172] [C] Figure 29 shows a pendulum device 301 shown in Figure 23, where spring members are provided for positioning the pendulum member 202. As with the pendulum device 201 shown in Figure 27, spring members 210a and 210b may be provided parallel to the Y axis between the pendulum member 202 and the object to be damped 220 or a member that vibrates integrally with the object to be damped 220, and in this case too, the same effects as those of the pendulum device 201 shown in Figure 27 can be obtained. In Figure 29, the spring members 210a and 210b are provided between the fulcrum Q and the pendulum-side magnetic member 222a, but they may also be provided between the fulcrum Q and the pendulum-side magnetic member 222b.

[0173] (Modification 10) The object to be damped is not limited to the building 20, but may also be, for example, a moving object such as a train, a bridge, a pier, or a pipe.

[0174] [A] When the pendulum device according to this embodiment is attached to a pipe as a vibration absorber, for example, as shown in Figures 30(a) and (b), if the pipe 320 vibrates in the vertical direction, the pendulum device 201 shown in Figure 17 or 18 is used. The pendulum device 201 is then placed to the side of the pipe 320 so that the pendulum member 202, when stationary, extends in the X-axis direction of the pipe 320 in Figure 30, and the pendulum device 201 is arranged so that the pendulum member 202 performs pendulum motion in the Z-X plane in response to vertical vibration of the pipe 320. In Figure 30(a), the left direction is the Y-axis, the direction toward the viewer from the page is the X-axis, the downward direction is the Z-axis, and the Z-axis direction is the direction of gravity. Figure 30(b) is a view of the pipe 320 in Figure 30(a) as seen from the Y-axis direction.

[0175] Furthermore, as shown in Figures 31(a) and (b), when the pipe 320 vibrates in the horizontal direction, the pendulum device 201 shown in Figure 19 or 20 is used. The pendulum device 201 is disposed below the pipe 320 so that the pendulum member 202 in a stationary state extends in the Z-axis direction of the pipe 320 in Figure 31, and the pendulum device 201 is provided so that the pendulum member 202 performs pendulum motion in the Z-X plane in response to the horizontal vibration of the pipe 320. In Figure 31(a), the left direction is the Y-axis, the upward direction is the X-axis, the direction toward the paper is the Z-axis, and the Z-axis direction is the direction of gravity. Figure 31(b) is a view of the pipe 320 shown in Figure 31(a) as seen from the Y-axis direction.

[0176] [B] When the pendulum device according to this embodiment is attached to a train car as a vibration absorber, as shown in Figures 32(a) and (b), in the case of left-right vibration in the direction of travel of the car 420, the pendulum device 201 shown in Figure 19 or 20 is used, as in the case of suppressing horizontal vibration of the piping 320 shown in Figure 31. Then, the pendulum device 201 may be arranged on the ceiling or the like inside the car so that the pendulum member 202 extends downwardly in Figure 32 when stationary, and the pendulum device 201 is installed so that the movable part of the pendulum member 202 vibrates in a vertical plane left-right in the direction of travel of the car 420. By arranging it in this manner, it is possible to stabilize left-right vibration in the direction of travel of the car 420.

[0177] Furthermore, for example, when the pendulum device according to this embodiment is attached to a bridge as a vibration control device to suppress the bridge's vertical vibration, the pendulum device 201 shown in FIG. 17 or 18 is used, as in the case of suppressing the vertical vibration of the pipe 320 shown in FIG. 30 . The pendulum device 201 is then installed so that the pendulum member 202 performs pendulum motion in a vertical plane in response to the bridge's vertical vibration. In this case, when the bridge's natural frequency is Ω, it is preferable to set the natural frequency ω of the pendulum member 2 so that ω = Ω / 2. Furthermore, when suppressing the vertical vibration of a bridge or the like, it is also effective to use the pendulum device 301 shown in FIG. 23 , and in this case, it is preferable to install it near the center of the bridge or the like in the longitudinal direction. The pendulum device 301 shown in FIG. 23 and the pendulum device 301 shown in FIG. 24 can also be effectively applied to elevated roads.

