A viscous damper parameter design method based on optimal additional damping ratio

Abstract

The present application relates to building energy dissipation and shock absorption technical field, disclose a kind of based on optimal additional damping ratio viscous damper parameter design method, including the following steps: the first-order natural frequency of non-damping structure is calculated;The vertex displacement amplitude of structure under the action of frequently occurring earthquake is calculated;The inter-story displacement amplitude of the i floor of structure arranged with damper and the corresponding inter-story displacement amplitude average are calculated;The first-order equivalent modal stiffness of viscous damper connecting component is calculated;The traversal numerical solution of damper damping index is calculated;The value of damping coefficient when additional damping ratio obtains maximum is calculated and so on step.The present application can calculate the specific value of viscous damper damping coefficient and damping index when additional damping ratio obtains maximum according to the basic parameter of structure, and the corresponding maximum value of additional damping ratio is calculated, and it has important significance to damage control and optimization design of damper parameter of viscous damper shock absorption structure under the action of earthquake.

Description

Technical Field

[0001] This invention relates to the field of building energy dissipation and vibration reduction technology, specifically to a method for designing viscous damper parameters based on the optimal additional damping ratio. Background Technology

[0002] A viscous damper is a velocity-type energy dissipator that enhances the energy dissipation capacity of a structure under seismic loading by providing an additional damping ratio. Since the static stiffness of a viscous damper is zero, the degree of damage to the structure under seismic loading is negatively correlated with the additional damping ratio provided by the damper; that is, the higher the additional damping ratio, the less severe the damage. Therefore, in practical structural design, designers often aim to achieve a higher additional damping ratio by optimizing the damper's parameters. This effectively controls the degree of damage to the structure under seismic loading, improves its seismic safety, and ultimately achieves better economic benefits.

[0003] However, the strain energy of the structure Displacement amplitude of the structure Damping coefficient of viscous damper C Damping index α, stiffness of energy dissipation connection components These parameters all affect the value of the additional damping ratio. Furthermore, when these parameters change simultaneously, it is often difficult for designers to determine where the maximum value of the additional damping ratio is obtained. Summary of the Invention

[0004] Therefore, this invention proposes a design method for viscous damper parameters based on the optimal additional damping ratio. This method can solve for the damper parameters based on the constraint equations satisfied by the parameters when the additional damping ratio of the structure reaches its maximum value. C The values ​​of α and α are of great significance for the damage control of viscous damper damping structures under seismic loading and for the optimization design of damper parameters.

[0005] To achieve the above-mentioned technical effects, the present invention is implemented through the following technical solution: A method for designing viscous damper parameters based on the optimal additional damping ratio includes the following steps: S1. Establish a non-damped structural model without viscous dampers and calculate the first-order natural frequency of the non-damped structure. ; S2. Calculate the amplitude of the top displacement of the structural model established in step S1 under frequent earthquakes. ; S3. Calculate the absolute displacement amplitude of each floor of the structure. ; S4, Calculate the structure with dampers. Inter-story displacement amplitude And the average value of inter-story displacement of floors with dampers ; S5. Calculate the first-order equivalent modal stiffness of the viscous damper connection components. ; S6. Calculate the first-order generalized stiffness of the main frame structure. ; S7. Calculate the ergodic numerical solution of the damping index α of the viscous damper based on the implicit equation. S8. Calculate the damping coefficient when the additional damping ratio reaches its maximum value. C The possible values ​​of: S9. Calculate the maximum additional damping ratio of the structure based on the parameters obtained in steps S5, S6, S7, and 8. ; S10. The maximum additional damping ratio of the structure calculated in step S9 is... Compared with the inherent damping ratio of the structure The superposition is performed, and the equivalent linearized model of the viscous damper vibration reduction structure is substituted to carry out structural reinforcement design and seismic performance verification.

