Method for designing oscillation damping device and structure including oscillation damping device

Abstract

To provide a design method of a rocking vibration control device having high absorption capacity of vibration energy by introducing a synchronization effect and allowing rational design, and a structure having the rocking vibration control device.SOLUTION: The oscillation damping device 18 is attached to a first member 10 and a second member 11 disposed in parallel with each other on the 1a of the structure body. The oscillation damping member 18 includes a seesaw member 21 attached to the first member 10, a first long material 23 and a second long material 24 arranged so as to cross each other and connecting the seesaw member 21 and the second member, and an inertial mass damper 25 attached between the seesaw member 21 and the first member 10. A mathematical model of the structure 1 in which the first long material 23 and the second long material 24 are expressed as one spring arranged in series with the inertial mass damper 25 is applied to the optimum tuning conditional expression of the equivalent contraction model to design the rocking vibration damping device satisfying the tuning condition.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a method for designing a vibration damping device so as to synchronize with the main body of a structure to which the device is attached, and to a structure equipped with a vibration damping device. [Background technology]

[0002] Patent Document 1, for example, describes a vibration damping device that includes a seesaw member attached to a lower or upper beam, a damper disposed between the seesaw member and the lower or upper beam, and a pair of rod members disposed diagonally so as to intersect with each other, one end of which is pin-connected to the seesaw member and the other end of which is pin-connected to the corner between the upper or lower beam and the column. The vibration damping device uses a Chebyshev's approximate linear motion mechanism to convert the translational motion of a structure such as a building into rotational motion of the seesaw member, thereby enabling efficient energy absorption by the damper connected to the seesaw member. Due to the characteristics of the approximate linear mechanism, the length of the rod or other member connecting the structure and the seesaw member does not change in the absence of a damper. This feature allows the device to be constructed using thin axial force members such as rods or cables.

[0003] Inertial mass dampers (inertial mass elements) are used in seismic isolation systems and vibration control systems for buildings and other structures (e.g., Patent Documents 2 to 4). Inertial mass dampers are devices or mechanisms that use a rotating weight or other element to generate a restoring force proportional to the relative acceleration occurring between their end points. Because the restoring force generated in such an inertial mass damper is proportional to the relative acceleration between its end points, the proportionality constant has the dimension of mass. Various vibration control methods have been proposed that actively utilize this pseudo-mass (inertial mass) (e.g., Patent Documents 5 to 7).

[0004] Furthermore, a technology has been proposed to increase the vibration control effect by connecting an inertial mass damper and an attached spring in series and "synchronizing" the characteristics (natural vibration) of the vibration system of the inertial mass and the attached spring with the structure to be vibration controlled (for example, Patent Document 8), and Patent Document 9 applies this type of configuration to a high-rise building. Also, Non-Patent Document 1 shows the optimal tuning conditions for a single mass system. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] International Publication No. 2010 / 116779 [Patent Document 2] Japanese Patent Application Laid-Open No. 2012-189104 [Patent Document 3] Japanese Patent Application Laid-Open No. 2012-37005 [Patent Document 4] Japanese Patent Application Laid-Open No. 2017-44328 [Patent Document 5] Japanese Patent Application Laid-Open No. 2008-101769 [Patent Document 6] Japanese Patent Application Laid-Open No. 2009-180346 [Patent Document 7] Japanese Patent Application Laid-Open No. 2009-293691 [Patent Document 8] Japanese Patent Application Publication No. 2018-71565 [Patent Document 9] Japanese Patent Application Publication No. 2023-67759 [Non-patent literature]

[0006] [Non-Patent Document 1] Kenji Saito et al., "Optimal response control of a single mass structure using a linear viscous damper with inertial connection elements and considerations on the Kelvin modeling method," Structural Engineering Journal Vol. 53B, 2007, pp. 53-66 Summary of the Invention [Problem to be solved by the invention]

[0007] Tuned vibration control methods require ingenuity in the placement of "additional springs" that are placed in series with the dampers. For example, it is practically very difficult to realize "additional springs" using axially loaded members such as braces. Axial loaded members cannot avoid the problem of buckling, an unstable phenomenon, and to prevent buckling, the secondary radius of cross section must be sufficiently large, which results in an enlarged cross section of the member. For this reason, when attempting to use axially loaded members as "additional springs," one faces the problem that their stiffness is generally too high for the "optimal tuning" value that corresponds to the inertial mass.

[0008] Patent Document 9 describes the use of a cable as an additional spring (tension spring). Another possible method is to use a long, cantilevered bending member as the additional spring. However, these methods pose problems in terms of layout planning, such as the need to install a separate cable to achieve the synchronization effect, or the additional spring itself becoming very large, which has a significant impact on the design plan.

[0009] On the other hand, the oscillation vibration control device has the advantage that a thin axial force member, such as a rod member, can be used to connect the seesaw member to the structure body. However, such a thin axial force member reduces the damper's efficiency as a vibration control system. In other words, since the displacement occurring in the structure to be vibration-controlled is a mechanism that occurs across both the damper and the thin axial force member, the relative flexibility of the thin axial force member reduces the effective movement of the damper, thereby reducing its energy absorption capacity.