[0178] (Variation 11) It is also possible to strengthen the nonlinearity of the pendulum device according to this embodiment and apply it to an energy harvester. Normally, the harvester resonates and can extract energy only when the excitation frequency γ is close to the natural frequency ω of the harvester (oscillator, in this case, the pendulum member). In other words, as shown in FIG. 33 , energy can be extracted only when the excitation frequency γ is within a limited range. By using the pendulum device according to this embodiment and adjusting the characteristics of the pendulum member to have soft spring characteristics or hard spring characteristics, a resonance state can be achieved over a wider range of excitation frequencies γ, as shown in FIG. 34 , allowing for efficient energy harvesting.

[0179] To achieve the characteristics shown in Fig. 34, a pendulum device having both hard and soft spring characteristics is required. For example, the pendulum device 301 shown in Fig. 23, which was explained in Modification 8, can be used. In Fig. 23, pendulum A has soft spring characteristics, and pendulum B has hard spring characteristics. By adjusting the distance between the magnets of pendulums A and B independently, the nonlinear characteristics of the pendulums can be set more freely.

[0180] For example, when the excitation frequency γ is lower than the linear natural frequency ω of the pendulum device 301, the electromagnet of pendulum A, which has soft spring characteristics, is activated, and the electromagnet of pendulum B is stopped. Conversely, when the excitation frequency γ is higher than the linear natural frequency ω of the pendulum device 1, the electromagnet of pendulum A is stopped, and the electromagnet of pendulum B, which has hard spring characteristics, is activated. This makes it possible to perform energy harvesting over a wider range of excitation frequencies γ, as shown in Fig. 34. The pendulum device 301 shown in Fig. 23 may be arranged so that it vibrates in the same direction as the vibration direction of the object to be vibration-damped.

[0181] Furthermore, the present invention is not limited to the pendulum device 301 shown in Fig. 23 , and other pendulum devices may also be applied to the energy harvester. For example, as shown in Fig. 32 , a pendulum device may be attached to a vehicle, and a pendulum member may be caused to swing in a pendulum motion as the vehicle swings left and right relative to the traveling direction, and the vibration may be converted into electrical energy. Alternatively, a pendulum device may be provided on a bridge, and a pendulum member may be caused to swing in a pendulum motion as the bridge swings up and down, and the vibration may be converted into electrical energy. Alternatively, a pendulum device may be disposed so that the pendulum member swings in a pendulum motion due to waves, and the vibration of the pendulum member caused by the waves may be converted into electrical energy.

[0182] The generator that converts vibrations into electrical energy can be, for example, a piezoelectric generator, an electromagnetic induction generator, an electrostatic generator, etc. For example, when the pendulum device is attached to a vehicle, as shown in Figure 32(b), a generator 420a that converts vibrations into electrical energy can be provided near the fulcrum Q of the pendulum member, and electrical energy can be extracted from this.

[0183] <Method of adjusting arrangement of magnetic members and movement characteristics of pendulum member> In the pendulum member 102 moving in a conical pendulum motion as shown in Figure 14 (when the magnetic pole face of the fixed magnetic member 104 is sufficiently wide), when the extension direction of the pendulum member 102 is vertical as shown in Figure 35, let r be the distance from the surface of the fixed magnetic member 104 to the center of gravity of the pendulum-side magnetic member 122, and x be the difference in height between the surface of the fixed magnetic member 104 and the center of gravity of the pendulum-side magnetic member 122 when the displacement angle of the pendulum member 102 from the vertical direction is θ, and let l be the distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic member 122. x is expressed by the following equation (31):

[0184]

[0185] Furthermore, the restoring force F of the pendulum member 102 due to the magnetic force can be approximated using equation (31) as shown in the following equation (32): k in equation (32) is a constant consisting of magnetic permeability and magnetic flux density.

[0186]

[0187] On the other hand, the restoring force of the pendulum member 102 due to gravity can be approximated as shown in the following equation (33). In equation (33), m is the mass of the pendulum member 102, and θ" is the angular acceleration of the displacement angle θ. In the configuration shown in Figure 35, the restoring force F due to the magnetic force is directed vertically upward.