[0006] This invention provides a method for designing viscous damper parameters based on the optimal additional damping ratio, specifically including the following steps: S1. Establish a non-damped structural model without viscous dampers and calculate the first-order natural frequency of the non-damped structure. ; S2. Calculate the amplitude of the top displacement of the structural model established in step S1 under frequent earthquakes. ; S3. Calculate the absolute displacement amplitude of each floor of the structure. The calculation formula is as follows: (1), In the formula, This is the first mode shape of the structure; S4, Calculate the structure with dampers. Inter-story displacement amplitude And the average value of inter-story displacement of floors with dampers The calculation formula is as follows: (2), (3), In the formula, n The number of floors equipped with dampers; S5. Calculate the first-order equivalent modal stiffness of the viscous damper connection components. The calculation formula is as follows: (4), In the formula, For the first j The overall stiffness of the layered damper connection components. For the first floor with dampers j Layer vibration mode displacement, N The total number of viscous dampers on the same floor in the same direction; S6. Calculate the first-order generalized stiffness of the main frame structure. The calculation formula is as follows: (5), In the formula, The stiffness matrix of the main structure; for The transpose of the matrix; S7. Calculate the ergodic numerical solution of the damping index α of the viscous damper based on the implicit equation. The calculation formula is as follows: (6), In the formula, For the summation variable; or The implicit function parameter is defined as the displacement utilization coefficient, satisfying the implicit equation: (7); S8. Calculate the damping coefficient when the additional damping ratio reaches its maximum value. C The value of is calculated using the following formula: (8); S9. Calculate the maximum additional damping ratio of the structure based on the parameters obtained in steps S5, S6, S7, and 8. The calculation formula is as follows: (9), The formula for calculating the gamma function Γ is: (10) In the formula, For ordinary variables, t For integration variables, e It is a natural constant; S10. The maximum additional damping ratio of the structure calculated in step S9 is... Compared with the inherent damping ratio of the structure The superposition is performed, and the equivalent linearized model of the viscous damper vibration reduction structure is substituted to carry out structural reinforcement design and seismic performance verification.

[0007] Furthermore, in step S1, when calculating the first-order natural frequency f of the non-damped structure, the eigenvector method or the Ritz vector method can be used for solution; in step S2, the amplitude of the top displacement of the structure under frequent earthquakes is calculated. When this is the case, the modal decomposition response spectrum method or time history analysis method can be used for calculation.

[0008] Furthermore, in step S3, the first-order vibration mode It can be represented as: (11), In the formula, This represents the modal displacements of each floor of the structure; First mode The calculation is performed by solving the eigenvalue equation, and the formula is as follows: (12) In the formula, M The mass matrix of the structure, oh The first natural circular frequency of the structure is... oh =2 πf .

[0009] Furthermore, in step S5, the first-order equivalent modal stiffness of the viscous damper connecting component is calculated. K L At that time, the first j Stiffness of layer damper connection components K j The calculation should be based on the type of damper connection components, and the calculation formula is as follows: (1) For support-type connections, K j Calculate using the following formula: (13) In the formula, , , Let be the elastic modulus, cross-sectional area, and effective length of the support connecting the j-th layer damper, respectively. Let be the angle between the j-th layer damper connecting support and the horizontal direction; (2) For wall-mounted connections, K j Calculate using the following formula: (14) In the formula, E c , G c For the first j The elastic modulus and shear modulus of the concrete used in the layer damper connecting wall; shear modulusG c =0.4 E c ; , h j , I、c The first j The cross-sectional area, height, moment of inertia, and shape factor of the layer damper connecting wall; shape factor c =1.2.

[0010] Furthermore, step S7 solves for the parameters. α When traversing numerical solutions, the damping index of the viscous damper is calculated using Newton's iteration method or the bisection method. α The value range of is (0, 1], implicit function parameter or The range of values ​​for is (0, 1).

[0011] Furthermore, in step S7, the parameters are solved using equation (6). α When traversing numerical solutions, implicit function parameters or The number of values ​​that can be traversed within the range (0, 1) should be no less than 10,000.

[0012] Furthermore, the truncation error of the infinite series on the right side of formula (6) in step S7 should not exceed 10. -8 This is to ensure sufficient computational accuracy for the numerical equations.

[0013] Furthermore, in step S9, the calculated maximum additional damping ratio of the structure is... It should not exceed 0.25. If it exceeds 0.25, it should be reduced. .

