JP2016089533A - Vibration damping system for structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a vibration damping system for a structure, which can sufficiently absorb primary-mode vibrations of the structure with an additional vibration system by increasing inter-story displacements caused by the primary-mode vibrations of the structure transmitted to a second mass damper, and can therefore appropriately suppress the vibrations of the structure.SOLUTION: A first mass dampers 2 arranged in multiple stories of a structure B include first inertial-mass elements 14 for suppressing vibrations of the structure B in a predetermined vibration mode of the secondary or higher order. Second mass dampers 32L,32R include second inertial-mass elements 32c and viscosity damping element 32g, and are connected to the uppermost one of the multiple stories via transmission members 31L,31R and to the lowermost story such that the second mass dampers 32L,32R and the transmission members 31L,31R constitute an additional vibration system 3. The stiffness of the transmission members 31L,31R, the mass of the second inertial-mass elements 32c, and the damping coefficients of the viscosity damping elements 32g are set such that the natural frequency of the additional vibration system 3 synchronizes with the primary natural frequency of the structure B.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a vibration suppressing device for a structure that suppresses vibration of a structure having a plurality of layers.

  Conventionally, for example, a device disclosed in Patent Document 1 is known as a vibration suppressing device for this type of structure. This vibration suppression device is applied to a high-rise building, and includes an additional vibration system provided on each of the third and fourth floors of the building, and a vibration isolation provided on each of the first and second floors of the building. It has a mechanism. The additional vibration system is a mass damper and an additional spring connected in series with each other. The mass of the mass damper and the rigidity of the additional spring are such that the natural frequency of the additional vibration system is synchronized with the primary natural frequency of the building. Is set. In addition, the vibration isolation mechanism is configured by a mass damper, and the mass of the mass damper is set so as not to be transmitted to the upper layer by blocking the vibration of a predetermined vibration mode of the building.

Patent No. 5316849

  As described above, in the conventional vibration suppression device, the vibration isolation mechanism is provided in a layer different from that of the additional vibration system, and the vibration isolation mechanism only interrupts the vibration in a predetermined vibration mode of the building. The displacement due to the vibration of the primary mode of the building transmitted to the mass damper of the vibration system cannot be increased. As a result, the vibration energy of the primary mode of the building cannot be sufficiently absorbed by the additional vibration system, and as a result, the vibration of the building cannot be appropriately suppressed.

  The present invention has been made to solve the above-described problems, and by increasing the interlayer displacement due to the vibration of the primary mode of the structure transmitted to the second mass damper, the primary mode of the structure is improved. It is an object of the present invention to provide a vibration suppressing device for a structure that can sufficiently absorb the vibration of the structure with an additional vibration system, and thus can appropriately suppress the vibration of the structure.

  In order to achieve the above object, the invention according to claim 1 is a structure vibration suppressing device for suppressing vibration of a structure having a plurality of layers, and is a predetermined vibration mode of a second or higher order of the structure. And a first mass damper that is provided in a plurality of layers and in which the first inertial mass element moves in accordance with the vibration of the structure, has elasticity, and has a plurality of A transmission member coupled to one of the uppermost layer and the lowermost layer of the layers, a second inertial mass element and a viscous damping element for suppressing vibration of the structure, and the uppermost layer and A second mass damper connected to the other of the lowest layer and the transmission member to form an additional vibration system together with the transmission member, and to move the second inertial mass element in accordance with the vibration of the structure. Of stiffness, mass of second inertial mass element and damping factor of viscous damping element Is the natural frequency of the additional vibration system to tune to the primary natural frequency of the structure, characterized in that it is set.

  According to this configuration, the first mass damper provided in the plurality of layers of the structure has the first inertial mass element for suppressing the vibration in the predetermined vibration mode of the second or higher order of the structure, The first inertial mass element moves with the vibration of the structure. Thereby, the vibration of the predetermined vibration mode of the structure can be suppressed by obtaining the inertial mass effect by the first inertial mass element during the vibration of the structure.

  Further, the second mass damper has a second inertial mass element and a viscous damping element for suppressing vibration of the structure, and the uppermost layer and the lowermost layer (hereinafter, respectively) of the plurality of layers. One of “the uppermost layer” and “the lowermost layer”) via a transmission member and connected to the other of the uppermost layer and the lowermost layer. Further, an additional vibration system is configured by the transmission member and the second mass damper, and the second inertial mass element moves in accordance with the vibration of the structure. Further, the rigidity of the transmission member, the mass of the second inertial mass element, and the damping coefficient of the viscous damping element are set so that the natural frequency of the additional vibration system is synchronized with the primary natural frequency of the structure. With the above configuration, when the structure vibrates, the inertial mass effect by the second inertial mass element and the viscous damping effect by the viscous damping element are obtained, and the vibration of the primary mode of the structure is absorbed by the additional vibration system.

  In this case, since the second mass damper is connected to the uppermost layer and the lowermost layer, the primary mode of the structure transmitted to the second mass damper is compared with the case where the second mass damper is connected to one layer. It is possible to increase the inter-layer displacement (hereinafter referred to as “mass damper transmission inter-layer displacement”) due to the vibration of. Although the details will be described later, by providing the first mass damper described above in a plurality of layers, the interlayer displacement between the uppermost layer and the lowermost layer due to the vibration of the primary mode is increased, and the mass damper transmission interlayer displacement is reduced. It can be further increased. As described above, since a larger inertial mass effect is obtained by the second inertial mass element, the vibration of the primary mode of the structure can be sufficiently absorbed by the additional vibration system. As described above, according to the present invention, since the vibration damping effect by the first mass damper and the additional vibration system can be obtained synergistically, the vibration of the structure can be appropriately suppressed.