[0010] In view of the above background, an object of the present invention is to provide a design method for a vibration damping device that introduces a tuning effect to achieve high vibration energy absorption capacity and enable rational design, and to provide a structure equipped with such a vibration damping device. [Means for solving the problem]

[0011] In order to solve the above-mentioned problems, one aspect of the present invention is a method for designing one or more oscillation vibration damping devices (18) to be installed in a structural body (1a), wherein the structural body includes, for each of the oscillation vibration damping devices, a first member (10) extending in a predetermined direction and a second member (11) extending in the predetermined direction and spaced apart from the first member in a spacing direction perpendicular to the predetermined direction, and the first member and the second member are configured to be displaced while maintaining a state in which they are parallel to each other when vibration is transmitted to one of the first member and the second member, and the oscillation vibration damping device Each of the first and second elongated members includes a seesaw member (21) attached to the first member so as to be rotatable about an axial direction perpendicular to the predetermined direction and the separating direction, and a first elongated member (23) and a second elongated member (24) arranged so as to intersect with each other along a plane including the predetermined direction and the separating direction, wherein one end of each of the first and second elongated members is joined to opposite ends of the seesaw member so as to be rotatable about the axial direction, and the other end is joined to the second member so as to be rotatable about the axial direction. and an inertial mass damper (25) attached to the first member at one end and to the seesaw member at the other end in order to suppress rotation of the seesaw member about the axial direction, and the design method includes a step of representing, for each of the rocking vibration damping devices, the rocking vibration damping device and a portion of the structure main body that is to be damped by the rocking vibration damping device in a mathematical model including mass, damping, and rigidity as elements, and in the mathematical model, the first elongated member and the second elongated member are arranged in series with the inertial mass damper and have rigidity. a step of fitting the mathematical model to an equivalent condensed model (35) including the step represented as one spring (34), a one-degree-of-freedom system (36) including a mass point, a spring, and a dashpot, and a tuning system (37) in which an additional spring (42) is connected in series to a damper (41) and is arranged in parallel with the spring and the dashpot of the one-degree-of-freedom system, wherein the portion of the structure main body that is to be damped by the oscillation vibration damping device corresponds to the one-degree-of-freedom system, and the inertial mass damper corresponds to the damper of the tuning system;and a step of applying the mathematical model assuming that one of the springs representing the first elongated member and the second elongated member corresponds to the additional spring, and a step of setting parameters of the inertial mass damper and the first elongated member and the second elongated member so as to satisfy an optimal tuning condition equation, which is a relational equation between parameters of the single degree of freedom system and the tuning system.

[0012] According to this aspect, the introduction of a tuning effect increases the vibration energy absorption capacity of the oscillation vibration damping device. Rather than providing a new spring as an "additional spring" for tuning, the first and second long members that exist as components of the oscillation vibration damping device are used as the "additional spring" for tuning, eliminating the need to add new members, resulting in a rational design. In conventional oscillation vibration damping systems, the first and second long members, which correspond to soft axial force members that reduce the energy absorption capacity of the damper, are effective in achieving the tuning effect, improving energy absorption capacity in the opposite way to conventional systems, resulting in a rational design.

[0013] In the above aspect, the structure main body (1a) may be a building main body (1a), the first member (10) and the second member (11) may be beam members, the building main body may include column members (8, 9) that support the beam members, and the sway vibration damping device may be arranged in a column-beam frame (2) that includes the beam members and the column members.

[0014] According to this aspect, the oscillation vibration damping device installed in the building can be designed to have a tuning effect.

[0015] In the above aspect, the building body (1a) may include a plurality of stories, and the vibration damping device (18) may be disposed across two or more of the stories.

[0016] According to this aspect, the rocking vibration damping device is installed across the floors of the building, so that vibrations can be efficiently suppressed.

[0017] In the above aspect, the step of representing with the mathematical model may include representing the building main body (1a) with a multi-degree-of-freedom system model (31), and the step of applying the mathematical model may include performing an eigenvalue analysis of the mathematical model to determine the effective mass and effective stiffness of a principal mode, and setting the effective mass and effective stiffness to the mass and stiffness of the single-degree-of-freedom system in the equivalent condensed model (35).

[0018] According to this aspect, it is possible to determine the tuning conditions of a rocking vibration damping device installed in a building having multiple stories.

[0019] In the above aspect, the equivalent reduced model (35) has the relationship shown in the following equation:

number

number

[0020] According to this configuration, the tuning conditions of a rocking vibration damping device installed in a building having multiple stories can be determined relatively easily.

[0021] In the above embodiment, at least one of the first members (10) may be a foundation beam.

[0022] According to this aspect, the first member to which the inertial mass damper is attached is part of a rigid member that is in contact with the ground, which is a fixed point, so the inertial mass damper reduces the input energy to the building body during an earthquake, making it possible to slim down the building.

[0023] In the above aspect, a tension force exceeding the compressive force applied to the first elongated member and the second elongated member (24) when vibration is transmitted to the structure main body (1a) may be introduced into the first elongated member (23) and the second elongated member (24).

[0024] According to this aspect, by applying tension to the first and second elongated members, the stiffness (spring constant (k b Even if the heights of the first and second elongated members are low, buckling of the first and second elongated members can be prevented.