[0014] The beneficial effects of this invention are as follows: 1. This invention can calculate the damping coefficient of the viscous damper when the additional damping ratio reaches its maximum value based on the basic parameters of the structure. C and damping index α The specific values ​​are determined, and the corresponding maximum additional damping ratio is calculated. This is of great significance for the damage control of viscous damper seismic isolation structures under seismic loading and for the optimization design of damper parameters. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a plan view of the viscous damper; Figure 3 This is a diagram of a non-damping structural model; Figure 4 This is a parameter setting diagram for solving the first-order natural frequency using the Ritz vector method; Figure 5 This is a diagram showing the calculated displacement amplitude at the top of the structure. Figure 6 It is the damping index of the viscous damper. α The distribution diagram of the traversal numerical solutions; Figure 7 This is a diagram showing the damping ratio settings of the equivalent linearized model of the viscous damper vibration reduction structure. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] like Figure 1 As shown, the present invention provides a method for designing viscous damper parameters based on the optimal additional damping ratio, comprising the following steps: S1. Establish a non-damped structural model without viscous dampers and calculate the first-order natural frequency of the non-damped structure. ; S2. Calculate the amplitude of the top displacement of the structural model established in step S1 under frequent earthquakes. ; S3. Calculate the absolute displacement amplitude of each floor of the structure. ; S4, Calculate the structure with dampers. Inter-story displacement amplitude And the average value of inter-story displacement of floors with dampers ; S5. Calculate the first-order equivalent modal stiffness of the viscous damper connection components. ; S6. Calculate the first-order generalized stiffness of the main frame structure. ; S7. Calculate the ergodic numerical solution of the damping index α of the viscous damper based on the implicit equation. S8. Calculate the damping coefficient when the additional damping ratio reaches its maximum value. C The possible values ​​of: S9. Calculate the maximum additional damping ratio of the structure based on the parameters obtained in steps S5, S6, S7, and 8. ; S10. The maximum additional damping ratio of the structure calculated in step S9 is... Compared with the inherent damping ratio of the structure The superposition is performed, and the equivalent linearized model of the viscous damper vibration reduction structure is substituted to carry out structural reinforcement design and seismic performance verification.

[0019] This invention provides a method for designing viscous damper parameters based on the optimal additional damping ratio, specifically including the following steps: S1. Establish a non-damped structural model without viscous dampers and calculate the first-order natural frequency of the non-damped structure. ; S2. Calculate the amplitude of the top displacement of the structural model established in step S1 under frequent earthquakes. ; S3. Calculate the absolute displacement amplitude of each floor of the structure. The calculation formula is as follows: (1), In the formula, This is the first mode shape of the structure; S4, Calculate the structure with dampers. Inter-story displacement amplitude And the average value of inter-story displacement of floors with dampers The calculation formula is as follows: (2), (3), In the formula, n The number of floors equipped with dampers; S5. Calculate the first-order equivalent modal stiffness of the viscous damper connection components. The calculation formula is as follows: (4), In the formula, For the first j The overall stiffness of the layered damper connection components. For the first floor with dampers j Layer vibration mode displacement, N The total number of viscous dampers on the same floor in the same direction; S6. Calculate the first-order generalized stiffness of the main frame structure. The calculation formula is as follows: (5), In the formula, The stiffness matrix of the main structure; for The transpose of the matrix; S7. Calculate the ergodic numerical solution of the damping index α of the viscous damper based on the implicit equation. The calculation formula is as follows: (6), In the formula, For the summation variable; or The implicit function parameter is defined as the displacement utilization coefficient, satisfying the implicit equation: (7); S8. Calculate the damping coefficient when the additional damping ratio reaches its maximum value. C The value of is calculated using the following formula: (8); S9. Calculate the maximum additional damping ratio of the structure based on the parameters obtained in steps S5, S6, S7, and 8. The calculation formula is as follows: (9), The formula for calculating the gamma function Γ is: (10) In the formula, For ordinary variables, t For integration variables, e It is a natural constant; S10. The maximum additional damping ratio of the structure calculated in step S9 is... Compared with the inherent damping ratio of the structure The superposition is performed, and the equivalent linearized model of the viscous damper vibration reduction structure is substituted to carry out structural reinforcement design and seismic performance verification.