  According to a second aspect of the present invention, in the vibration suppressing device for a structure according to the first aspect, the first mass damper includes a plurality of mass dampers and is provided in each of the plurality of layers.

  According to this configuration, since the first mass damper is provided in each of the plurality of layers, the vibration of the structure can be more appropriately suppressed.

It is a model figure which shows the vibration suppression apparatus by this embodiment with the building to which this is applied. It is a figure which shows the 1st mass damper and the lower part of a building roughly. It is a figure which shows the 2nd mass damper and the lower part of a building roughly. It is sectional drawing which shows a 1st mass damper. It is sectional drawing which shows a part of 2nd mass damper. It is a table | surface which shows the specification data of a building. It is a table | surface which shows the eigenvector of the primary mode of the building in which only the 1st mass damper was provided (the additional vibration system is not provided). It is a figure which shows an example of the relationship between the frequency of a building in which the vibration suppression apparatus (1st mass damper and additional vibration system) by this embodiment was provided, and response magnification. It is a figure which shows an example of the relationship between the vibration frequency of a building in which the vibration suppression apparatus (only 1st mass damper) by the comparative example was provided, and response magnification. It is a table | surface which shows the eigenvector of the primary mode of only the building in which the vibration suppression apparatus (1st mass damper and additional vibration system) by this embodiment is not provided.

  Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 shows a vibration suppressing device 1 according to the present embodiment together with a building B to which the vibration suppressing device 1 is applied. The building B is a high-rise building erected on the foundation F. As shown in FIG. 3, the left and right columns PL and PR extending vertically in parallel to each other and a plurality of beams extending horizontally in the left and right directions parallel to each other It has a cross-beam shaped ramen structure in which BU, BM1, BM2, and BD (only four are shown in FIG. 3) are joined together. Hereinafter, the four beams BU, BM1, BM2, and BD shown in FIG. 3 are referred to as “upper beam BU”, “first intermediate beam BM1”, “second intermediate beam BM2”, and “lower beam BD”, respectively.

  The left and right columns PL and PR, and the upper and lower beams BU and BD are all made of H-section steel. Note that the left and right columns PL and PR, and the upper and lower beams BU and BD may be formed of square steel pipes or the like. Further, the first and second intermediate beams BM1 and BM2 are formed of a pair of beams facing each other in the front-rear direction, similar to that disclosed in Japanese Patent No. 5314201 by the applicant of the present invention. The detailed explanation is omitted.

  As shown in FIGS. 1 to 3, the vibration suppression device 1 includes a first mass damper 2 provided in each of a plurality of layers (hereinafter referred to as “vibration suppression control layer”) constituting a lower portion of a building B, and a vibration suppression device. An additional vibration system 3 provided in the control layer is provided. 1 to 3 show examples in which three, four, and five layers are used as the vibration suppression control layer. The left and right columns PL, PR, the upper beam BU, and the first intermediate beam BM1 are used. A five-layer space is defined, and a four-layer space is formed by the left and right columns PL, PR, the first intermediate beam BM1 and the second intermediate beam BM2, and the left and right columns PL, PR, the second intermediate beam BM2 and the bottom. A three-layer space is defined by the side beam BD. The number of layers constituting the vibration suppression control layer is not limited to three as long as it is plural, and any other appropriate number can be adopted, and all layers of the building can be used as the vibration suppression control layer. It may be used as In the present embodiment, a plurality of layers below the building B are used as the vibration suppression control layer, but a plurality of layers above the building may be used, or a plurality of layers at the center of the building may be used. May be used.

  Since each first mass damper 2 is configured in the same manner as the mass damper described in FIG. 3 of Japanese Patent No. 5314201 by the applicant, the configuration and operation will be briefly described below. As shown in FIG. 4, the first mass damper 2 has an inner cylinder 12, a ball screw 13, a rotating mass 14, and a limiting mechanism 15. The inner cylinder 12 is made of a cylindrical steel material. One end of the inner cylinder 12 is open, and the other end is attached to the first flange 16 via a universal joint.

  The ball screw 13 has a screw shaft 13a and a nut 13c that is rotatably engaged with the screw shaft 13a via a large number of balls 13b. One end of the screw shaft 13a is accommodated in the opening of the inner cylinder 12 described above, and the other end of the screw shaft 13a is attached to the second flange 17 via a universal joint. The nut 13 c is rotatably supported by the inner cylinder 12 via a bearing 18.

  The rotary mass 14 is made of a material having a large specific gravity, for example, iron, and is formed in a cylindrical shape. The rotating mass 14 covers the inner cylinder 12 and the ball screw 13 and is rotatably supported by the inner cylinder 12 via a bearing 19. Note that unlike the mass damper described in FIG. 3 of Japanese Patent No. 5314201, a viscous body is not provided between the rotary mass 14 and the inner cylinder 12.

  In the first mass damper 2 configured as described above, when a relative displacement occurs between the inner cylinder 12 and the screw shaft 13a, the limiting mechanism 15 is operated in a state where the relative displacement is converted into a rotational motion by the ball screw 13. The rotation mass 14 is rotated by being transmitted to the rotation mass 14.