[0188]

[0189] In equation (32), the coefficient of the first-order term, "(k / r ２ ) represents the linear component, and "-(kl / r ３ ) represents the nonlinear component. Here, the linear component a １ = (k / r ２ ), nonlinear component a ３ = -(kl / r ３ ), then the linear component a １ and the nonlinear component a ３ Ratio a ３ / a １ is expressed by the following equation (34).

[0190]

[0191] Therefore, it can be seen that a nonlinear effect can be easily obtained by making "l" larger than "r". Here, when the opposing surfaces of the pendulum-side magnetic member 122 and the fixed magnetic member 104 are of opposite polarity and attract each other, a １ Haa １ >0, and has positive linear stiffness, a ３ Haa ３ <0, and the nonlinear stiffness has soft spring characteristics. １ Gaa １ >0, a restoring force can be generated. When the opposing surfaces of the pendulum-side magnetic member 122 and the fixed magnetic member 104 have the same polarity and repel each other, a １ Haa １ < 0, and has negative linear stiffness, a ３ Haa ３ >0, and the nonlinear stiffness has hard spring characteristics. １ Gaa １ <0, and the linear stiffness is negative, so the pendulum device cannot have a restoring force.

[0192] In addition, when the restoring force of gravity can be utilized, for example, in the case of the pendulum device 201 shown in FIG. １ Even if the linear stiffness is negative and the force is <0, the effect of gravity can cancel this out, resulting in a positive linear stiffness overall. In this case, a restoring force exists, and at the same time, the magnetic member has hard spring characteristics. The pendulum member 102 that moves in a conical pendulum motion shown in FIG. 15 (when the magnetic pole faces of the fixed magnetic member 104 are not sufficiently wide) also has similar characteristics. In this case, a1, which represents the coefficient of the linear component, and a3, which represents the coefficient of the nonlinear component, can be calculated using the following procedure.

[0193] 15 , when the extension direction of the pendulum member 102 is vertical as shown in Fig. 36 , 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 r, 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 when the displacement angle of the pendulum member 102 from the vertical direction is θ is x, and the distance from the fulcrum Q to the center of gravity of the pendulum-side magnetic member 122 is the equivalent length l of the pendulum. In the configuration shown in Fig. 36 , the restoring force F due to the magnetic force is a force in the 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. On the movement locus of the center of gravity of the pendulum-side magnetic member 122 when the pendulum member 102 moves in a pendulum motion, the angle formed by the tangent line at the position of the center of gravity of the pendulum-side magnetic member 122 when the displacement angle is θ and the vector representing the restoring force F due to the magnetic force is defined as α.

[0194] The restoring force F of the pendulum member 102 due to the magnetic force can be expressed by the following equation (35): k in equation (35) is a constant consisting of magnetic permeability and magnetic flux density.

[0195]

[0196] Furthermore, from equation (35), the following approximate equation (36) can be derived.

[0197]

[0198] On the other hand, the restoring force of the pendulum member 102 due to gravity can be approximated as shown in the following equation (37): In equation (37), m is the mass of the pendulum member 102, and θ″ is the angular acceleration of the displacement angle θ.

[0199]

[0200] In equation (36), the coefficient of the first-order term is "(kl + kr)θ / r ３ " represents the linear component, and "-k(r+l)(r ２ +9rl+9l ２ ) θ ３ / 6r ３ " represents the nonlinear component. Here, the linear component a １=(kl+kr) / r ３ , nonlinear component a ３ =-k(r+l)(r ２ +9rl+9l ２ ) / 6r ３ Then, the linear component a １ and the nonlinear component a ３ Ratio a ３ / a １ is expressed by the following equation (38).

[0201]

[0202] Therefore, it can be seen that a nonlinear effect of magnetic force can be easily obtained by making "l" larger compared to "r". Note that the scope of the present invention is not limited to the exemplary embodiments shown and described, but also includes all embodiments that provide effects equivalent to those intended by the present invention. Furthermore, the scope of the present invention can be defined by any desired combination of specific features among all the respective features disclosed.

[0203] The present invention can be configured, for example, as follows: (1) A pendulum device comprising: a pendulum member, at least a part of which is made of a first magnetic member, that is subjected to a restoring force due to gravity and that moves in a pendulum motion around a fulcrum, and a fixed member, at least a part of which is made of a second magnetic member, that applies a magnetic repulsive or attractive force to the pendulum member as a magnetic restoring force, wherein 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, the pendulum member is provided with a magnetic restoring force that cancels out a nonlinear component of the restoring force due to gravity acting on the pendulum member.