[0020] Furthermore, in step S1, when calculating the first-order natural frequency f of the non-damped structure, the eigenvector method or the Ritz vector method can be used for the solution. In step S2, the amplitude of the top displacement of the structure under frequent earthquakes is calculated. When this is the case, the modal response spectrum method or time history analysis method can be used for calculation. When using the time history analysis method, according to the requirements of the code "Code for Seismic Design of Buildings" (GB / T50011-2010), seven seismic waves should be used for time history analysis, and the displacement amplitude should be... x A The average value of all seismic wave calculation results is taken; when time history analysis is performed using three seismic waves according to the requirements of the code "Code for Seismic Design of Buildings" (GB / T 50011-2010), the displacement amplitude is...x A Take the envelope value of all seismic wave calculation results.

[0021] Furthermore, in step S3, the first-order vibration mode It can be represented as: (11), In the formula, This represents the modal displacements of each floor of the structure; First mode The calculation is performed by solving the eigenvalue equation, and the formula is as follows: (12) In the formula, M The mass matrix of the structure, oh The first natural circular frequency of the structure is... oh =2 πf .

[0022] Furthermore, in step S5, the first-order equivalent modal stiffness of the viscous damper connecting component is calculated. K L At that time, the first j Stiffness of layer damper connection components K j The calculation should be based on the type of damper connection components, and the calculation formula is as follows: (1) For support-type connections, K j Calculate using the following formula: (13) In the formula, , , Let be the elastic modulus, cross-sectional area, and effective length of the support connecting the j-th layer damper, respectively. Let be the angle between the j-th layer damper connecting support and the horizontal direction; (2) For wall-mounted connections, K j Calculate using the following formula: (14) In the formula, E c , G c For the first j The elastic modulus and shear modulus of the concrete used in the layer damper connecting wall; shear modulus G c =0.4 E c ; ,h j , I、c The first j The cross-sectional area, height, moment of inertia, and shape factor of the layer damper connecting wall; shape factor c =1.2.

[0023] Furthermore, step S7 solves for the parameters. α When traversing numerical solutions, the damping index of the viscous damper is calculated using Newton's iteration method or the bisection method. α The value range of is (0, 1], implicit function parameter or The range of values ​​for is (0, 1).

[0024] Furthermore, in step S7, the parameters are solved using equation (6). α When traversing numerical solutions, implicit function parameters or The number of values ​​that can be traversed within the range (0, 1) should be no less than 10,000.

[0025] Furthermore, the truncation error of the infinite series on the right side of formula (6) in step S7 should not exceed 10. -8 This is to ensure sufficient computational accuracy for the numerical equations.

[0026] Furthermore, in step S9, the calculated maximum additional damping ratio of the structure is... It should not exceed 0.25. If it exceeds 0.25, it should be reduced. .

[0027] Verification Example

[0028] A four-story reinforced concrete frame structure has a story height of 3.9 m and a total structural height of 15.6 m. According to the code "Code for Seismic Design of Buildings" (GB / T50011-2010), the seismic fortification intensity is 8 degrees (0.2g), the basic seismic acceleration is 0.2g, and the site characteristic period is... T g =0.45s, inherent damping ratio of the structure To improve seismic safety under strong earthquakes, this structure employs viscous dampers for energy dissipation and vibration reduction. Damping is implemented on floors 1-3 of the structure, with the same number of dampers on each floor. Figure 2 This is a diagram showing the layout of the viscous dampers on the building plan.

[0029] The following section describes the parameter design of the viscous damper under the optimal additional damping ratio: Step S1: Establish a non-damped structural model without viscous dampers, such as... Figure 3 As shown, This embodiment uses the Ritz vector method to calculate the first-order natural frequency of a non-damped structure. The calculation method is as follows: Open SAP2000 software, select the load case data interface, and set the parameters in this interface. The parameter settings are as follows: Figure 4 As shown, enter "Modal" as the load case name, select "Modal Analysis" as the load case type, select "Zero Initial Condition - No Stress State" for the structural stiffness, check "Ritz Vector" in the mode type, enter 30 for the maximum number of modes and 1 for the minimum number of modes, select "LoadPattern-Dead-0-99" for the applied load, and click "OK" after setting the parameters. This will give you a list of the calculated first-order natural frequencies of the non-damped structure. Table 1. First-order natural frequencies of the structure f Calculation results list

[0030] The first-order natural frequencies of the non-damped structure can be obtained from the table above. f =1.42 Hz.

[0031] Step S2: Calculate the amplitude of the top displacement of the structure under frequent earthquakes using the modal response spectrum method. ,like Figure 5 As shown.