  The limiting mechanism 15 includes a ring-shaped rotary sliding material 15a, a plurality of screws 15b, and springs 15c (only two are shown). The rotary mass 14 rotates integrally with the nut 13c until the load acting in the axial direction of the first mass damper 2 (hereinafter referred to as “axial load”) reaches a limit load determined according to the tightening degree of the screw 15b. . On the other hand, when the axial load of the first mass damper 2 reaches the limit load, slip occurs between the rotary sliding material 15a and the nut 13c or the rotary mass 14.

  FIG. 2 shows the first mass damper 2 provided in five of the vibration suppression control layers. As shown in FIG. 2, the first flange 16 of the first mass damper 2 includes a connecting steel pipe 20. Are attached to the first connecting member EN1 fixed to the joint between the upper beam BU and the right column PR, and the second flange 17 is connected to the junction between the first intermediate beam BM1 and the left column PL. It is attached to the fixed second connecting member EN2. Accordingly, the first mass damper 2 is obliquely connected to the upper beam BU and the first intermediate beam BM1 in a brace shape.

  Although not shown, the first mass damper 2 provided in the four layers of the vibration suppression control layer is provided in the first intermediate beam BM1 and the second intermediate beam BM2 (see FIG. 3) in the third layer. The one mass damper 2 is obliquely connected to the second intermediate beam BM2 and the lower beam BD in a brace shape in the same manner as the first mass damper 2 provided in the five layers described above.

  Next, a method for setting the additional mass md of the rotating mass 14 of the first mass damper 2 of each layer (apparent mass amplified by the rotating inertia effect of the rotating mass 14) will be described in detail. First, the vibration mode of the building B controlled by the first mass damper 2 of each layer (hereinafter referred to as “target vibration mode”) is set. In this case, the target vibration mode is set to a predetermined vibration mode of secondary or higher. Specifically, the vibration mode having a larger order has a smaller influence degree, and therefore, the vibration mode is set to a predetermined vibration mode having a relatively small order such as a second order or a third order.

  Next, eigenvalue analysis of the building B is performed to calculate the natural circular frequency ω (j) of the building B in the set target vibration mode (procedure 1). Here, the subscript j represents the order of the target vibration mode and is an integer of 2 or more.

Next, the additional mass md (n) of the rotating mass 14 is calculated by the following equation (1) using the calculated natural circular frequency ω (j) and the corresponding layer stiffness k (n) (procedure) 2). Here, the subscript n represents the number of layers (the number of floors), and is one of 3 to 5 in this embodiment.
md (n) = k (n) / ω (j) ² (1)

When the orders of the set target vibration modes are different from each other, the above procedure 2 may be performed for each of the vibration suppression control layers. For example, when the target vibration modes of the third layer, the fourth layer, and the fifth layer of the vibration suppression control layer are set to the second order mode, the third order mode, and the fourth order mode, the addition of the three-layer rotating mass 14 The mass md (3) is md (3) = k (3) / ω (2) ² , and the additional mass md (4) of the four-layer rotating mass 14 is md (4) = k (4) / ω. (3) ² Further, the additional mass md (5) of the five layers of the rotating mass 14 is md (5) = k (5) / ω (4) ² .

  On the other hand, when at least two orders of the set target vibration modes are the same (hereinafter, the plurality of target vibration modes having the same order are referred to as “same order target vibration modes”), first, The additional mass md (n) of the rotating mass 14 corresponding to a plurality of target vibration modes having different orders is set to any one additional mass md (n) of the plurality of rotating masses 14 corresponding to the same order target vibration mode. And calculate according to procedure 2.

  Next, the eigenvalue analysis of the building B provided with the first mass dampers 2 of the plurality of calculated additional masses md (n) is performed again, thereby calculating the natural circular frequency ω (j) in the homogeneous order target vibration mode. (Procedure 3). Next, by using the newly calculated natural circular frequency ω (j), the additional mass md (n (n)) of the plurality of rotating masses 14 corresponding to the same-order target vibration mode is performed by the procedure 2 described above. ) Is calculated (procedure 4). The above procedures 3 and 4 are repeated until all the additional masses md (n) of the plurality of rotating masses 14 corresponding to the same-order target vibration mode are calculated.

  As described above, when at least two orders of the plurality of target vibration modes are the same, the additional mass md () is considered in consideration of the influence of the first mass damper 2 on the natural circular frequency ω (j) of the building B. n) is calculated.

  Even when the orders of the plurality of target vibration modes are different from each other, the first mass damper 2 takes into account the influence on the natural circular frequency ω (j) of the building B by the first mass damper 2 as in the procedures 3 and 4. The additional mass md (n) of the mass damper 2 may be calculated.

  With the above configuration, in the vibration suppression device 1, when the building B vibrates, the interlayer displacement of each layer accompanying the vibration is transmitted to the first mass damper 2, so that the rotating mass 14 rotates. By obtaining the inertial mass effect, the vibration of the predetermined target vibration mode of the secondary or higher of the building B is suppressed.

  The additional vibration system 3 is basically configured in the same manner as the additional vibration system disclosed in Japanese Patent No. 5314201 by the applicant of the present invention, and the configuration and operation thereof will be briefly described below. As shown in FIG. 3, the additional vibration system 3 includes left and right transmission members 31L and 31R and second mass dampers 32L and 32R. 31 L of left transmission members are comprised with the pillar material which consists of H-shaped steel, The upper end part is connected via the 1st connection member en1 to the junction part of the left pillar PL and the upper beam BU. The left transmission member 31L extends obliquely from the first connecting member en1 toward the lower beam BD, and penetrates the first and second intermediate beams BM1 and BM2 in the vertical direction.

