Coupled damping structure design method and coupled damping structure design system

Abstract

To provide a design method and a design system which obtain information in which arrangement of a damper in a height direction of a coupled damping structure is optimized.SOLUTION: The method includes: setting an analysis model of a coupled damping structure having a first structure and a second structure; setting a constraint condition including an upper limit value of ridge-to-ridge displacement between the first structure and the second structure with respect to the analysis model; changing the number of installation layers being the number of layers in which a damper is disposed between the first structure and the second structure, to input a seismic force to the analysis model and obtain a response; and performing multiobjective optimization with the number of installation layers and a seismic layer shear force coefficient as variables under the constraint condition to calculate a Pareto solution of the number of installation layers and the seismic layer shear force coefficient.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present invention relates to a design method and a design system for a linked vibration-damping structure. [Background technology]

[0002] A linked vibration-damping structure is a structural form that efficiently absorbs vibration energy such as earthquake motion by connecting two structures with dampers, which are vibration-damping materials. The number and arrangement of dampers in a linked vibration-damping structure are important parameters that determine the earthquake resistance of the building to which the linked vibration-damping structure is applied. A method that uses fixed-point theory has been proposed as a method for optimizing the number of dampers in a linked vibration-damping structure (see, for example, Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Mitsuru Kageyama, Yuzuru Yasui, Kazuto Sedo, "Derivation of optimal solutions for connecting springs and dampers in a basic model of connected vibration control", Journal of Structural Engineering, Architectural Institute of Japan, March 2000, Vol. 65, No. 529, pp. 97-104 Summary of the Invention [Problem to be solved by the invention]

[0004] On the other hand, it is difficult to determine the optimal arrangement of dampers in the height direction of a linked vibration control structure, taking into account the nonlinearity of the damper's damping performance. For this reason, the decision on the damper arrangement has often relied on the designer's experience. [Means for solving the problem]

[0005] A design method for a linked vibration-controlled structure that solves the above-mentioned problems includes setting up an analytical model of a linked vibration-controlled structure having a first structure and a second structure, setting constraints on the analytical model including an upper limit value for the inter-building displacement between the first structure and the second structure, varying the number of installed layers, which is the number of layers on which dampers are placed between the first structure and the second structure, inputting seismic forces to the analytical model to obtain a response, and performing a multi-objective optimization calculation under the constraints using the number of installed layers and the earthquake story shear force coefficient as variables to calculate a Pareto solution for the number of installed layers and the earthquake story shear force coefficient.

[0006] A design system for linked vibration-controlled structures that solves the above-mentioned problems sets up an analytical model of a linked vibration-controlled structure having a first structure and a second structure, sets constraints on the analytical model including an upper limit on the inter-building displacement between the first structure and the second structure, changes the number of installed layers, which is the number of layers on which dampers are placed between the first structure and the second structure, inputs seismic forces to the analytical model to obtain a response, and calculates a Pareto solution for the number of installed layers and the earthquake story shear force coefficient by performing a multi-objective optimization calculation under the constraints using the number of installed layers and the earthquake story shear force coefficient as variables. Effect of the Invention

[0007] According to the present invention, it is possible to obtain information that optimizes the arrangement of dampers in the height direction of a linked vibration-damping structure. [Brief description of the drawings]

[0008] [Figure 1] 1 is a cross-sectional view in the height direction that typically illustrates one embodiment of a linked vibration damping structure. [Diagram 2] 4 is a plan view showing the arrangement of dampers in the linked vibration damping structure of the embodiment. FIG. [Diagram 3] FIG. 2 is a diagram illustrating a hardware configuration of the design system according to the embodiment. [Figure 4] FIG. 2 is a block diagram of a design system according to the embodiment. [Diagram 5] 4 is a flowchart showing the procedure of a design method according to the embodiment. [Figure 6] 4 is a diagram showing an analytical model of the linked vibration damping structure of the embodiment. FIG. [Figure 7] FIG. 2 is a diagram showing a distribution of Pareto solutions, which is an example of a result of multi-objective optimization according to the embodiment. [Figure 8] FIG. 2 is a diagram showing a distribution of Pareto solutions, which is an example of a result of multi-objective optimization according to the embodiment. [Figure 9] FIG. 13 is a diagram showing a breakdown of cases in which constraint conditions are not satisfied in the embodiment. [Figure 10] 13 is a table showing damper arrangements for some Pareto solutions in the embodiment. [Figure 11] FIG. 11 is a diagram showing the distribution of story shear force coefficients in the height direction for each Pareto solution shown in the table of FIG. [Figure 12] FIG. 11 is a diagram showing the distribution of inter-story drift angles in the height direction for each representative Pareto solution shown in the table of FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, one embodiment of a design method and a design system for a linked vibration-damping structure will be described with reference to Figs. 1 to 12. (Vibration-control buildings) FIG. 1 shows a schematic cross section of a vibration-controlled building 10 having a linked vibration-controlled structure.