[0032] Step S3: Solve the eigenvalue equations to calculate the first mode shape of the structure. Then, the absolute displacement amplitude of each floor of the structure is calculated. x : (15) Right now: (16) The first mode shape of the structure is obtained by solving. for: (17) Then the absolute displacement amplitude of each floor of the structure x for: (18) Step S4: Calculate the first step of the structure with dampers. i Inter-layer displacement amplitude : (19) (20) (twenty one), The average value of the inter-story displacement of the floor with dampers for: (twenty two), Step S5: The damper connection components are connected using cantilever walls. The cantilever walls connected to the dampers on each floor have the same dimensions, specifically: vertical height. h =1750mm, cross-sectional width b =1600mm, cross-sectional thickness t =250mm, concrete strength grade is C30, then the stiffness of the connecting component is... K j for: (twenty three), The first-order equivalent modal stiffness of the viscous damper connecting component K L for: (twenty four), Step S6: Calculate the first-order generalized stiffness of the main frame structure. K m : (25) Step S7: Calculate the damping index of the viscous damper based on the implicit equation. α The traversal of numerical solutions, implicit function parameters or The number of traversals within the range (0, 1) is taken as 20000, and the corresponding damping index is calculated based on the implicit equation. α The distribution of ergodic numerical solutions is as follows Figure 6 As shown, based on the actual needs of the project, the following is taken: or The numerical solution corresponding to =0.72278, i.e., taking α =0.3.

[0033] Step S8: Calculate the parameters obtained in steps S1, S4, S5, and S7. f , , K L , α Substituting into equation (8), the damping coefficient is calculated when the additional damping ratio reaches its maximum value. C The possible values ​​of: (26) Step S9: Calculate the parameters obtained in steps S4, S5, and S6. K L , K m , or Substitute into equation (9) to calculate the maximum additional damping ratio of the structure. : (27) because Then take .

[0034] Step 10: Calculate the maximum additional damping ratio of the structure obtained in step S9. Compared with the inherent damping ratio of the structure To superimpose, that is Then, the total damping ratio of 0.3 is substituted into the equivalent linearized model of the viscous damper structure for structural reinforcement design and seismic performance verification. The interface parameter settings for participating in the seismic performance verification of the YJKCAD software are as follows: Figure 7 As shown, in the interface parameter settings, select earthquake information. In the design earthquake grouping of earthquake information, check the box for III, select the fortification intensity for 8 (0.2g), select site category for II, input the characteristic period for 0.45, and input the period reduction factor for 0.7. In the characteristic value input parameter column, select WYD-RITZ for analysis type, set the default value of the number of user-defined vibration modes to 15, and input 95 for the number of vibration modes automatically confirmed by the program. In the column for determining the earthquake internal force symbol by the principal vibration mode, select level I for the seismic resistance grade of the concrete frame, level I for the seismic resistance grade of the shear wall, level III for the seismic resistance grade of the steel frame, do not check the seismic resistance grade of the seismic structural measures, and check the seismic resistance grade of the shear wall in the bottom reinforcement zone of the frame-supported shear wall structure. Automatically increase the seismic resistance level by one level, select the seismic structural measures below the first basement level to gradually decrease the seismic resistance level, and select seismic measures level four; in the structural damping ratio (%) column, select "uniform throughout the building" and enter 30; in the accidental eccentricity column, select "consider accidental eccentricity" and enter 0.05 after X and 0.05 after Y; select "equivalent torque method (traditional method)" for accidental eccentricity calculation method; select "automatically calculate seismic action in the most unfavorable earthquake direction"; enter 0.5 for the representative value combination coefficient of live load and gravity load, enter 0.45 for the maximum value of seismic influence coefficient, and enter 0.9 for the maximum value of seismic influence coefficient used for the verification of weak stories in regular concrete frame structures below 12 stories. After the parameter settings are completed, proceed to the next step of design and calculation.

