A method for designing a tuned mass damper structure

Abstract

The application relates to a design method of a mass-spring damper vibration reduction structure, which can realize accurate and efficient control of specific multi-order and high-order modal responses of the structure, selects relative deformation of a mass-spring system installation position as a main degree of freedom, targets the shape of a structure deformation as a vibration mode of the structure, decouples a multi-degree-of-freedom original structure into a plurality of main degree-of-freedom systems of additional masses, calculates mass-spring system parameters required by a control target mode through an analytical expression, and determines an arrangement position. Compared with the prior art, the application can accurately reduce the response of a target mode without changing the period and vibration mode of other modes, and has the advantages of high precision, low calculation amount and easy realization.

Description

Technical Field

[0001] This invention relates to the field of energy dissipation and vibration reduction technology in building structures, and in particular to a method for designing inertial-compression vibration reduction structures. Background Technology

[0002] Multimode vibration contributes significantly to structural response. For structures sensitive to multiple components over a wide frequency range of seismic excitation, tuned damping systems are often used in damping design to control their multimode response. Inertial capacitive tuned damping systems, which include two-node acceleration-related inertial enhancement elements, can flexibly adjust the dynamic characteristics of the structure and have the potential to efficiently reduce the modal response of the structure.

[0003] An inertial container is a two-node inertial vibration-absorbing element, and its significant advantages in structural control have attracted widespread attention in recent years. Inertial containers exhibit significant mass-enhancing characteristics; the inertial force they generate is proportional to the relative acceleration at their two ends. They can achieve structural inertial adjustment with almost no change to the physical mass of the structure and without increasing seismic input. An inertial container system, including inertial elements, spring elements, and damping energy-dissipating elements, can flexibly tune the dynamic characteristics of a structure in terms of inertia, stiffness, and damping. The coordinated work of the mechanical components can transfer a large portion of the energy input from external excitation into the structure to the inertial container system for absorption and dissipation, giving the system a significant advantage in efficient energy absorption and dissipation, thereby reducing the structural vibration response.

[0004] However, existing modal control design methods for inertial capacitive systems either employ optimal tuning formulas based on empirical assumptions, lacking intuitive physical meaning and neglecting the essential understanding and intuitive interpretation of the unique two-node relative acceleration correlation characteristics of the inertial container, making it difficult to fully utilize the inertial enhancement and tuning effects of the inertial capacitive element; or they start with complex multi-degree-of-freedom motion control equations, using optimization algorithms to perform numerous iterations based on empirical assumptions to determine the optimal design parameters. These design methods cannot avoid the influence of unrelated modes outside the target, resulting in low control accuracy, and the design parameters are too large and uneconomical, also weakening the control effect on the target mode. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a high-precision, low-computational-intensity, and easy-to-implement inertial-capacitive damping structure design method based on targeted modal response control.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] This invention provides a method for designing an inertial-capacitive damping structure, the method comprising:

[0008] Using the relative deformation of the inertial-capacitive system installation position as the primary degree of freedom and the mode shape of the targeted control mode as the structural deformation shape, the original multi-degree-of-freedom structure is decoupled into multiple primary degree-of-freedom systems with additional inertial capacities. The parameters of the inertial-capacitive system required to control the target mode are calculated analytically, and the arrangement position is determined.

[0009] Preferably, the method includes the following steps:

[0010] Step S1: Based on the dynamic characteristic analysis of the original multi-degree-of-freedom structure, determine the controlled target mode of the structure and the installation position of the inertial-capacitive system;

[0011] Step S2: Using the relative deformation at the installation location of the inertial-capacitive system as the main degree of freedom, decouple the original structure into an equivalent main degree of freedom system with a specific frequency and deformation shape;

[0012] Step S3: Select the equivalent damping ratio added to the main degree of freedom system and determine the normalized design parameters of the inertial-capacitive system with different connection methods.

[0013] Step S4: Repeat steps S1 to S3 to design response control for all target modes;

[0014] Step S5: Combine the design results of all target modes to obtain the summary results of the parameters and installation positions of each inertial capacitive system;

[0015] Step S6: Verify the structural performance. If it does not meet the requirements, repeat steps S1 to S5 to redetermine the equivalent damping ratio corresponding to the target mode and the inertial capacitive system.

[0016] Preferably, step S1 specifically involves: performing dynamic characteristic analysis on the original structure, evaluating the contribution of each modal response to the actual response of the structure, selecting the target mode to be controlled, and analyzing the floor with the largest relative deformation in the target modal shape as the installation location of the inertial capacitance system.

[0017] Preferably, step S2 specifically involves: establishing a master degree-of-freedom system through modal decomposition; for the target mode, taking the mode shape as the structural deformation shape and the relative deformation at the installation position of the inertial-capacitive system as the master degree of freedom, and decoupling the original structure into an equivalent master degree-of-freedom system with a specific circular frequency and deformation shape.

[0018] Preferably, in step S2, the original structure is decoupled into an equivalent master degree of freedom system with a specific circular frequency and deformable shape, specifically as follows:

[0019] 1) For a specific mode shape φ i ={φ 1,i … φ α,i … φ β,i … φ N,i} T , φα,i φ β,i For any two degrees of freedom α and β in a specific mode shape φ i The position in the middle corresponds to the displacement response u. α and u β The expressions are as follows:

[0020]

[0021] Where the subscript i represents the corresponding mode shape number; q i For a specific vibration mode φ i Generalized coordinates;

[0022] 2) Calculate the relative deformation Δu between degrees of freedom α and β, expressed as:

[0023] Δu=u α -u β =(φ α,i -φ β,i )·q i (2)

[0024] 3) Specific vibration mode φ i ={φ 1,i ... φ α,i ... φ β,i ... φ N,i} T Standardization yields specific vibration modes

[0025] 4) Calculate the dynamic response Δu of the relative deformation between degrees of freedom α and β:

[0026] 5) The actual displacement response u of the structure is obtained by modal superposition.