[0010] The vibration-controlled building 10 has a first structure 20 and a second structure 30. The first structure 20 has a void space 11 inside. The second structure 30 is located in the void space 11. The first structure 20 surrounds the front, back and each side of the second structure 30 via a space. Here, the first structure 20 is a rigid frame structure. The second structure 30 is made of reinforced concrete using earthquake-resistant walls as the outer perimeter walls. The first structure 20 is on the 36th floor and the second structure 30 is on the 27th floor, with an open void above the second structure 30. The first structure 20 and the second structure 30 are integrated at the 4th floor level.

[0011] As shown in FIG. 2, a damper 40, which is a vibration-damping member, is installed between the first structure 20 and the second structure 30. The damper 40 connects the same floors of the first structure 20 and the second structure 30. The connected vibration-damping structure is composed of the first structure 20, the second structure 30, and the damper 40. The dampers 40 are respectively arranged in the X direction and the Y direction perpendicular to the X direction on the plane of the vibration-damping building 10. The number of dampers 40 may be optimized using fixed point theory. Here, two dampers 40 are installed in the X direction. Also, one damper 40 is arranged in the Y direction.

[0012] The number of installation layers Nd is the number of layers on which the damper 40 is installed between the first structure 20 and the second structure 30. The number of installation layers Nd of the damper 40 in the X direction and the number of installation layers Nd of the damper 40 in the Y direction may be the same or different. In addition, the floor on which the damper 40 is installed (e.g., the "6th floor") may be different in the X direction and the Y direction.

[0013] The second structure 30 has higher rigidity than the first structure 20. Therefore, the natural period of the second structure 30 is shorter than the natural period of the first structure 20. The vibration-controlled building 10 exerts a high vibration control effect by applying a large deformation to the damper 40 between the first structure 20 and the second structure 30, which have a large difference in natural period. The damper 40 is a member whose damping force increases according to the speed. The damping force of the damper 40 increases nonlinearly as the axial speed increases.

[0014] (Design System) 3 shows a hardware configuration of an information processing device H10 constituting a design system for optimizing the arrangement of the damper 40. The information processing device H10 includes a communication device H11, an input device H12, a display device H13, a storage device H14, and a processor H15. Note that this hardware configuration is an example, and it is also possible to realize the system using other hardware.

[0015] The communication device H11 is an interface that establishes a communication path with another device and transmits and receives data, for example, a network interface or a wireless interface.

[0016] The input device H12 is a device that accepts input of various information based on the operation of a person in charge. The input device H12 is, for example, a touch panel, a mouse, a keyboard, etc. The display device H13 is, for example, a display that displays various information.

[0017] The storage device H14 (computer-readable medium) stores data and various programs for executing various functions. Examples of the storage device H14 include ROM, RAM, and a hard disk. The storage device H14 includes any available recording medium that can be accessed by a general-purpose or dedicated computer. The storage device H14 stores a design program and various data used to execute the program.

[0018] The processor H15 controls each process using the programs and data stored in the storage device H14. Examples of the processor H15 include a CPU and an MPU. The processor H15 loads the programs into the RAM and executes various processes for each process.

[0019] The processor H15 is not limited to a processor that performs software processing for all the processes it executes. For example, the processor H15 may be equipped with a dedicated hardware circuit (e.g., an application specific integrated circuit (ASIC)) that performs hardware processing for at least a part of the processes it executes. That is, the processor H15 may be configured as any of the following: [1] One or more processors that operate according to a computer program (software). [2] One or more dedicated hardware circuits that perform at least some of the various processes [3] Circuits that include combinations of these

[0020] The functions of the design system 50 realized by executing the design program will be described with reference to Fig. 4. The design system 50 includes an analysis model setting unit 51, a constraint condition setting unit 52, and an optimization calculation unit 53.