  The right transmission member 31R is composed of a pillar material made of H-shaped steel like the left transmission member 31L, and its upper end is connected to the joint between the right pillar PR and the upper beam BU via the second connecting member en2. It is connected. Further, the right transmission member 31R extends obliquely from the second coupling member en2 toward the lower beam BD, and penetrates the first and second intermediate beams BM1 and BM2 in the vertical direction. In addition, the left and right transmission members 31L and 31R are connected to each other at the lower ends thereof via the first connecting member 33, and are V-shaped symmetrically about the vertical line extending from the first connecting member 33. Has been placed.

  A second connecting member 34 is attached to the lower surface of the first connecting member 33, and a guide mechanism is provided between the second connecting member 34 and the lower beam BD. The configuration of the guide mechanism is described in Japanese Patent No. 5314201 by the present applicant, and thus detailed description thereof is omitted.

  Each of the left and right second mass dampers 32L and 32R is configured basically in the same manner as the first mass damper 2 described above, and includes an inner cylinder 32a, a ball screw 32b, a rotary mass 32c, a limiting mechanism (not shown), a first and a second Compared with the first mass damper 2, the second flange 32d and 32e are provided, and the only difference is that they further include a pair of seals 32f and 32f and a viscous body 32g shown in FIG. As shown in FIG. 5, the seals 32f and 32f are formed in a ring shape, and are provided between the inner cylinder 32a and the rotary mass 32c. The viscous body 32g is made of silicon oil, and fills a space defined by the inner cylinder 32a, the rotary mass 32c, and the seals 32f and 32f. In each of the second mass dampers 32L (32R), when a relative displacement is generated between the screw shafts of the inner cylinder 32a and the ball screw 32b, the relative displacement is converted into a rotational motion by the ball screw 32b via a limiting mechanism. The rotation mass 32c is rotated by being transmitted to the rotation mass 32c.

  The first flange 32d of the left second mass damper 32L is attached to a fixture 35 provided integrally with the left end portion of the lower beam BD, whereby the second mass damper 32L is connected to the lower beam BD. Has been. In addition, the second flange 32e of the second mass damper 32L is attached to the left side surface of the second connecting member 34, whereby the second mass damper 32L is connected to the left and right transmission members 31L and 31R. The second mass damper 32L is allowed to rotate only with respect to the second connecting member 34 and the fixture 35 about the axis extending in the front-rear direction by the universal joint of the first and second flanges 32d and 32e.

  The first flange 32d of the second mass damper 32R on the right side is attached to a fixture 36 that is integrally provided at the right end of the lower beam BD, whereby the second mass damper 32R is connected to the lower beam BD. Has been. Further, the second flange 32e of the second mass damper 32R is attached to the right side surface of the second connecting member 34, whereby the second mass damper 32R is connected to the left and right transmission members 31L and 31R. As described above, the left and right second mass dampers 32 </ b> L and 32 </ b> R are provided symmetrically with respect to each other about the second connecting member 34. The second mass damper 32R is only allowed to rotate with respect to the second connecting member 34 and the attachment 36 about the axis extending in the front-rear direction by the universal joint of the first and second flanges 32d, 32e.

  As described above, the second mass dampers 32L and 32R are connected to the upper beam BU, that is, the uppermost layer (hereinafter referred to as the “uppermost layer”) of the vibration suppression control layers via the transmission members 31L and 31R. At the same time, it is connected to the lower beam BD, that is, the lowest layer of the vibration suppression control layer (hereinafter referred to as the “lowermost layer”). In the embodiment, the pair of left and right second mass dampers 32L and 32R are used, but one of the both 32L and 32R may be omitted.

  Next, the specifications of the additional vibration system 3, that is, the rigidity of the left and right transmission members 31L and 31R (hereinafter referred to as “transmission member rigidity”) kbt, the additional mass mdt of the rotating mass 32c of the second mass dampers 32L and 32R, the viscosity A method for setting the attenuation coefficient cdt of the body 32g will be described in detail. The specifications of the additional vibration system 3 are such that the natural frequency is tuned to the primary natural frequency of the building B provided in each of the vibration suppression control layers by the first mass damper 2, and the peak of the response magnification curve is obtained by optimal damping. Is set to minimize. Here, the optimum tuning conditions are those calculated based on the fixed point theory.

ここで、ｍ（ｎ）は、建物Ｂの各層の質量であり、Ｌは建物Ｂの層の総数（質点数）である。 First, the first mass damper 2 performs the eigenvalue analysis of the building B provided in each of the vibration suppression control layers, thereby calculating the first natural circular frequency ω (1) and the first mode eigenvector ₁ u (n). To do. The eigenvector ₁ u (n) of the primary mode is calculated for all the layers of the building B. Next, using the calculated eigenvector ₁ u (n) of the first-order mode, the broad-sense node mass of the first-order mode of the building B (the first-order mode of the building B is expressed as a one-mass system analysis model by the following equation (2). ₁ M ₀ is calculated, hereinafter referred to as “the first mode broad-sense node mass of the building”.

Here, m (n) is the mass of each layer of the building B, and L is the total number (mass score) of the layers of the building B.

  Next, the additional mass mdt of the rotating mass 32c of the second mass dampers 32L and 32R is set. In this case, the additional mass mdt is set to an arbitrary value such that a mass ratio μ described later is smaller than 0.25, and is set to a relatively large value in order to obtain a large inertial mass effect of the rotating mass 32c. Is preferred.