[0025] One aspect of the present invention is a structure (1) comprising a structure body (1a) and one or more oscillation vibration damping devices (18) installed in the structure body, wherein the structure body comprises, for each of the oscillation vibration damping devices, a first member (10) extending in a predetermined direction and a second member (11) extending in the predetermined direction and spaced apart from the first member in a spacing direction perpendicular to the predetermined direction, and wherein when vibration is transmitted to one of the first member and the second member, the first member and the second member are displaced while maintaining a state in which they are parallel to each other. Each of the oscillation vibration damping devices comprises a seesaw member (21) attached to the first member so as to be rotatable about an axial direction perpendicular to the predetermined direction and the separating direction, and a first elongated member (23) and a second elongated member (24) arranged so as to intersect with each other along a plane including the predetermined direction and the separating direction, and each of the first elongated member and the second elongated member is joined at one end to opposite ends of the seesaw member so as to be rotatable about the axial direction, and at the other end to the second member so as to be rotatable about the axial direction. and an inertial mass damper (25) attached between the seesaw member and the first member to suppress rotation of the seesaw member around the axial direction, and for each of the oscillation vibration damping devices, the oscillation vibration damping device and a portion of the structure main body that is the target of vibration damping by the oscillation vibration damping device are expressed by a mathematical model that includes mass, damping, and rigidity as elements, and in which the first elongated member and the second elongated member are expressed as one spring (34) arranged in series with the inertial mass damper. When the mathematical model is applied to an equivalent reduced model (35) including a one-degree-of-freedom system (36) and a tuning system (37) including a damper (41) and an additional spring (42) connected in series to the damper, the portion of the structure body that is the target of vibration damping by the vibration damping device corresponds to the one-degree-of-freedom system, the inertial mass damper corresponds to the damper of the tuning system, and one of the springs representing the first elongated member and the second elongated member corresponds to the additional spring, the damping coefficient (c d ) and inertial mass (m d ), and the spring constant (k b) is configured to satisfy the optimal tuning condition equation of the equivalent condensed model.

[0026] According to this aspect, a tuning effect is introduced, increasing the vibration energy absorption capacity of the oscillation vibration damping device. Rather than providing a new spring as an "additional spring" for tuning, the first and second long members that exist as components of the oscillation vibration damping device are used as "additional springs" for tuning, eliminating the need to add new parts and resulting in a rational structure. In conventional oscillation vibration damping systems, the first and second long members, which correspond to soft axial force members that reduce the energy absorption capacity of the damper, are effective in achieving a tuning effect, and, contrary to conventional systems, improve energy absorption capacity, resulting in a rational structure. [Effects of the Invention]

[0027] According to the above aspects, it is possible to provide a design method for an oscillation vibration damping device that introduces a tuning effect, has a high vibration energy absorption capacity, and enables rational design, as well as a structure equipped with such an oscillation vibration damping device. [Brief explanation of the drawings]

[0028] [Figure 1] Plan view of the first floor of the building frame according to the embodiment [Figure 2] Plan view of the second floor of the building frame according to the embodiment [Figure 3] Cross-sectional view along line III-III in Figure 1 [Figure 4] FIG. 1 illustrates a mathematical model of a building according to an embodiment. [Figure 5] Diagram showing equivalent reduced model [Figure 6] Figure showing the displacement state of the equivalent reduced model [Figure 7] Graph showing the magnification of the response displacement of each story relative to the displacement input to the ground DETAILED DESCRIPTION OF THE INVENTION

[0029] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Fig. 1 is a plan view of a first floor portion of a column and beam frame 2 of a building main body 1a in a building 1 (structure) according to the embodiment, Fig. 2 is a plan view of a second floor portion of the column and beam frame 2 of the building main body 1a, and Fig. 3 is a cross-sectional view taken along line III-III in Fig. 1.

[0030] As shown in Figures 1 to 3, the building body 1a is an apartment building with a column and beam frame 2, three floors, and two rows of dwelling units 3 lined up in the girder direction on each floor, with a central corridor 4 sandwiched between the two rows of dwelling units 3 in the beam direction. A veranda 5 is provided on the opposite side of the central corridor 4 of each dwelling unit 3. The column and beam frame 2 includes columns 6 and beams 7.

[0031] At one side edge of the central corridor 4, the building body 1a is disposed at the boundary between the dwelling units 3 and the central corridor 4. The building body 1a includes a first column 8 and a second column 9, which are disposed adjacent to each other and spaced apart in the longitudinal direction, a first beam 10 connected to the first column 8 and the second column 9 at the first floor floor, and a second beam 11 connected to the first column 8 and the second column 9 at the third floor floor (second floor ceiling). In this embodiment, the first beam 10 is a foundation beam, but it may also be a main beam other than a foundation beam. Each of the first column 8, second column 9, first beam 10, and second beam 11 forms a rectangular frame 12. Within the frame 12, no beam 7 extending in the longitudinal direction is provided at the second floor floor. At the other side edge of the central corridor 4, columns 6 and beams 7 are arranged on the first floor floor and the third floor floor in a manner similar to that on the other side edge, but on the second floor floor, a third beam 13 is provided that extends in the girder direction and is joined to the column 6.

[0032] The building body 1a further includes a wall 14 disposed within the frame 12 and separating the dwelling units 3 from the central corridor 4. Inside the wall 14, a meter box 15 is provided, which is a space for collecting and storing meters for electricity, gas, and water. The meter box 15 also houses the wiring and piping connected to these meters. The wall 14 includes a doorway 16 on each floor that connects the dwelling units 3 to the central corridor 4, and a door 17 that opens and closes the doorway 16. The doorway 16 and door 17 form the entrance to the dwelling units 3.