[0021] The analytical model setting unit 51 sets an analytical model of a linked vibration-damping structure having the first structure 20 and the second structure 30. The constraint condition setting unit 52 sets constraint conditions including an upper limit value of the inter-building displacement between the first structure 20 and the second structure 30. The constraint condition setting unit 52 also sets constraint conditions including an upper limit value of the inter-story deformation angle and a maximum damping force of the damper 40 in the constraint conditions.

[0022] The optimization calculation unit 53 includes a response analysis unit 54 and a multi-objective optimization calculation unit 55. The optimization calculation unit 53 acquires an analysis model from an analysis model setting unit 51. In addition, the optimization calculation unit 53 acquires constraint conditions from a constraint condition setting unit 52. The processor H15 functions as the optimization calculation unit 53 by executing one or more programs stored in the storage device H14.

[0023] The response analysis unit 54 changes the number of floors Nd on which the dampers 40 are installed, and inputs the seismic force to the analysis model to obtain the response. The multi-objective optimization calculation unit 55 obtains the analysis result from the response analysis unit 54. The multi-objective optimization calculation unit 55 performs multi-objective optimization calculation under constraint conditions with the number of installed stories Nd and the earthquake story shear force coefficient C4 as variables, thereby calculating a Pareto solution of the number of installed stories Nd and the earthquake story shear force coefficient C4.

[0024] The design system 50 also has a calculation result storage unit 56. The response analysis unit 54 records the analysis results in the calculation result storage unit 56. The multi-objective optimization calculation unit 55 records the calculation results in the calculation result storage unit 56. The optimization calculation unit 53 reads out the analysis results or calculation results from the calculation result storage unit 56 in accordance with a user instruction input to the input device H12, and outputs them to the display device H13.

[0025] (Optimization process) The procedure for optimizing the arrangement of the damper 40 will be described with reference to Fig. 5. The order of steps S1 to S8 can be changed as long as multi-objective optimization calculations can be performed based on the results of response analysis. The analytical model setting unit 51 sets an analytical model 60 for the vibration-controlled building 10 to be optimized (step S1).

[0026] An example of the analysis model 60 will be described with reference to FIG. 6. FIG. 6 shows a part of the analysis model 60. In this analysis model 60, the first structure 20 has N floors, and the second structure 30 has k floors lower than the N floors. In this example, the first structure 20 uses an equivalent bending shear model, and the second structure 30 uses a fiber model. The connection part of the floor (fourth floor in FIG. 6) where the first structure 20 and the second structure 30 are integrated is replaced with a rotational spring element 65. The analysis model 60 includes damper elements 62 and mass points 61 corresponding to each floor. The damper 40 connected to the first structure 20 and the second structure is a damping top whose damping force changes nonlinearly with respect to the axial velocity. In the analysis model 60, the damper element 62 is a viscous element 63 and a mass element 64 arranged in parallel therewith. In this example, the damper 40 is installed every two floors, but it may be set every floor or every multiple floors of three or more floors. Furthermore, the dampers 40 do not have to be set for every certain number of floors. The range of the number of floors on which the dampers 40 can be installed and the range of floors on which the dampers 40 can be installed (hereinafter referred to as "installable floors") are determined in advance. The range of the number of floors on which the dampers 40 can be installed is, for example, 1 to 12 floors. Furthermore, the range of floors on which the dampers 40 can be installed is, for example, from the 6th floor to the 28th floor. In this embodiment, the arrangement of the dampers 40 is optimized independently for each of the X direction and the Y direction.

[0027] 5, the constraint condition setting unit 52 sets the constraint conditions (step S2). The constraint conditions include the following three conditions. Condition 1: The story drift angles g1(xi) during earthquakes in the X and Y directions are less than or equal to the respective upper limit values ​​G1. Second condition: The earthquake-induced inter-building displacement g2(xi) in the X and Y directions is less than or equal to the respective upper limit value G2. Third condition: The maximum damping force g3(xi) of the damper during an earthquake in the X and Y directions is less than or equal to the respective upper limit value G3.