Next, using the set additional mass mdt and the eigenvector ₁ u (n) of the primary mode that is the control target mode of the additional vibration system 3, the primary mode of the additional vibration system 3 is broadly defined by the following equation (3). The additional mass of the rotating mass 32c (hereinafter referred to as “additional vibration system primary mode broad additional mass”) ₁ Mdt is calculated.
₁ Mdt = { ₁ u (x) ₋₁ u (y−1)} ² mdt (3)
Here, x is the number of layers in the uppermost layer (the highest layer among the vibration suppression control layers) (5 in this embodiment), and y is the lowest layer (the highest layer among the vibration suppression control layers). The number of layers (lower layer) (3 in this embodiment). That is, ₁ u (x) _-1 u (y-1) is ₁ u (5) _-1 u (2) in the present embodiment, and the eigenvectors ₁ u (5) and 1 It represents the difference between the two layers of eigenvectors ₁ u (2) in the next mode. Thus, from _one to the ground of the primary mode vibration system is a relative deformation difference up to five layers _{u (5), 1 u (} 2) the relative deformation difference between the ground of the primary mode vibration system to the two layers By subtracting, the relative deformation difference from the 3rd layer to the 5th layer of the primary mode vibration system is obtained.

Next, the mass ratio μ is calculated by dividing the primary mode broad-sense added mass ₁ Mdt of the additional vibration system by the calculated primary mode broad-sense node mass ₁ M ₀ of the building ( ₁ Mdt / ₁ M ₀ ). .

ここで、ωｄｔは付加振動系３の固有円振動数である。また、ω（１）は、前述したように、第１マスダンパ２が設けられた建物Ｂの１次固有円振動数であり、このことは、後述する式（６）及び（７）についても同様である。 Next, the optimal tuning frequency ratio optγ is calculated by the following equation (4) using the calculated mass ratio μ. This equation (4) is derived using the soft spring solution of the displacement response magnification optimum adjustment condition solution. For details, see “Displacement control design of buildings Norio Inoue / Yukiko Isuko”. Please refer.

Here, ωdt is the natural circular frequency of the additional vibration system 3. Further, ω (1) is the primary natural circular frequency of the building B in which the first mass damper 2 is provided as described above, and this also applies to the expressions (6) and (7) described later. It is.

Next, using the mass ratio μ, the optimum damping constant optthd of the viscous body 32g is calculated by the following equation (5). This equation (5) is also derived using the soft spring solution of the displacement response magnification optimum adjustment condition solution, similarly to the above equation (4).

Next, the transmission member rigidity kbt is calculated by the following equation (6) using the calculated optimum tuning frequency ratio optγ, the primary natural circular frequency ω (1) of the building B, and the additional mass mdt.
kbt = ω (1) ² · optγ ² · mdt (6)
This equation (6) is derived from ωdt ² = kbt / mdt and equation (4).

Next, using the calculated optimum damping constant opthd, the primary natural circular frequency ω (1) of the building B, the optimum tuning frequency ratio optγ, and the additional mass mdt, the following equation (7) is used to calculate the viscosity of the viscous body 32g. An attenuation coefficient cdt is calculated.
cdt = 2 · opthd · ω (1) · optγ · mdt (7)
This equation (7) is derived from cdt / mdt = 2 · optth · ωdt and equation (4).

  With the above configuration, in the vibration suppression device 1, when the building B vibrates, the interlayer displacement between the uppermost layer and the lowermost layer accompanying the vibration is transferred to the second mass dampers 32 </ b> L and 32 </ b> R via the left and right transmission members 31 </ b> L and 31 </ b> R. By being transmitted, the rotary mass 32c rotates. Thus, an inertial mass effect by the rotating mass 32c and a viscous damping effect by the viscous body 32g are obtained, and the vibration of the primary mode of the building B is the additional vibration system 3 including the transmission members 31L and 31R and the second mass dampers 32L and 32R. Absorbed in.

  Next, a specific design example and characteristics of the vibration suppression device 1 will be described with reference to FIGS. FIG. 6 shows specification data of the building B, specifically, the number of layers of the building B, the mass m (n) of each layer: unit ton, and the stiffness k (n): unit kN / cm. As is clear from the above, the building B is a 20-story (floor) building. The first mass damper 2 provided in the lower layer tends to have a higher damping effect. Focusing on this point, the lower layer of the vibration suppression control layer, the lower order vibration mode is set as the target vibration mode. In this example, as described above, three to five layers are used as the vibration suppression control layer, and the target vibration mode of the third and fourth layers is set to the secondary mode, and the target vibration mode of the five layers is set to the tertiary mode. Set.

  In this case, the orders of the three-layer and four-layer target vibration modes are the same (same-order target vibration mode), and the orders of the five-layer target vibration modes are different from the orders of the three-layer and four-layer target vibration modes. ing. Therefore, according to the method for calculating the additional mass md (n) of the rotary mass 32c described above, first, the additional masses md (5) and md (4) of the five-layer and four-layer rotary mass 32c are calculated, and then 3 The additional mass md (3) of the rotating mass 32c of the layer was calculated.

  Specifically, first, since the orders of the target vibration modes of the 5th layer and the 4th layer are 3 and 2, respectively, vibration suppression according to the present embodiment used for calculating the additional masses md (5) and md (4), respectively. The third-order natural circular frequency ω (3) and the second-order natural circular frequency ω (2) of only the building B where no device is provided were calculated by performing eigenvalue analysis. As a result, ω (3) = 11.07921 (rad / s) and ω (2) = 6.82067 (rad / s).