[0204] (2) The pendulum device according to (1) above, wherein the pendulum member is rotatably suspended from the fulcrum.

[0205] (3) The pendulum device according to (1) or (2) above, wherein the pendulum motion is any one of simple pendulum motion, spherical pendulum motion, and conical pendulum motion.

[0206] (4) The pendulum device according to (1) above, characterized in that the pendulum member has rigidity, is capable of simple pendulum motion in a vertical plane around the fulcrum, and when in a stationary state, is maintained in a horizontal state by a restoring force due to the magnetic force, which is a repulsive or attractive force between the first magnetic member and the second magnetic member.

[0207] (5) The pendulum device described in (1) above is characterized in that, when the fixed member is in a stationary state, the end of the fixed member faces the end of the pendulum member on an extension of the opposite side of the fulcrum of the pendulum member, and when in a stationary state, the pendulum device is maintained in a horizontal state by a restoring force due to the magnetic force, which is the attractive force between the first magnetic member and the second magnetic member.

[0208] (6) The pendulum device according to any one of (1) to (4) above, wherein the pendulum motion is a simple pendulum motion, the pendulum device has a pair of second magnetic members, the pair of second magnetic members are arranged facing each other with the pendulum member sandwiched between them in the direction of motion of the simple pendulum motion, and the first magnetic member is arranged for each second magnetic member so as to face the second magnetic member.

[0209] (7) The pendulum device described in any one of (1) to (3) above, characterized in that the second magnetic member is arranged to surround the pendulum member, and the first magnetic member and the second magnetic member are arranged so that the magnetic poles on the sides facing each other are the same pole or opposite poles.

[0210] (8) The pendulum device according to any one of (1) to (7) above, wherein the first magnetic member and the second magnetic member are each formed of a permanent magnet or an electromagnet.

[0211] (9) The pendulum device described in any one of (1) to (8) above, characterized in that the external shapes of the first magnetic member and the second magnetic member are either cylindrical, prismatic, spherical, arc-shaped, ring-shaped, hollow cylindrical, curved, or flat.

[0212] (10) The pendulum device described in any one of (1) to (4) and (6) to (8) above, characterized in that the external shape of the second magnetic member is flat or curved, and the first magnetic member and the second magnetic member are arranged so that the magnetic poles on the sides facing each other are the same pole or opposite poles.

[0213] (11) The pendulum device according to any one of (1) to (10) above, wherein the fulcrum is provided directly on the object to be damped or on a structural part fixed to the object to be damped.

[0214] (12) A vibration control device that controls vibration of an object to be vibration-controlled using a pendulum device that performs pendulum motion, characterized in that the pendulum device is the pendulum device described in any one of (1) to (11) above.

[0215] (13) A method for designing a vibration control device that controls vibration of an object to be controlled using a pendulum member that is subjected to a restoring force due to gravity and moves in a pendulum motion around a fulcrum, comprising: arranging a first magnetic member on at least a part of the pendulum member; arranging a second magnetic member in a position that applies a magnetic repulsive or attractive force to the first magnetic member as a magnetic restoring force; and adjusting at least one of the magnetic flux densities of the first magnetic member and the second magnetic member, the relative positions of the first magnetic member and the second magnetic member, and the mass of the pendulum member so that a nonlinear component of the restoring force due to gravity acting on the pendulum member and a nonlinear component of the restoring force due to the magnetic force between the first magnetic member and the second magnetic member are canceled out.

[0216] (14) A pendulum device characterized in that a first magnetic member is disposed in at least a part of a pendulum member that is subjected to a restoring force due to gravity and that moves in a pendulum motion around a fulcrum, a second magnetic member is disposed in a position that applies a magnetic repulsive or attractive force to the first magnetic member as a restoring force due to magnetic force, and at least one of the magnetic flux densities of the first magnetic member and the second magnetic member, the relative positions of the first magnetic member and the second magnetic member, and the mass of the pendulum member is adjustable so that a nonlinear component of the restoring force due to gravity acting on the pendulum member and a nonlinear component of the restoring force due to magnetic force between the first magnetic member and the second magnetic member are canceled out.