[0028] Variable g j The "i" in (xi) refers to the floor number. "xi" is a design variable that indicates the presence or absence of the damper 40 on the "i" floor. Among the conditions, the second condition in particular is a condition specific to linked vibration control structures. In the first constraint, the upper limit G1 of the earthquake inter-story drift angle g1(xi) in the X direction and the upper limit G1 of the earthquake inter-story drift angle g1(xi) in the Y direction are set to, for example, "1 / 120rad". In the second constraint, the upper limit G2 of the earthquake inter-building displacement g2(xi) in the X direction is set to, for example, "800mm", and the upper limit G2 of the earthquake inter-building displacement g2(xi) in the Y direction is set to, for example, "950mm". In the third constraint, the upper limit G3 of the earthquake damper maximum damping force g3(xi) in the X direction and the upper limit G3 of the earthquake damper maximum damping force g3(xi) in the Y direction are set to, for example, "1300kN".

[0029] Next, the response analysis unit 54 sets the input earthquake motion (step S3). For example, in addition to the three waves (Hachinohe phase, Kobe phase, and random phase) conforming to level 2 of the notice spectrum as the input earthquake motion, the Kamimachi fault zone earthquake motion is adopted as the earthquake motion of level 3. For the earthquake motion of level 3, the EW direction wave is used in the X direction, and the NS direction wave is used in the Y direction.

[0030] The response analysis unit 54 performs a response analysis for each arrangement pattern of the dampers 40. The arrangement pattern of the dampers 40 differs depending on the number of installation stories Nd and the floor on which the dampers 40 are installed. First, the response analysis unit 54 sets the number of layers to be installed Nd (step S4). The response analysis unit 54 sets one value from "1 layer" to "12 layers", which are the number of layers that can be arranged. The value of the number of layers to be installed Nd can be specified by the designer (user).

[0031] The response analysis unit 54 sets the floor on which the damper 40 is to be installed so that the number of floors Nd for installation is the number set in step S4 (step S5). For example, if the range of floors on which the damper 40 can be installed is from the 6th floor to the 28th floor and the number of floors Nd for installation is "1 floor", the response analysis unit 54 sets one of the floors on which the damper 40 can be installed. Also, if the number of floors Nd for installation is "4 floors", the response analysis unit 54 sets four of the floors on which the damper 40 can be installed (for example, the 8th floor, 24th floor, 26th floor, and 28th floor).

[0032] Furthermore, the response analysis unit 54 performs a response analysis by inputting the response spectrum of the earthquake motion set in step S3 into the analysis model 60 (step S6). The waveform of the response spectrum changes over time. The response analysis unit 54 places damper elements 62 on the installation floor set in step S5 for the analysis model 60 set in step S1. Furthermore, the response analysis unit 54 calculates the values ​​of the earthquake story drift angle g1, earthquake inter-building displacement g2, and earthquake damper maximum damping force g3, which change over time, and the earthquake story shear force coefficient C4, by a time history response analysis.

[0033] The response analysis unit 54 judges whether the response analysis has been completed for all patterns (step S7). If there are patterns to be analyzed, the response analysis unit 54 judges that the response analysis has not been completed (step S7: NO), and repeats steps S4 to S6. That is, when the number of installation floors Nd is "four floors", for example, the response analysis unit 54 performs response analysis for the case where the dampers 40 are installed on "8th floor, 24th floor, 26th floor, and 28th floor" in the first round, and changes the combination of floors where the dampers 40 are installed in the second round (for example, "8th floor, 22nd floor, 24th floor, and 26th floor"). However, instead of targeting all expected patterns, only a predetermined pattern may be targeted.

[0034] When the response analysis unit 54 determines that the response analysis is completed (step S7: YES), the multi-objective optimization calculation unit 55 uses the analysis result of the response analysis unit 54 to perform a multi-objective optimization calculation with the number of installation stories Nd of the dampers 40 and the earthquake story shear force coefficient C4 as objective functions under the constraint conditions set in step S2 (step S8). The optimization problem can be expressed by the following formulas (1) and (2).

number

number

[0035] "i" indicates a floor (6th to 28th floors) on which the damper 40 of the vibration-controlled building 10 can be installed. "xi" takes the value of "0" or "1." When "xi=0", it indicates that the damper 40 is not installed on the "i" floor, and when "xi=1", it indicates that the damper 40 is installed on the "i" floor. The variable g in Equation (2) j (xi) is a variable representing the first condition, the second condition, and the third condition (j=1, 2, 3).