[0033] The building 1 is equipped with a vibration damping device 18 housed in a meter box 15 in a wall 14. The meter box 15 is designed in a shape that can house the vibration damping device 18. The sway vibration damping device 18 is a device equipped with a so-called sway vibration damping mechanism, and includes: a seesaw member 21 attached to the first beam 10 via a plate 19 and a pin joint 20 so as to be rotatable around an axis perpendicular to the structural plane of the frame 12; a first long member 23 having one end rotatably joined to the seesaw member 21 around the axis and the other end rotatably joined to the upper end of the first column 8 and one end of the second beam 11 via a gusset plate 22 near the joint; a second long member 24 having one end rotatably joined to the seesaw member 21 around the axis and the other end rotatably joined to the upper end of the second column 9 and the other end of the second beam 11 via a gusset plate 22; and a pair of inertial mass dampers 25 attached to the seesaw member 21 and the first beam 10 to suppress rotation of the seesaw member 21 around the axis. The first and second elongated members 23, 24 intersect each other above the pin joint body 20, and their lower ends are joined to both ends of the seesaw member 21. The intersection position of the first and second elongated members 23, 24 is located closer to the first beam 10 than the center between the first beam 10 and the second beam 11.

[0034] The plate 19 is preferably made of steel and is placed on the upper surface of the first beam 10. The pin joint 20 is placed on the upper surface of the plate 19 and fixed to the first beam 10 by anchor bolts (not shown) or the like, and supports the seesaw member 21 so that it can rotate around its axis. The pin joint 20 may be formed by, for example, a clevis.

[0035] The seesaw member 21 includes a long member that extends substantially parallel to the extension direction of the first beam 10 in the absence of an earthquake, and a steel material such as a shaped steel can be used as the long member.

[0036] The first and second elongated members 23, 24 are, for example, tie rods. The first elongated member 23 includes two steel rods with forked ends so that they can be pin-connected to other members, and a turnbuckle 26 connecting the other ends of the two steel rods. The second elongated member 24 is, as a whole, rod-shaped with forked ends so that it can be pin-connected to other members, and the rod shape is composed of three steel rods connected by one turnbuckle 26 and one cross turnbuckle 27. The cross turnbuckle 27 has a through-hole (not shown) through which the first elongated member 23 is inserted. It is preferable that the lengths of the first and second elongated members 23, 24 are approximately equal to each other, and that the angles of the first and second elongated members 23, 24 relative to the second beam 11 are approximately equal to each other. It is preferable to adjust the first and second elongated members 23, 24 using turnbuckles 26 and / or cross turnbuckles 27 to preliminarily introduce tension into both the first and second elongated members 23, 24 so that tension is applied to both of them during non-earthquake situations. The floor slab 28 that crosses the frame 12, i.e., the floor slab 28 of the second floor, has through holes 29 through which the first and second elongated members 23, 24 pass. The turnbuckles 26 may not be provided in the first and second elongated members 23, 24. Alternatively, the cross turnbuckles 27 may be omitted, and the first and second elongated members 23, 24 may be positioned so that they are slightly offset from each other in the axial direction. It is preferable that tension be introduced into the first and second elongated members 23, 24. Long, slender members other than tie rods may be used as the first and second elongated members 23, 24. In particular, when the tension force introduced exceeds the compressive force applied to the first and second long members 23, 24, a component that can withstand tensile forces but cannot withstand compressive forces, such as PC steel wire, may be used as the main part of the first and second long members 23, 24.

[0037] The pair of inertial mass dampers 25 are arranged to sandwich the pin joint 20, and each has its lower end fixed to the first beam 10 and its upper end fixed near both ends in the extension direction of the seesaw member 21. The pair of inertial mass dampers 25 apply damping forces to both ends of the seesaw member 21 in the vertical direction.

[0038] The vibration damping device 18 acts to suppress deformation of the frame 12 during an earthquake. The following description focuses on the frame 12.

[0039] During an earthquake, when the second beam 11 is subjected to a seismic force (inertial force) directed toward the right in FIG. 3 relative to the first beam 10, the second beam 11 moves while remaining parallel to the first beam 10, causing the first and second columns 8 and 9 to tilt and / or curve to the right, and the rectangular frame 12 deforms. In the deformed frame 12, the diagonal line connecting the upper right corner and the lower left corner is longer, and the diagonal line connecting the upper left corner and the lower right corner is shorter, compared to before deformation. Because the diagonal line connecting the upper right corner and the lower left corner of the frame 12 is longer, a tensile force is generated in the second elongated member 24, and this tensile force acts on the frame 12 in a direction that resists the seismic force. Furthermore, the tensile force generated in the second elongated member 24 causes the seesaw member 21 to rotate clockwise around its axis. This rotation increases the distance between the joints of both ends of the first elongated member 23, i.e., the distance between the upper left corner of the frame 12 and one end (the right end in FIG. 3 ) of the seesaw member 21. The increase in the distance between the upper left corner of the frame 12 and the right end of the seesaw member 21 due to this rotation is roughly equal to the decrease in the length of the first elongated member 23 in the direction of compression caused by the shortening of the diagonal line connecting the upper left corner and the lower right corner of the frame 12. Therefore, the length of the first elongated member 23 remains roughly the same as the length during a non-earthquake, and compressive force is suppressed from being applied to the first elongated member 23.