[0217] (15) A pendulum device characterized in that a first magnetic member is disposed in at least a part of a pendulum member that is subjected to a restoring force due to gravity and that moves in a pendulum motion around a fulcrum, a second magnetic member is disposed in a position that applies a magnetic repulsive or attractive force to the first magnetic member as a restoring force due to magnetic force, and at least one of the magnetic flux densities of the first and second magnetic members, the relative positions of the first and second magnetic members, and the mass of the pendulum member is adjustable so that the restoring force characteristics of the sum of the restoring force due to gravity and the restoring force due to magnetic force have soft spring characteristics or hard spring characteristics due to the synergistic effect of the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first and second magnetic members.

[0218] (16) A magnetic bearing comprising: a first pendulum member, at least a part of which is made up of a first magnetic member, on which a restoring force due to gravity acts and which moves in a pendulum motion around a fulcrum; a first fixed member, at least a part of which is made up of a second magnetic member, which applies a repulsive force due to a magnetic force to the first pendulum member, the repulsive force having a nonlinear component of a magnitude that cancels out the nonlinear component of the restoring force due to gravity acting on the first pendulum member; a second pendulum member, at least a part of which is made up of a third magnetic member, on which a restoring force due to gravity acts and which moves in a pendulum motion around the fulcrum; and a second fixed member, at least a part of which is made up of a fourth magnetic member, which applies a magnetic attractive force to the second pendulum member, the magnetic attractive force having a nonlinear component of a magnitude that cancels out the nonlinear component of the restoring force due to gravity acting on the second pendulum member, a pendulum device characterized in that the second pendulum member is provided on an extension of the first pendulum member as a single pendulum member having rigidity continuous with the first pendulum member, and is provided so as to be able to perform simple pendulum motion around the fulcrum in a vertical plane, and further, when in a stationary state, is maintained in a horizontal state by a repulsive force due to the magnetic force between the first magnetic member and the second magnetic member, and an attractive force due to the magnetic force between the third magnetic member and the fourth magnetic member.

[0219] (17) The pendulum device described in (16) above, characterized in that at least one of the first magnetic member, the second magnetic member, the third magnetic member and the fourth magnetic member is constituted by an electromagnet, and at least one of the hard spring characteristics of the first pendulum member, which change due to the repulsive force of the magnetic force, and the soft spring characteristics of the second pendulum member, which change due to the attractive force of the magnetic force, can be changed by at least one of changing the magnitude of the magnetic force of the electromagnet and deactivating the electromagnet.

[0220] (18) The pendulum device according to (17) above, wherein the first magnetic member and the second magnetic member are each constituted by a permanent magnet or an electromagnet, and the third magnetic member and the fourth magnetic member are each constituted by a permanent magnet or an electromagnet.

[0221] (19) The pendulum device according to any one of (16) to (18) above, further comprising a generator that converts the vibration of the first pendulum member or the second pendulum member into electrical energy.

[0222] (20) A pendulum device comprising: a pendulum member, which is subjected to a restoring force due to gravity and moves in a pendulum motion around a fulcrum, and at least a part of which is made up of a first magnetic member; and a fixed member, which applies a magnetic repulsive or attractive force to the pendulum member as a restoring force due to magnetic force, and at least a part of which is made up of a second magnetic member; wherein the pendulum member has a restoring force due to magnetic force that cancels out a nonlinear component of the restoring force due to gravity acting on the pendulum member.

[0223] (21) A pendulum device comprising: a pendulum member having a Z-axis in a mutually orthogonal XYZ coordinate system, having rigidity, one end rotatably attached to a fulcrum, pendulum motion in the XY plane around the fulcrum, and at least a portion of which is made up of a first magnetic member; and a fixed member that applies a magnetic repulsive or attractive force to the pendulum member, and at least a portion of which is made up of a second magnetic member.