Next, the calculated third-order natural circular frequency ω (3) and second-order natural circular frequency ω (2), and the rigidity k (5), k (4) of the fifth and fourth layers shown in FIG. In addition, the additional masses md (5) and md (4) of the five-layer and four-layer rotary masses 32c were calculated by the formula (1). As a result, md (5) = (18927.6 · 100) / (11.07921) ² = 15420 (ton) and md (4) = (19497.2 · 100) / (6.82067) ² = 41910 (ton).

  Next, eigenvalue analysis is performed on the building B in which the calculated first mass damper 2 of the additional mass md (5) is provided in five layers and the first mass damper 2 of the additional mass md (4) is provided in four layers. Thus, the secondary natural circular frequency ω (2) of the building B used for calculating the additional mass md (3) of the three-layer rotating mass 32c was calculated. As a result, ω (2) = 6.21847 (rad / s).

  As described above, the secondary natural circular frequency ω (2) is different between the case where the first mass damper 2 whose target vibration mode is the secondary mode is not provided (= 6.82067) and the case where it is provided (= 6.21847). It turns out that it becomes a different value.

Next, using the calculated secondary natural circular frequency ω (2) and the three-layer stiffness k (3) shown in FIG. 6, the additional mass md (3) of the three-layer rotating mass 32c is calculated according to the equation (1). Was calculated. As a result, md (3) = (22265.6 · 100) / (6.21847) ² = 57579 (ton).

Next, by performing eigenvalue analysis of the building B in which the first mass dampers 2-2 of the calculated additional masses md (3) to md (5) are respectively provided in the third to fifth layers, the primary of the building B The natural circular frequency ω (1) and the eigenvector ₁ u (n) of the primary mode of all layers were calculated. As a result, ω (1) = 2.41818 (rad / s) and ₁ u (n) was as shown in FIG.

Next, using the calculated eigenvector ₁ u (n) of the first-order mode and the mass m (n) of each layer of the building B shown in FIG. 6, the first-order mode broad-sense node mass ₁ M of the building is obtained by the above equation (2). ₀ was calculated. As a result, ₁ M ₀ = 12708.6.

Next, the additional mass mdt of the rotating mass 32c of the additional vibration system 3 was set to 24000 (ton) according to the above-described viewpoint. Further, in this example, the vibration suppression control layers are 3 to 5 layers. Therefore, the eigenvectors ₁ u (5) and ₁ u (2) of the first and second layers of the calculated first-order mode eigenvectors ₁ u (n) and the set additional mass mdt Using the above equation (3), the primary mode broad additional mass ₁ Mdt of the additional vibration system was calculated. As a result, ₁ Mdt = (0.2831−0.1047) ² 24000 = 763.8.

Next, when the mass ratio μ was calculated by dividing the calculated first-order mode broad-sense node mass ₁ M ₀ of the building by the first-order mode broad sense additional mass ₁ Mdt of the additional vibration system, μ = 763.8 / 12708.6 = 0.0601 became.

  Next, using the calculated mass ratio μ, the optimum tuning frequency ratio optγ and the optimum damping constant optthd were calculated by the above equations (4) and (5), respectively. As a result, optγ = 1.06864 and optd = 0.1552.

Next, the transmission member rigidity kbt was calculated by the above equation (6) using the calculated optimum tuning frequency ratio optγ, the primary natural circular frequency ω (1) of the building B, and the additional mass mdt. As a result, kbt = 2.51418 ² · 1.06864 ² · 24000 = 173247 (kN / m).

  Next, using the calculated optimal damping constant opthd, the optimal tuning frequency ratio optγ, the primary natural circular frequency ω (1) of the building B and the additional mass mdt, the damping coefficient cdt is calculated by the above equation (7). did. As a result, cdt = 2, 0.1552, 2.51418, 1.06864, 24000 = 20015 (kNs / m).

  In this example, the transmission member rigidity kbt is set to be higher in accordance with the mass ratio μ in order to improve the correction by applying the concentrated vibration suppression of the expressions (4) and (5) and the robustness. In this case, since the mass ratio μ is about 0.06, the transmission member rigidity kbt is multiplied by 1.25, and kbt = 173247 × 1.25 = 216558 (kNs / m). Of course, the transmission member rigidity kbt calculated by the equation (6) may be used as it is.

  FIG. 8 shows the relationship between the frequency (Hz) of the building B according to this example and the response magnification of the absolute coordinate system. FIG. 9 shows the frequency of the building B according to the comparative example and the response magnification of the absolute coordinate system. Shows the relationship. This comparative example is an example in which only the first mass damper 2 is provided in the vibration suppression control layer without providing the additional vibration system 3, and the conditions regarding the building B are the same as in this example. 8 and 9, the thick solid line indicates the relationship between the frequency (Hz) of building B in 5 layers and the response magnification, and the alternate long and short dash line, dashed line, and alternate long and two short dashes line indicate 10 layers, 15 layers, and The relationship between the frequency (Hz) of building B in 20 layers and the response magnification is shown. Further, in FIGS. 8 and 9, f1 is the primary natural frequency of only the building B where the vibration suppression device according to the present embodiment is not provided, and f2 and f3 are respectively provided with the vibration suppression device according to the present embodiment. These are the secondary natural frequency and the tertiary natural frequency of only the building B that is not provided.

  As apparent from the comparison between FIG. 8 and FIG. 9, according to this example, the vibration of the building B can be appropriately suppressed as a whole and the damping effect on the vibration of the primary mode as compared with the comparative example. Can be seen to be outstanding.