[0040] Subsequently, when the direction of earthquake vibration changes and the second beam 11 is subjected to a seismic force directed to the left in Figure 3 relative to the first beam 10, a tensile force is generated in the first long member 23 due to the damping force from the inertial mass damper 25, even while the first and second columns 8, 9 are returning from their right-side tilted and / or curved state to a vertical state, and this tensile force acts on the frame 12 in a direction that resists the seismic force.

[0041] When the first and second columns 8, 9 tilt and / or bend to the left, the diagonal line connecting the upper left corner and the lower right corner of the deformed frame 12 becomes longer and the diagonal line connecting the upper right corner and the lower left corner becomes shorter compared to before deformation. Because the diagonal line connecting the upper left corner and the lower right corner of the frame 12 becomes longer, a tensile force is generated in the first elongated member 23, and this tensile force acts on the frame 12 in a direction that resists the seismic force. Furthermore, the tensile force generated in the first elongated member 23 causes the seesaw member 21 to rotate counterclockwise around its axis. This rotation increases the distance between the joint between the two ends of the second elongated member 24, i.e., between the upper right corner of the frame 12 and the other end of the seesaw member 21 (the left end in FIG. 3 ). The increase in the distance between the upper right corner of frame 12 and the left end of seesaw member 21 due to this rotation is roughly equal to the decrease in length in the direction compressing second long material 24 due to the shortening of the diagonal line connecting the upper right corner and the lower left corner of frame 12, so the length of second long material 24 remains roughly the same as its length during non-earthquake conditions, and the application of compressive force to second long material 24 is suppressed.

[0042] Subsequently, when the direction of earthquake vibration changes and the second beam 11 is subjected to a seismic force directed to the right in Figure 1 relative to the first beam 10, a tensile force is generated in the second long member 24 due to the damping force from the inertial mass damper 25, even while the first and second columns 8, 9 are returning from their leftward tilted and / or curved state to a vertical state, and this tensile force acts on the frame 12 in a direction that resists the seismic force.

[0043] The oscillation vibration suppression device 18 repeats the above-described movements during an earthquake, thereby preventing excessive deformation of the frame 12.

[0044] In addition, the rocking vibration damping device 18 is also arranged inside the protruding member 30 (see Figure 1) provided on the gable face of the building main body 1a to accommodate rocking in the span direction. The axis of rotation of the pin joint 20 and the first and second elongated members 23, 24 of the rocking vibration damping device 18 arranged on the gable face is in the longitudinal direction. In addition, the rocking vibration damping device 18 to accommodate rocking in the span direction may be arranged inside the partition wall.

[0045] Alternatively, the first and second beams 10, 11 may be spaced apart by three or more stories, and one oscillation vibration damping device 18 may be disposed across three or more stories. In this case, within the frame 12, the doorways 16 on each story are disposed offset in the girder direction relative to the doorways 16 on at least one other story so as not to overlap with the oscillation vibration damping devices 18. For example, if the first and second beams 10, 11 are spaced apart by four stories, the doorways 16 on the lower two stories may be disposed near the first and second columns 8, 9 so that their positions in the girder direction coincide with each other, and the doorways 16 on the upper two stories may be disposed in the center between the first and second columns 8, 9 so that their positions in the girder direction coincide with each other (not shown). Furthermore, within one frame 12, one doorway 16 may be provided on each story, or three or more doorways 16 may be provided, and the number of doorways 16 on each story may be the same or different.

[0046] The vibration damping device 18 is designed to synchronize with the building body 1a. FIG. 4 is a diagram showing the building 1 represented by a multi-degree-of-freedom system model 31. As shown in FIGS. 3 and 4, the building body 1a is represented by mass points 32 representing each floor and shear springs 33 connecting adjacent mass points 32 on the top and bottom or connecting the ground G to the mass point 32 on the bottom floor (left part of FIG. 4). The mass point 32 on the first floor has a mass m1 equivalent to the total mass of the columns 6, beams 7, floor slabs 28, etc. from the vertical midpoint of the columns 6 on the first floor to the vertical midpoint of the columns 6 on the second floor. The mass point 32 on the second floor has a mass m2 equivalent to the total mass of the columns 6, beams 7, floor slabs 28, etc. from the vertical midpoint of the columns 6 on the second floor to the vertical midpoint of the columns 6 on the third floor. Mass point 32 on the third floor, which is the top floor, has mass m3, which corresponds to the total mass of columns 6, beams 7, floor slabs 28, etc., located above the vertical midpoint of columns 6 on the third floor. Building body 1a includes equipment (not shown) installed on floor slabs 28, etc., and masses m1, m2, and m3 of mass point 32 may include the mass of the equipment installed on the corresponding floor. Shear springs 33 indicate the rigidity of columns 6 and beams 7. Shear spring 33, located between ground G and mass point 32 on the first floor, has spring constant k1. Shear spring 33, located between mass point 32 on the first floor and mass point 32 on the second floor, has spring constant k2. Shear spring 33, located between mass point 32 on the second floor and mass point 32 on the third floor, has spring constant k3.

[0047] The oscillation damping device 18 is modeled by regarding the first long member 23 and the second long member 24 as a spring 34 connected in series to the inertial mass damper 25 (right part of FIG. 4). The spring 34 has a spring constant k b The modeled inertial mass damper 25 has a horizontally displaced damping coefficient c d and inertial mass m d The vibration damping device 18 is connected to the first beam 10, which is a foundation beam supported by the ground G, and the second beam 11, which is included in the mass point 32 of the second layer, and therefore the modeled vibration damping device 18 is connected to the ground G and the mass point 32 of the second layer.