[0224] REFERENCE SIGNS LIST 1, 101, 201, 301 Pendulum device 2, 102, 202 Pendulum member 2' Disk-shaped pendulum member 21 Pendulum body 22, 22a, 22b, 122, 222, 222a, 222b Pendulum-side magnetic member 3 Pendulum support member 31 Support mechanism 32 Shaft 4a, 4b, 104, 104a, 204, 204a, 204b Fixed magnetic member 5a, 5b Magnetic member support portion 51a, 51b First member 52a, 52b Second member 6 Support portion body 10 Vibration damping device 20 Building 220 Object to be damped 320 Pipe 420 Vehicle

Claims

1. A pendulum device comprising: a pendulum member which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum, and at least a part of which is composed of a first magnetic member; and a fixed member which applies a magnetic repulsive or attractive force to said pendulum member as a magnetic restoring force, and which is at least a part of which is composed of a second magnetic member; wherein by adjusting at least one of the magnetic flux density of at least one of said first magnetic member and said second magnetic member, the relative position of said first magnetic member and said second magnetic member, and the mass of said pendulum member, a magnetic restoring force is provided which cancels out the nonlinear component of the restoring force due to gravity acting on said pendulum member.

2. The pendulum device according to claim 1, wherein said pendulum member is rotatably suspended from said fulcrum.

3. The pendulum device according to claim 1, wherein the pendulum motion is any one of a simple pendulum motion, a spherical pendulum motion, and a conical pendulum motion.

4. The pendulum device according to claim 1, wherein the pendulum member has rigidity, is capable of simple pendulum motion in a vertical plane centered on the fulcrum, and when in a stationary state is maintained in a horizontal state by a restoring force due to the magnetic force, which is a repulsive or attractive force between the first magnetic member and the second magnetic member.

5. The pendulum device described in claim 1, characterized in that, when the fixed member is in a stationary state, an end of the fixed member faces an end of the pendulum member on an extension of the opposite side of the fulcrum of the pendulum member, and, when in a stationary state, the pendulum device is maintained in a horizontal state by a restoring force due to the magnetic force, which is an attractive force between the first magnetic member and the second magnetic member.

6. A pendulum device as described in any one of claims 1 to 4, characterized in that the pendulum motion is a simple pendulum motion, there is a pair of second magnetic members, the pair of second magnetic members are arranged facing each other with the pendulum member in between in the direction of motion of the simple pendulum motion, and the first magnetic member is arranged for each of the second magnetic members so as to face each other.

7. A pendulum device as described in any one of claims 1 to 3, characterized in that the second magnetic member is arranged to surround the pendulum member, and the first magnetic member and the second magnetic member are arranged so that the magnetic poles of the sides facing each other are the same pole or opposite poles.

8. A pendulum device as claimed in any one of claims 1 to 5, wherein the first magnetic member and the second magnetic member are each constituted by a permanent magnet or an electromagnet.

9. A pendulum device as described in any one of claims 1 to 5, characterized in that the external shapes of the first magnetic member and the second magnetic member are each one of the following: cylindrical, rectangular, spherical, arc-shaped, ring-shaped, hollow cylindrical, curved, and flat.

10. A pendulum device as described in any one of claims 1 to 5, characterized in that the external shape of the second magnetic member is flat or curved, and the first magnetic member and the second magnetic member are arranged so that the magnetic poles on the sides facing each other are the same pole or opposite poles.

11. A pendulum device as claimed in any one of claims 1 to 5, characterized in that the fulcrum is provided directly on the object to be damped or on a structural part fixed to the object to be damped.

12. A vibration damping device that damps the vibration of an object to be damped by using a pendulum device that performs pendulum motion, characterized in that the pendulum device is a pendulum device as described in any one of claims 1 to 5.

13. A method for designing a vibration control device that controls the vibration of an object to be controlled by using a pendulum member that performs pendulum motion around a fulcrum under the action of a restoring force due to gravity, comprising the steps of: arranging a first magnetic member on at least a part of the pendulum member; arranging a second magnetic member in a position that applies a magnetic repulsive or attractive force to the first magnetic member as a magnetic restoring force; and adjusting at least one of the magnetic flux densities of the first magnetic member and the second magnetic member, the relative positions of the first magnetic member and the second magnetic member, and the mass of the pendulum member so that the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first magnetic member and the second magnetic member are offset.