Further, regarding the present example, when the eigenvalue analysis of only the building B is performed in the state where the vibration suppression device according to the present embodiment is not provided, the eigenvector ₁ u ′ (n) of the first-order mode is as shown in FIG. Became. As shown in the figure, the eigenvector ₁ u ′ (5) of the 5-layer primary mode is 0.26624, and the eigenvector ₁ u ′ (2) of the 2-layer primary mode is 0.10631. On the other hand, as shown in FIG. 7, the first mass damper 2 has eigenvectors ₁ u (5), ₁ u (5) of the _first and fifth layers of the building B in which the first mass damper 2 is provided in the vibration suppression control layer. 2) are 0.2831 and 0.1047, respectively.

ここで、添え字_sはモードの次数であり、添え字（ｔ）は時間である。また、_sβは、刺激係数であり、地震加速度の分布ベクトルを固有モードに展開したときの係数に相当する。さらに、_sｑ₀（ｔ）は、建物Ｂの各次の固有振動であり、建物Ｂの各次の固有周期及び各次の減衰定数によって定まる。この式（８）の詳細については、「最新 耐震構造解析 柴田明徳著」を参照されたい。 As is clear from the above, the difference between the eigenvector ₁ u (5) of the five-layer primary mode and the eigenvector ₁ u (2) of the two-layer primary mode is that the first mass damper 2 is provided in the vibration suppression control layer. When it is, it is larger than when it is not provided. Here, from the modal analysis, as is the response of the building B {Y (t)}, between each subsequent eigenvectors _{s u}, the following equation (8) holds.

Here, the subscript _s is the order of the mode, and the subscript (t) is time. Further, _s β is a stimulation coefficient, and corresponds to a coefficient when the seismic acceleration distribution vector is expanded to the eigenmode. Furthermore, _s q ₀ (t) is the natural vibration of each order of the building B, and is determined by the natural period of each order of the building B and the damping constant of each order. For details on this equation (8), refer to “Latest Seismic Structural Analysis by Akinori Shibata”.

As shown in equation (8), the larger the s-order eigenvector { _s u} and the stimulation coefficient _s β of the building B, the greater the influence of the s-order mode on the response {Y (t)}. Is established. As is clear from this relationship, the difference between the eigenvector ₁ u (5) of the 5-layer primary mode and the eigenvector ₁ u (2) of the 2-layer primary mode is larger. This indicates that the interlayer displacement between the 5th layer and the 3rd layer due to the vibration of the primary mode is larger (soft layer effect). This also applies to the case where any other layer is used as the vibration suppression control layer. Therefore, by providing the first mass damper 2 in the vibration suppression control layer, the interlayer displacement between the uppermost layer and the lowermost layer due to the vibration of the primary mode of the building B can be increased.

  As described above, according to the present embodiment, the first mass damper 2 provided in the vibration suppression control layer composed of a plurality of layers of the building B suppresses vibrations in the predetermined target vibration mode of the secondary or higher of the building B. The rotating mass 14 is rotated with the vibration of the building B. Thereby, the vibration of the object vibration mode of the building B can be suppressed by obtaining the inertial mass effect by the rotating mass 14 when the building B vibrates.

  In addition, the second mass dampers 32L and 32R have a rotating mass 32c and a viscous body 32g for suppressing the vibration of the building B, and the right and left are dependent on the uppermost layer (the uppermost layer of the vibration suppression control layer). The transmission members 31L and 31R are connected to the lowest layer (the lowest layer of the vibration suppression control layer). Further, the additional vibration system 3 is configured by the transmission members 31L and 31R and the second mass dampers 32L and 32R, and the rotating mass 32c rotates with the vibration of the building B. The transmission member stiffness (stiffness of the transmission members 31L and 31R) kbt, the additional mass mdt of the rotating mass 32c, and the damping coefficient cdt of the viscous body 32g are synchronized with the primary natural frequency of the building B. It is set to be. With the above configuration, when the building B vibrates, an inertial mass effect by the rotating mass 32c of the second mass dampers 32L and 32R and a viscous damping effect by the viscous body 32g are obtained, and the vibration of the primary mode of the building B is added to the additional vibration system 3. Absorbed in.

  In this case, since the second mass dampers 32L and 32R are connected to the uppermost layer and the lowermost layer, the second mass dampers 32L and 32R are connected to the second mass dampers 32L and 32R as compared with the case where the second mass dampers 32L and 32R are connected to one layer. Interlayer displacement (hereinafter referred to as “mass damper transmission interlayer displacement”) due to vibration of the primary mode of building B to be transmitted can be increased. Further, as described above, by providing the first mass damper 2 in the vibration suppression control layer, the interlayer displacement between the uppermost layer and the lowermost layer due to the vibration of the primary mode is increased, and the mass damper transmission interlayer displacement is further increased. Can be increased. As described above, since a larger inertial mass effect can be obtained by the rotating mass 32c of the second mass dampers 32L and 32R, the vibration of the primary mode of the building B can be sufficiently absorbed by the additional vibration system 3. As described above, according to the present embodiment, the vibration suppression effect by the first mass damper 2 and the additional vibration system 3 can be obtained synergistically, so that the vibration of the building B can be appropriately suppressed.

  Moreover, since the 1st mass damper 2 is provided in each layer of the damping control layer which consists of a several layer, the vibration of the building B can be suppressed more appropriately.