[0048] When multiple vibration damping devices 18 are provided, a model is created for each of the vibration damping devices 18 in the building 1 for the portion of the building 1 that is the target of vibration damping by that vibration damping device 18. Modeling of the building 1 can be done by a method other than the above, as long as it is a mathematical model that expresses the building 1 using three elements: mass, damping, and rigidity (spring constant). For example, the three-dimensional building 1 and vibration damping devices 18 may be modeled as they are.

[0049] 5 is a diagram showing an equivalent condensed model 35. As shown in FIG. 5, the equivalent condensed model 35 includes a single-degree-of-freedom system 36 and a tuning system 37 added to the single-degree-of-freedom system 36.

[0050] The single-degree-of-freedom system 36 has a mass m s and a spring 39 and a dashpot 40 that are arranged in parallel to each other and connect the mass point 38 to the ground G. The spring 39 has a spring constant k s The dashpot 40 has a damping coefficient c s It has.

[0051] The tuning system 37 includes a damper 41 and an additional spring 42 connected in series to the damper 41, and is arranged in parallel with the spring 39 and dashpot 40 of the single-degree-of-freedom system 36, and connects the mass point 38 to the ground G. The damper 41 has an inertial mass m eq and damping coefficient c eq The additional spring 42 has a spring constant k eq It has.

[0052] FIG. 6 is a diagram showing the displacement of the equivalent reduced model 35. s indicates the displacement of the single degree of freedom system 36. d indicates the displacement of the damper 41. b indicates the displacement of the additional spring 42. g indicates the displacement of the ground G.

[0053] The optimal tuning condition equation for tuning the tuning system 37 to the single degree of freedom system 36 is shown in Non-Patent Document 1 as follows:

number

number

[0054] By applying the mathematical model of the building 1 to the above-mentioned equivalent condensed model 35 and setting parameters so as to satisfy the optimal tuning condition equation, it is possible to design a vibration damping device 18 that tunes to the building main body 1a. In this embodiment, the building 1 has multiple floors, and the mathematical model of the building 1 is a model of a multi-mass system, so that applying this to the equivalent condensed model 35 requires the use of a modal analysis technique. That is, an eigenvalue analysis is performed on the mathematical model of the multi-mass system that represents the building main body 1a, and the effective mass and effective stiffness of the main modes are found, and these effective masses and effective stiffnesses are calculated by multiplying the mass m of the mass point 38 in the one-degree-of-freedom system 36 of the equivalent condensed model 35. s and the spring constant k of spring 39 sBy doing so, the model of the multi-mass system can be fitted to the equivalent condensed model 35. The mathematical model is fitted to the equivalent condensed model 35 by regarding the part of the building body 1a that is the target of vibration control by the vibration damping device 18 as corresponding to a single degree of freedom system 36, the inertial mass damper 25 as corresponding to a damper 41 of a tuning system 37, and the single spring 34 representing the first long member 23 and the second long member 24 as corresponding to an additional spring 42.

[0055] Each parameter of the single degree of freedom system 36 is known, and the displacement, velocity, and acceleration are set according to the magnitude of the assumed earthquake. Therefore, the inertial mass m of the damper 41 (inertial mass damper 25) eq Once this is determined, the optimum spring constant k of the additional spring 42 (first elongated member 23 and second elongated member 24) can be calculated using the above optimum tuning condition equation. eq (k b ), the optimum damping coefficient c of the damper 41 (inertial mass damper 25) eq (c d ) is obtained. The spring constant k of the additional spring 42 is eq Determine the optimal inertia mass m of the damper 41. eq and the damping coefficient c eq may be required.

[0056] The effects of this embodiment will be described with reference to Figures 1 to 6. The oscillation vibration damping device 18 is a mechanism that concentrates deformation of the building 1 onto the seesaw member 21 to absorb energy, and the introduction of the synchronization effect increases the energy absorption capacity of the oscillation vibration damping device 18.

[0057] Instead of providing a new spring as the additional spring 42 for tuning, the first and second elongated members 23, 24 that exist as components of the oscillation vibration damping device 18 are used, resulting in a rational design.

[0058] In conventional vibration damping systems, the slender and soft axial force members (corresponding to the first and second long members 23, 24) reduce the effective movement of the damper, reducing the energy absorption capacity of the damper. However, in this embodiment, the softness of the first and second long members 23, 24 makes it possible to obtain a tuning effect, improving the energy absorption capacity of the inertial mass damper 25. In this way, by utilizing the first and second long members 23, 24, which were considered weaknesses in conventional technology, as advantages, a more rational design is possible.

[0059] The oscillation vibration damping device 18 can be placed in a space such as the meter box 15, minimizing the impact on the design plan.

[0060] In general, an inertial mass damper 25 has the characteristic of reducing the input energy to a structure whose vibration is to be controlled when it is installed on a member that contacts a fixed point (usually the ground in the case of a structure; a fulcrum that is assumed to have no displacement when the vibration control target is mathematically modeled). In this embodiment, the inertial mass damper 25 is installed on the first beam 10, which is the foundation beam, and the foundation beam can be considered part of a rigid member that contacts the ground G, which is the fixed point. Therefore, the inertial mass damper 25 installed on the first beam 10 reduces the input energy to the building body 1a during an earthquake, making it possible to slim down the building 1.