[0036] There is no solution in which both the number of installed stories Nd of dampers 40 and the earthquake story shear force coefficient C4 are simultaneously minimized. Equation (1) indicates that the Pareto solutions are a set of solutions that minimize the number of installed stories Nd of dampers 40 and the earthquake story shear force coefficient C4 among the sets of the number of installed stories Nd of dampers 40 and the earthquake story shear force coefficient C4 in patterns that satisfy the constraint conditions. Equation (2) indicates the constraint conditions. After calculating the Pareto solutions of the number of installed stories Nd and the earthquake story shear force coefficient C4, the multi-objective optimization calculation unit 55 records them in the calculation result storage unit 56. In the above embodiment, after the response analysis (steps S4 to S6), a multi-objective optimization calculation is performed (step S7). However, the multi-objective optimization calculation may be performed each time the response analysis is completed for one damper 40 arrangement pattern.

[0037] (Multi-objective optimization calculation result) 7 and 8, the results of the multi-objective optimization calculation will be described with reference to examples of the calculation results. The optimization calculation unit 53 outputs the calculation results to the display device H13 in response to the operation of the input device H12 by the designer. Fig. 7 shows an example of the distribution of Pareto solutions when the input earthquake motion is applied in the X direction. The horizontal axis is the number of stories Nd on which dampers 40 are installed, and the vertical axis is the earthquake story shear force coefficient C4. In the example of Fig. 7, even with the same number of stories Nd, there are patterns that do not satisfy the constraint conditions ("not feasible" in Fig. 7) and patterns that satisfy the constraint conditions ("feasible" in Fig. 7) depending on the floor on which dampers 40 are installed.

[0038] The larger the number of stories Nd in which dampers 40 are installed, the smaller the earthquake story shear force coefficient C4. In other words, there is a trade-off between the two objective functions. In FIG. 7, the Pareto solutions are multiple optimal solutions on the Pareto front that minimize the two objective functions among a set of feasible solutions. In the example of FIG. 7, among multiple feasible solutions for each story where the number of stories Nd in which dampers 40 are installed is 4 to 10, the solution with the smallest earthquake story shear force coefficient C4 is the solution.

[0039] FIG. 8 shows an example of the distribution of Pareto solutions when the load direction is the Y direction. The horizontal axis is the number of installed stories Nd of the dampers 40, and the vertical axis is the earthquake story shear force coefficient C4. In the Pareto solution distribution in the Y direction, the two objective functions are also in a trade-off relationship. In FIG. 8 as well, the Pareto solutions are multiple optimal solutions on the Pareto front that minimize the two objective functions among a set of feasible solutions. In the example of FIG. 8, the Pareto solutions are the solutions with the smallest earthquake story shear force coefficient C4 among multiple feasible solutions for each story where the number of installed stories Nd is 6 to 11.

[0040] Furthermore, information regarding the effect of reducing the earthquake story shear force coefficient C4 can be obtained from the distribution of the Pareto solutions. For example, in the distributions shown in Figures 7 and 8, it can be seen that the effect of reducing the earthquake story shear force coefficient C4 by the dampers 40 becomes gentle in the region where the number of stories Nd where the dampers 40 are installed is 8 or more in both the X and Y directions. For this reason, the cost-effectiveness of adding dampers 40 decreases.

[0041] The designer refers to the results of the multi-objective optimization calculation. Then, from among the multiple Pareto solutions, the designer selects a solution (preferred solution) that meets various conditions other than the constraint conditions. At this time, an optimized pattern is presented to the designer from a large number of patterns that are assumed based on the combination of the number of installation floors Nd and the floor on which the damper 40 is installed, so the designer can efficiently obtain a Pareto solution without having to verify all patterns. In addition, since the results of the multi-objective optimization calculation performed by the design system 50 can be used, the designer does not have to determine the placement of the damper 40 based solely on experience.