  Furthermore, as described above, since the conventional vibration suppression device cannot appropriately suppress the vibration of the building, it is conceivable to provide an additional vibration system for the entire building in order to eliminate such a problem. However, in that case, the vibration suppression device is increased in size and the manufacturing cost is increased. On the other hand, according to the present embodiment, since the vibration damping effect by the first mass damper 2 and the additional vibration system 3 is synergistically obtained as described above, the first mass damper 2 is placed on all the layers of the building B. Even if it is not provided, the vibration of the building B can be appropriately suppressed only by providing the building B partially. Therefore, it is possible to reduce the size and manufacturing cost of the vibration suppression device 1 as a whole.

  Further, since the second mass dampers 32L and 32R connected to the uppermost layer and the lowermost layer of the vibration suppression control layer have the viscous body 32g, the viscous damping effect can be applied to the entire vibration suppression control layer. In the present embodiment, the first mass damper 2 is not provided with a viscous damping element. Therefore, the manufacturing cost of the vibration suppressing device 1 can be further reduced accordingly.

  In addition, this invention can be implemented in various aspects, without being limited to the described embodiment. For example, in the embodiment, the first mass damper 2 is provided in each of the vibration suppression control layers, but may be provided in at least one of the vibration suppression control layers. In this case, the first mass damper 2 may be provided in each of a plurality of continuous layers constituting a part of the vibration suppression control layer, or may be provided every n layers (n ≧ 1). Also in this case, similarly to the embodiment, the interlayer displacement between the uppermost layer and the lowermost layer due to the vibration of the primary mode can be increased.

  In the embodiment, the first mass damper 2 is obliquely connected to the corresponding beams BU, BM1, BM2, and BD in a brace shape. However, the first mass damper 2 is described in FIG. 2 of Japanese Patent No. 5023129 by the present applicant. As shown in the figure, they may be connected via a pair of transmission members extending in the vertical direction with a space in the left-right direction so as to extend horizontally. Alternatively, as with the second mass dampers 32L and 32R, each of the first mass dampers 2 is constituted by two mass dampers, and these two mass dampers are paired with a pair of transmissions arranged in a V shape (or an inverted V shape). You may connect with an up-and-down beam via a member.

  Further, in the embodiment, the transmission members 31L and 31R are made of a pillar made of H-shaped steel, but are made of other appropriate members having elasticity, for example, a square steel pipe or a cable made of steel wire. May be. In the embodiment, the left and right transmission members 31L and 31R are arranged in a V shape, but as shown in FIG. 1 of Japanese Patent No. 5314201 by the present applicant, they are arranged in an inverted V shape. Alternatively, as described in, for example, FIG. 2 of Japanese Patent No. 5023129 by the present applicant, they may be arranged so as to extend in the vertical direction with a space therebetween in the left-right direction. Incidentally, when the transmission member is arranged in an inverted V shape, the second mass damper is connected to the upper beam instead of the lower beam. Further, in the embodiment, the first and second mass dampers 2, 32L, 32R are connected to the beams BU, BM1, BM2, BD extending in the left-right direction, but may be connected to the beams extending in the front-rear direction.

  In the embodiment, as the first and second mass dampers 2, 32L, and 32R, mass dampers having a rotary mass are used. However, the first and second mass dampers 2, 32L, and 32R are disclosed in Japanese Patent No. 5161395 and Japanese Patent No. 5191579 by the present applicant. A type of mass damper having a cylinder, a piston, and a working fluid may be used. Furthermore, in the embodiment, the viscous body 32g made of silicone oil is used as the viscous damping element of the second mass damper in the present invention. However, other suitable viscous bodies such as a viscosity made of synthetic resin such as polyisobutylene are used. The body may be used.

  In the embodiment, the first mass damper 2 is not provided with a viscous damping element, but may be provided. In this case, as the viscous damping element, for example, silicon oil may be used, or a viscous body made of a synthetic resin such as polyisobutylene may be used. Furthermore, in the embodiment, the restriction mechanism 15 is provided in the first and second mass dampers 2, 32L, 32R, but at least one of the restriction mechanisms 15 of the first and second mass dampers 2, 32L, 32R is omitted. May be. It goes without saying that variations relating to the above embodiments may be applied in appropriate combination. In addition, it is possible to appropriately change the detailed configuration within the scope of the gist of the present invention.

B Building (structure)
DESCRIPTION OF SYMBOLS 1 Vibration suppression apparatus 2 1st mass damper 3 Additional vibration system 14 Rotating mass (1st inertial mass element)
31L Left transmission member (transmission member)
31R Right transmission member (transmission member)
32L Second mass damper 32R Second mass damper 32c Rotating mass (second inertial mass element)
32g Viscous material (viscous damping element)

Claims (2)

A structure vibration suppressing device for suppressing vibration of a structure having a plurality of layers,
A first inertial mass element for suppressing vibration in a predetermined vibration mode of the second or higher order of the structure, provided in the plurality of layers, and the first inertial mass element according to the vibration of the structure; The first mass damper that moves,
A transmission member having elasticity and connected to one of the uppermost layer and the lowermost layer of the plurality of layers;
A second inertial mass element and a viscous damping element for suppressing vibrations of the structure, connected to the other of the uppermost layer and the lowermost layer and the transmission member, and added together with the transmission member A second mass damper that constitutes a vibration system and in which the second inertial mass element moves in accordance with the vibration of the structure;
The rigidity of the transmission member, the mass of the second inertial mass element, and the damping coefficient of the viscous damping element are set so that the natural frequency of the additional vibration system is synchronized with the primary natural frequency of the structure. An apparatus for suppressing vibration of a structure characterized by comprising:   2. The structure vibration suppression device according to claim 1, wherein the first mass damper includes a plurality of mass dampers and is provided in each of the plurality of layers.

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