[0061] By applying tension to the first and second elongated members 23, 24, the stiffness (spring constant k b ) is low, buckling of the first and second long members 23, 24 can be prevented. [Example]

[0062] Next, we will explain the procedure for implementing optimal tuning in a multi-degree-of-freedom system model 31 using this design method, and an example of implementing optimal tuning using an equivalent reduced model 35. The procedure for optimal tuning involves reducing a multi-layer frame model to an equivalent one-mass system (single-degree-of-freedom system 36) as shown in Figure 5 based on the results of the first mode obtained by eigenvalue analysis, applying the optimal tuning condition equation to the one-mass system model, and finally obtaining the specifications of the rocking vibration control device 18 and inertial mass damper 25 shown in Figure 3.

[0063] The vibration damping devices 18 installed from the n'th floor to the nth floor are related to their installation position (height) when they are converted into the equivalent reduced model 35 shown in Fig. 5, so a coefficient is required to correct for the deformation and load that occurs in the mechanism in order to take into account the effect of the installation position (height). If the change in the first-order eigenmode shape due to the installation of the vibration damping devices 18 is ignored, the correction coefficient can be obtained by the following equation.

number

number

[0064] The acceleration of the earthquake motion input from the ground G to Building 1 is u ·· g (In the equation below, the two dots are written directly above the letter "u"), then the equation of motion of the equivalent reduced model 35 is expressed as follows:

number

[0065] The specifications of the vibration damping device 18 that satisfies the optimum tuning conditions were determined using the above procedure, and the results are shown in Figure 7. The frame 12 in question is a three-story steel structure, with a natural period of the first mode of 0.35 seconds, a damping constant of 1.1%, and μ eq This is an example where the vibration damping devices 18 are installed on the second and third floors from the surface of the ground G, assuming that the coefficient of vibration damping is 0.10. Figure 7 shows the magnification of the response displacement of each floor relative to the displacement input to the ground G (Figure 7(A): Example where the vibration damping device 18 is installed on the second floor, Figure 7(B): Example where the vibration damping device 18 is installed on the third floor). In this case, the frequency ratio β is 1.13, and the damping constant h d is 21.0%, which is the same value for the second and third floor installations. d are equal because μ in the equivalent reduced model 35 eq This is because the same values ​​were assumed.

[0066] The equivalent condensed model 35 is able to reproduce the displacement response magnification of the multi-degree-of-freedom model 31 in which the oscillation vibration damping device 18 is installed, and because the peaks of the displacement response magnification are aligned to roughly the same height, it can be confirmed that the equivalent condensed model 35 is able to achieve the optimal tuning conditions of the multi-degree-of-freedom model 31. From the above, it can be seen that by applying the optimal tuning condition equations to the equivalent condensed model 35, the specifications of the first and second long members 23, 24 and the inertial mass damper 25 of the oscillation vibration damping device 18 in the multi-degree-of-freedom model 31 can be obtained.

[0067] Although the description of specific embodiments has been completed above, the present invention is not limited to the above-described embodiments and modifications, and can be implemented in a wide variety of modifications. The present invention may be applied not only to newly constructed buildings, but also to cases where a rocking vibration damping device is installed in the main body of an existing building. The seesaw member and one end of the first and second elongated members may be attached to a pillar rather than a beam. The present invention may also be used to suppress vibrations other than earthquakes, such as vibrations caused by wind or machinery. As long as the members to which the rocking vibration damping device is attached (members corresponding to the first and second beams) are arranged parallel to each other and displace while maintaining their parallel state when vibrations are transmitted, the present invention may also be applied to structures other than buildings. For example, the present invention may be applied to a structure having a floor seismic isolation mechanism for protecting precision machinery from vibrations caused by other machinery. [Explanation of symbols]

[0068] 1: Buildings (structures) 1a: Building body (structure body) 10: First beam (first member) 11: Second beam (second member) 18: Vibration damping device 21: Seesaw member 23:First long material 24:Second long material 25: Inertial mass damper 31: Multi-degree of freedom system model 34: Spring (model of first and second long members) 35: Equivalent reduced model 36: One degree of freedom system 37: Synchronization System 41: Damper 42: Additional spring