[0042] Furthermore, the multi-objective optimization calculation unit 55 uses the response analysis results to output a breakdown of cases that do not satisfy the constraint conditions (constrained rate). FIG. 9 is an example showing the breakdown of patterns that do not satisfy the constraint conditions. The patterns that do not satisfy the constraint conditions are those that are marked as "impossible" in FIG. 7 and FIG. 8. In the example of FIG. 9, in the X direction, the most common patterns do not satisfy the first condition (earthquake story drift angle g1(xi)), followed by the third condition (earthquake damper maximum damping force g3(xi)), and the least common patterns do not satisfy the second condition (earthquake inter-building displacement g2(xi)). In the Y direction, the most common patterns do not satisfy the first condition (earthquake story drift angle g1(xi)), followed by the second condition (earthquake inter-building displacement g2(xi)). In the Y direction, all patterns satisfy the third condition (earthquake damper maximum damping force g3(xi)). The designer can check the validity of the Pareto solution by checking the patterns that are not considered in the multi-objective optimization calculation.

[0043] Furthermore, the optimization calculation unit 53 outputs detailed information of the obtained Pareto solutions in response to the designer's operation of the input device H12. Fig. 10 shows the representative values ​​of the Pareto solutions. In Fig. 10, the representative values ​​for the number of installed floors Nd in the X direction are 4, 8, and 10. Also, the representative values ​​for the number of installed floors Nd in the Y direction are 6, 8, and 10. The representative values ​​can be selected by the designer. Also, the floors marked with a "○" in the table are the floors where dampers are installed.

[0044] 11 and 12 show the changes in the maximum story shear coefficient and the maximum story drift angle for each floor for the representative values ​​shown in the table of FIG. 11. The vertical axis shows each floor (each story) of the vibration-controlled building 10. The horizontal axis shows the maximum story shear coefficient and the maximum story drift angle, respectively. The maximum story shear coefficient and the maximum story drift angle are the maximum values ​​obtained in the time history response analysis. FIG. 11 shows the maximum story shear coefficient when the number of installed stories Nd in the X direction is 4, 8, and 10 stories, and the maximum story shear coefficient when the number of installed stories Nd in the Y direction is 6, 8, and 10 stories. FIG. 12 shows the maximum story drift angle when the number of installed stories Nd in the X direction is 4, 8, and 10 stories, and the maximum story drift angle when the number of installed stories Nd in the Y direction is 6, 8, and 10 stories.

[0045] In Figures 11 and 12, the designer can confirm the changes in the maximum story shear coefficient and the maximum story drift angle. For example, in both cases where the load direction is the X direction and the Y direction, the maximum story shear coefficient and the maximum story drift angle tend to become smaller as the number of installed stories Nd increases on the 25th floor or less. On the other hand, particularly in the X direction, the maximum story shear coefficient when the number of installed stories Nd is 10 stories is larger on the 25th floor or more than the maximum story shear coefficient when the number of installed stories Nd is 8 stories. This allows the designer to confirm that an increase in the number of dampers 40 is causing response amplification on the upper floors that was not taken into account in the optimization problem.

[0046] As described above, according to the above embodiment, the following effects can be obtained. (1) In the above embodiment, constraint conditions including inter-building displacement were set to optimize the placement of the dampers 40 in the linked vibration-damping structure. Then, under the constraint conditions, a multi-objective optimization calculation was performed with the number of installed stories Nd and the earthquake story shear force coefficient C4 as variables to calculate a Pareto solution. This allows the designer to determine a rational placement of the dampers 40 in the linked vibration-damping structure without relying solely on experience.

[0047] (2) In the above embodiment, the Pareto solutions are calculated for the X direction, which is the first direction, and the Y direction, which is the second direction. This makes it possible to optimize the arrangement of the damper 40 for each of the X direction and the Y direction.

[0048] (3) In the above embodiment, the constraint conditions are set to include the upper limit of the inter-story drift angle and the maximum damping force of the damper 40, thereby setting conditions suitable for the linked vibration-damping structure. Therefore, it is possible to obtain a Pareto solution that satisfies the conditions specific to the linked vibration-damping structure.

[0049] (4) In the above embodiment, for cases where it is determined that at least one of the constraints is not satisfied, the details of the unsatisfied conditions are calculated. Therefore, by obtaining detailed information other than the Pareto solution, the arrangement of the damper 40 can be verified.