14. A pendulum device comprising: a first magnetic member disposed in at least a part of a pendulum member which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum; a second magnetic member disposed in a position which applies a magnetic repulsive or attractive force to the first magnetic member as a restoring force due to magnetic force; and at least one of the magnetic flux densities of the first magnetic member and the second magnetic member, the relative positions of the first magnetic member and the second magnetic member, and the mass of the pendulum member, can be adjusted so that the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first magnetic member and the second magnetic member are offset.

15. A pendulum device comprising: a first magnetic member disposed on at least a part of a pendulum member which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum; a second magnetic member disposed in a position where a magnetic repulsive or attractive force is applied to the first magnetic member as a restoring force due to magnetic force; and at least one of the magnetic flux densities of the first magnetic member and the second magnetic member, the relative positions of the first magnetic member and the second magnetic member, and the mass of the pendulum member can be adjusted so that the restoring force characteristics of the sum of the restoring force due to gravity and the restoring force due to magnetic force have soft spring characteristics or hard spring characteristics due to the synergistic effect of the nonlinear component of the restoring force due to gravity acting on the pendulum member and the nonlinear component of the restoring force due to magnetic force between the first magnetic member and the second magnetic member.

16. A first pendulum member which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum and which is at least partially constituted by a first magnetic member; a first fixed member which imparts to the first pendulum member a repulsive force due to a magnetic force having a nonlinear component of a magnitude so as to cancel out the nonlinear component of the restoring force due to gravity acting on the first pendulum member and which is at least partially constituted by a second magnetic member; a second pendulum member which is subjected to a restoring force due to gravity and which moves in a pendulum motion around the fulcrum and which is at least partially constituted by a third magnetic member; and a second fixed member which is subjected to a restoring force due to gravity and which is at least partially constituted by a fourth magnetic member and which imparts to the second pendulum member a repulsive force due to a magnetic force having a nonlinear component of a magnitude so as to cancel out the nonlinear component of the restoring force due to gravity acting on the second pendulum member, said second pendulum member is provided on an extension of said first pendulum member as a single pendulum member having rigidity continuous with said first pendulum member, and is provided so as to be capable of simple pendulum motion about said fulcrum in a vertical plane, and further characterized in that when in a stationary state, said second pendulum member is maintained in a horizontal state by a repulsive force due to the magnetic force between said first magnetic member and said second magnetic member, and an attractive force due to the magnetic force between said third magnetic member and said fourth magnetic member.

17. The pendulum device described in claim 16, characterized in that at least one of the first magnetic member, the second magnetic member, the third magnetic member and the fourth magnetic member is composed of an electromagnet, and at least one of the hard spring characteristics of the first pendulum member which change due to the repulsive force of the magnetic force and the soft spring characteristics of the second pendulum member which change due to the attractive force of the magnetic force can be changed by at least one of changing the magnitude of the magnetic force of the electromagnet and deactivating the electromagnet.

18. The pendulum device according to claim 17, wherein the first magnetic member and the second magnetic member are each constituted by a permanent magnet or an electromagnet, and the third magnetic member and the fourth magnetic member are each constituted by a permanent magnet or an electromagnet.

19. The pendulum device according to any one of claims 16 to 18, further comprising a generator for converting the vibration of the first pendulum member or the second pendulum member into electrical energy.

20. A pendulum device comprising: a pendulum member which is subjected to a restoring force due to gravity and which moves in a pendulum motion around a fulcrum, and at least a part of which is constituted by a first magnetic member; and a fixed member which applies a magnetic repulsive or attractive force to said pendulum member as a magnetic restoring force, and which is constituted by at least a second magnetic member; wherein said pendulum member has a magnetic restoring force which cancels out the nonlinear component of the restoring force due to gravity acting on said pendulum member.

21. A pendulum device comprising: a pendulum member having a Z-axis in a mutually orthogonal XYZ coordinate system, having rigidity, one end rotatably attached to a fulcrum, which moves in a pendulum motion within the X-Y plane around the fulcrum, and at least a portion of which is constituted by a first magnetic member; and a fixed member which applies a magnetic repulsive or attractive force to the pendulum member, and at least a portion of which is constituted by a second magnetic member.

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