Claims

1. A method for designing one or more vibration damping devices to be installed on a structure body, comprising: the structure main body includes, for each of the oscillation vibration damping devices, a first member extending in a predetermined direction and a second member extending in the predetermined direction and spaced apart from the first member in a spacing direction perpendicular to the predetermined direction, and is configured such that when vibration is transmitted to one of the first member and the second member, the first member and the second member are displaced while maintaining a state in which they are parallel to each other; Each of the oscillation vibration damping devices comprises: a seesaw member attached to the first member so as to be rotatable about an axial direction perpendicular to the predetermined direction and the separating direction; a first elongated member and a second elongated member arranged to intersect each other along a plane including the predetermined direction and the separation direction, wherein one end of each of the first elongated member and the second elongated member is joined to opposite ends of the seesaw member so as to be rotatable around the axial direction, and the other end of each of the first elongated member and the second elongated member is joined to the second member so as to be rotatable around the axial direction; an inertial mass damper attached to the first member at one end and to the seesaw member at the other end to suppress rotation of the seesaw member about the axial direction; The design method includes: a step of representing, for each of the rocking vibration damping devices, the rocking vibration damping device and a portion of the structure main body that is to be damped by the rocking vibration damping device using a mathematical model including mass, damping, and rigidity as elements, in which the first elongated member and the second elongated member are represented in the mathematical model as a single spring having rigidity and arranged in series with the inertial mass damper; a step of fitting the mathematical model to an equivalent condensed model including a one-degree-of-freedom system including a mass point, a spring, and a dashpot, and a tuning system in which an additional spring is connected in series to a damper and is arranged in parallel to the spring and the dashpot of the one-degree-of-freedom system, wherein the part of the main body of the structure that is to be damped by the oscillation vibration damping device corresponds to the one-degree-of-freedom system, the inertial mass damper corresponds to the damper of the tuning system, and one of the springs representing the first elongated member and the second elongated member corresponds to the additional spring; A design method including a step of setting parameters of the inertial mass damper and the first and second elongated members so as to satisfy an optimal tuning condition equation, which is a relationship equation between the parameters of the single-degree-of-freedom system and the tuning system.

2. The structure body is a building body, the first member and the second member are beam members, the building main body includes a column member supporting the beam member, The design method according to claim 1 , wherein the sway vibration damping device is installed in a beam-column frame including the beam member and the column member.

3. The building body includes a plurality of stories, The design method according to claim 2 , wherein the oscillation vibration damping device is arranged across two or more of the stories.

4. The step of representing the building body using a mathematical model includes representing the building body using a multi-degree-of-freedom system model, 4. The design method according to claim 3, wherein the step of fitting the mathematical model includes performing an eigenvalue analysis of the mathematical model to determine an effective mass and an effective stiffness of a principal mode, and setting the effective mass and the effective stiffness as the mass and the stiffness of the single-degree-of-freedom system in the equivalent reduced model.

5. The equivalent reduced model has the relationship shown in the following equation: [Equation 1] The optimum tuning condition formula is expressed by the following formula: [Equation 2] b ｏｐｔ =ω ｄ / oh ｓ μ = m ｅｑ / m ｓ c ｅｑ / m ｅｑ =2h ｄ ｏｐｔ ・ω ｄ oh ｓ ２ =a ｓ / m ｓ oh ｄ ２ =a ｅｑ / m ｅｑ Here, m ｓ denotes the mass of the mass point of the single degree of freedom system, u ｓ denotes the displacement of the single degree of freedom system, c ｓ denotes the damping coefficient of the dashpot of the single degree of freedom system, k ｓ represents the spring constant of the spring of the single degree of freedom system, u ｇ indicates the displacement of the ground on which the building body is installed, m ｅｑ denotes the inertial mass of the damper of the equivalent reduced model, u ｄ denotes the displacement of the damper of the equivalent reduced model, c ｅｑ denotes the damping coefficient of the damper of the equivalent reduced model, k ｅｑ represents the spring constant of the additional spring of the equivalent reduced model, u ｂ denotes the displacement of the additional spring of the equivalent reduced model, 5. The design method according to claim 4, wherein the displacement is expressed as a derivative with respect to time using Newton's notation.

6. The design method of claim 2 , wherein at least one of the first members is a foundation beam.

7. A design method described in any one of claims 1 to 5, wherein a tension force exceeding a compressive force applied to the first elongated member and the second elongated member is introduced into the first elongated member and the second elongated member when vibration is transmitted to the main body of the structure.

8. A structure comprising a structure body and one or more vibration damping devices installed on the structure body, the structure main body includes, for each of the oscillation vibration damping devices, a first member extending in a predetermined direction and a second member extending in the predetermined direction and spaced apart from the first member in a spacing direction perpendicular to the predetermined direction, and is configured such that when vibration is transmitted to one of the first member and the second member, the first member and the second member are displaced while maintaining a state in which they are parallel to each other; Each of the oscillation vibration damping devices comprises: a seesaw member attached to the first member so as to be rotatable about an axial direction perpendicular to the predetermined direction and the separating direction; a first elongated member and a second elongated member arranged to intersect each other along a plane including the predetermined direction and the separation direction, wherein one end of each of the first elongated member and the second elongated member is joined to opposite ends of the seesaw member so as to be rotatable around the axial direction, and the other end of each of the first elongated member and the second elongated member is joined to the second member so as to be rotatable around the axial direction; an inertial mass damper attached between the seesaw member and the first member to suppress rotation of the seesaw member about the axial direction; For each of the sway vibration damping devices, the sway vibration damping device and a portion of the structure main body that is to be damped by the sway vibration damping device are represented by a mathematical model that includes mass, damping, and rigidity as elements, and that represents the first elongated member and the second elongated member as one spring arranged in series with the inertial mass damper, and the sway vibration damping device in the structure main body is represented by an equivalent condensed model that includes a one-degree-of-freedom system and a tuning system that includes a damper and an additional spring connected in series to the damper. a structure configured such that when the mathematical model is applied assuming that the part to be damped corresponds to the single-degree-of-freedom system, the inertial mass damper corresponds to the damper of the tuning system, and one of the springs representing the first long member and the second long member corresponds to the additional spring, the damping coefficient and inertial mass of the inertial mass damper and the spring constant of the spring representing the first long member and the second long member satisfy the optimal tuning condition equation of the equivalent condensed model.

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