[0050] The above-described embodiment can be modified as follows: Each embodiment and the following modified examples can be combined with each other to the extent that there is no technical contradiction. (Connected vibration-damping structure) In the above embodiment, the vibration-controlled building 10 may be composed of a U-shaped first structure 20 and a second structure 30. Alternatively, the vibration-controlled building 10 may be composed of a first structure 20 that is a plurality of independent buildings, and a second structure 30 that is connected to the first structure 20.

[0051] (Damper) There is no limitation on the type of the damper 40. An oil damper, a friction damper, a viscous damper, a viscoelastic damper, a hysteretic damper, or a combination of these may be used. Although the damper 40 is described as connecting the same floor of the first structure 20 and the second structure 30, the damper 40 may connect different floors. In other words, the damper 40 may connect the first structure 20 and the second structure 30 at different height positions.

[0052] (First structure and second structure) The first structure 20 may have a structure other than a rigid frame structure. The second structure 30 is made of reinforced concrete, steel framed concrete, or steel framed reinforced concrete. (constraints) In the above embodiment, the constraint conditions include the upper limit of the inter-building displacement, the upper limit of the story drift angle, and the maximum damping force of the damper 40. However, it is sufficient for the constraint conditions to include at least one of these.

[0053] (Multi-objective optimization operation) In the above embodiment, the Pareto solutions are calculated for both the X direction and the Y direction. Instead of this, the Pareto solutions may be calculated for only one of the X direction and the Y direction. (Restricted rate) In the above embodiment, the constraint ratio, which is a breakdown of the conditions that are not satisfied among the multiple conditions included in the constraint conditions, is displayed, but this process may be omitted. Alternatively, at least one value such as the arrangement of dampers 40 that do not satisfy the constraint conditions, the value of the earthquake-induced story drift angle, the earthquake-induced inter-building displacement, and the maximum damping force of the dampers 40 may be displayed as a breakdown of the conditions that are not satisfied. [Explanation of symbols]

[0054] 10...vibration-controlled building, 11...void space, 20...first structure, 30...second structure, 40...damper, 50...design system.

Claims

1. An analytical model of a coupled vibration-damping structure having a first structure and a second structure is set, setting a constraint condition including an upper limit value of an inter-building displacement between the first structure and the second structure for the analytical model; A response is obtained by inputting a seismic force to the analysis model while changing the number of installation layers, which is the number of layers in which a damper is arranged between the first structure and the second structure; A design method for a linked vibration-control structure, comprising: performing a multi-objective optimization calculation under the constraint conditions with the number of installed stories and the earthquake story shear force coefficient as variables to calculate a Pareto solution for the number of installed stories and the earthquake story shear force coefficient.

2. The design method for a linked vibration-damping structure according to claim 1 , further comprising the steps of: calculating the Pareto solutions for a first direction of the linked vibration-damping structure and a second direction perpendicular to the first direction, respectively.

3. The design method for a linked vibration-controlled structure according to claim 1 , wherein the constraints further include an upper limit value for an inter-story drift angle.

4. The design method for a linked vibration-damping structure according to claim 1 , wherein the constraints further include a maximum damping force of the damper.

5. 5. A design method for a linked vibration control structure as described in claim 3 or 4, further comprising calculating a breakdown of the unsatisfied conditions for a combination of the number of installed stories and earthquake story shear force coefficient that is determined to not satisfy at least one of the multiple conditions included in the constraint conditions.

6. The first structure is a frame having a void space therein, The design method for a linked vibration-damping structure according to claim 1 , wherein the second structure is a frame located in the void space.

7. An analytical model of a coupled vibration-damping structure having a first structure and a second structure is set, setting a constraint condition including an upper limit value of an inter-building displacement between the first structure and the second structure for the analytical model; A response is obtained by inputting a seismic force to the analysis model while changing the number of installation layers, which is the number of layers in which a damper is arranged between the first structure and the second structure; A design system for linked vibration-control structures that calculates Pareto solutions for the number of installed stories and the earthquake story shear force coefficient by performing multi-objective optimization calculations under the constraint conditions using the number of installed stories and the earthquake story shear force coefficient as variables.

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