[0035] In the description of this specification, references to terms such as "an embodiment," "example," and "specific example" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

Claims

1. A method for designing viscous damper parameters based on the optimal additional damping ratio, characterized in that, Specifically, the following steps are included: S1. Establish a non-damped structural model without viscous dampers and calculate the first-order natural frequency of the non-damped structure. ; S2. Calculate the amplitude of the top displacement of the structural model established in step S1 under frequent earthquakes. ; S3. Calculate the absolute displacement amplitude of each floor of the structure. The calculation formula is as follows: （1）， In the formula, This is the first mode shape of the structure; S4, Calculate the structure with dampers. Inter-story displacement amplitude And the average value of inter-story displacement amplitude of floors with dampers The calculation formula is as follows: （2）， （3）， In the formula, n The number of floors equipped with dampers; S5. Calculate the first-order equivalent modal stiffness of the viscous damper connection components. The calculation formula is as follows: （4）， In the formula, For the first j The overall stiffness of the layered damper connection components. For the first floor with dampers j Layer vibration mode displacement, N The total number of viscous dampers on the same floor in the same direction; S6. Calculate the first-order generalized stiffness of the main frame structure. The calculation formula is as follows: （5）， In the formula, The stiffness matrix of the main structure; for The transpose of the matrix; S7. Calculate the ergodic numerical solution of the damping index α of the viscous damper based on the implicit equation. The calculation formula is as follows: （6）， In the formula, For the summation variable; η The implicit function parameter is defined as the displacement utilization coefficient, which satisfies the implicit equation: （7）； S8. Calculate the damping coefficient when the additional damping ratio reaches its maximum value. C The value of is calculated using the following formula: （8）； S9. Calculate the maximum additional damping ratio of the structure based on the parameters obtained in steps S5, S6, S7, and 8. The calculation formula is as follows: （9）， The formula for calculating the gamma function Γ is: （10）， In the formula, For ordinary variables, t For integration variables, e It is a natural constant; S1 0. The maximum additional damping ratio of the structure calculated in step S9 is used as the reference. Compared with the inherent damping ratio of the structure The superposition is performed, and the equivalent linearized model of the viscous damper vibration reduction structure is substituted to carry out structural reinforcement design and seismic performance verification.

2. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 1, characterized in that, In step S1, the first-order natural frequency f of the non-damped structure is calculated using the eigenvector method or the Ritz vector method; in step S2, the amplitude of the top displacement of the structure under frequent earthquakes is calculated. When calculating, modal decomposition response spectrum method or time history analysis method is used.

3. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 1, characterized in that, In step S3, the first-order vibration mode Represented as: （11）， In the formula, This represents the modal displacements of each floor of the structure; First mode The calculation is performed by solving the eigenvalue equation, and the formula is as follows: （12）， In the formula, M The mass matrix of the structure, ω The first natural circular frequency of the structure is... ω =2 πf .

4. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 1, characterized in that, In step S5, the first-order equivalent modal stiffness of the viscous damper connecting component is calculated. K L At that time, the first j Stiffness of layer damper connection components K j The calculation should be based on the type of damper connection components, and the formula is as follows: (1) For support-type connections, K j Calculate using the following formula: （13）， In the formula, , , Let be the elastic modulus, cross-sectional area, and effective length of the support connecting the j-th layer damper, respectively. Let be the angle between the j-th layer damper connection support and the horizontal direction; (2) For wall-mounted connections, K j Calculate using the following formula: （14）， In the formula, E c , G c For the first j The elastic modulus and shear modulus of the concrete used in the layer damper connecting wall; shear modulus G c =0.4 E c ; , h j , I, γ The first j The cross-sectional area, height, moment of inertia, and shape factor of the layer damper connecting wall; shape factor γ =1.

2.

5. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 1, characterized in that, Step S7 solves for parameters. α When traversing numerical solutions, the damping index of the viscous damper is calculated using Newton's iteration method or the bisection method. α The value range of is (0, 1], implicit function parameter η The range of values ​​for is (0, 1).

6. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 5, characterized in that, In step S7, the parameters are solved using formula (6). α When traversing numerical solutions, implicit function parameters η The number of values ​​that can be traversed within the range (0, 1) should be no less than 10,000.

7. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 1, characterized in that, In step S7, the infinite series truncation error on the right side of formula (6) should not exceed 10. -8 This is to ensure sufficient computational accuracy for the numerical equations.

8. The method for designing viscous damper parameters based on the optimal additional damping ratio according to claim 1, characterized in that, In step S9, the calculated maximum additional damping ratio of the structure is obtained. It should not exceed 0.

25. If it exceeds 0.25, it should be reduced. .

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