[0027] Preferably, the specific vibration mode φ i ={φ 1,i ... φ α,i ... φ β,i ... φ N,i} T Standardization, specifically, means: defining a specific vibration mode φ i ={φ 1,i ... φ α,i ... φ β,i ... φ N,i} T Divide by φ α,i -φ β,i Standardization yields the standardized mode shape. The expression is:

[0028]

[0029] Where, φ α,i ≠φ β,i ;

[0030] Substituting equation (3) into equation (2), we obtain the dynamic response of the relative deformation between degrees of freedom α and β:

[0031]

[0032] Preferably, by determining the additional damping ratio ζ eq The normalized design parameters for calculating an inertial-capacitive system include the damping ratio ξ, the inertia-mass ratio μ, and the stiffness ratio κ.

[0033] Preferably, step S3 specifically involves: employing an inertial-capacitive system with a tuned viscous mass damper, i.e., an inertial-capacitive system in which the inertial-capacitive element and the damping element are connected in parallel and then in series with the stiffness element, and selecting the equivalent damping ratio ζ added to the main degrees of freedom system. eq Determine the normalized design parameters:

[0034]

[0035] Where, ζ eq ξ is the equivalent additional damping ratio of the inertial-capacitive system; μ, κ, and ξ are the inertia-mass ratio, stiffness ratio, and damping ratio of the inertial-capacitive system in the main degree of freedom system, respectively.

[0036] Preferably, step S3 specifically involves: using an inertial-capacitive system with a tuned inertial-capacitive damper, i.e., an inertial-capacitive system in which stiffness elements and damping elements are connected in parallel and then in series with inertial-capacitive elements, and selecting an equivalent damping ratio ζ to be added to the main degrees of freedom system. eq Determine the normalized design parameters:

[0037]

[0038] Where, ζ eq ξ is the equivalent additional damping ratio of the inertial-capacitive system; μ, κ, and ξ are the inertia-mass ratio, stiffness ratio, and damping ratio of the inertial-capacitive system in the main degree of freedom system, respectively.

[0039] Preferably, step S4 specifically involves: repeating steps S1 to S3, selecting different mode shapes and master degrees of freedom, performing specific target mode control by installing an inertial-capacitive system at any location on the structure, and designing response control for all target modes.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1) This invention presents a design method for the master degrees of freedom of an inertial capacitive system guided by targeted modal response control. This method fully considers the inertial adjustment mechanism related to the relative acceleration of the two nodes of the inertial container, and uses the inertial capacitive system to precisely tune any multi-order modal response of the structure to achieve targeted modal control without changing the modal information such as the period, mode shape and modal response of other unrelated modes. This significantly reduces the parameters of the inertial capacitive system, ensuring the response damping effect while saving costs.

[0042] 2) The equivalent additional damping ratio is adopted as the design index of the inertial capacitance system. The analytical closed-form design formula of the inertial capacitance system parameters is given, which avoids a lot of iterative calculations and values ​​based on engineering experience. It significantly improves the design efficiency of the inertial capacitance damping structure and has the advantages of high accuracy, low calculation volume and easy implementation. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the transformation of the original structure and installation inertia system in an embodiment of the present invention.

[0044] Figure 2 This is a flowchart illustrating the parameter design of an inertial capacitive system guided by targeted modal control, as described in an embodiment of the present invention.

[0045] Figure 3 This is a schematic diagram of the damper structure, in which, Figure 3 (a) Figure 3 (b) Schematic diagrams of inertial capacitive systems in the form of tuned inertial capacitive dampers and tuned viscous mass dampers, respectively;

[0046] Figure 4 The power spectral density of the top-level displacement response under different orders of controlled modes in this embodiment of the invention is shown on the vertical axis, which represents the power spectral density of the top-level displacement response of the main structure under white noise excitation. Figure 4 (a)~(d) represent controlling the peak value of each modal response individually;

[0047] Figure 5 This is a comparison diagram of the vibration modes of the uncontrolled structure and the controlled structure at the fundamental frequency of the vibration reduction structure according to an embodiment of the present invention. Detailed Implementation

[0048] 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, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0049] Example

[0050] Combination Figure 1 and Figure 2 This embodiment presents a structural design method for inertial-capacitive damping structure guided by targeted modal response control, including the following steps:

[0051] (1) Perform dynamic characteristic analysis on the original structure, evaluate the contribution of each modal response to the actual structural response, and select the target mode to be controlled. Analyze the floor with the largest relative deformation in the target mode shape and use it as the installation location of the inertial-capacitive system.

[0052] (2) A master degree-of-freedom system is established through modal decomposition. For the target mode, the mode shape is taken as the structural deformation shape, and the relative deformation at the installation position of the inertial-capacitive system is taken as the master degree of freedom. The original structure is decoupled into an equivalent master degree-of-freedom system with a specific circular frequency and deformation shape. Using a specific mode shape φ... i In a vibrating structure, any two degrees of freedom α and β are in φ i The position in the middle is φ α,i and φ β,i The displacement response is u α and u β It can be deduced that:

[0053]

[0054] The relative deformation between α and β is

[0055] Δu=u α -u β =(φ α,i -φ β,i )·q i (2)

[0056] φ i ={φ 1,i ... φ α,i ... φ β,i ... φ N,i} T Divide by φ α,i -φ β,i Standardize,

[0057]

[0058] In the formula φ α,i ≠φ β,i Substituting equation (3) into equation (2), we can convert it to:

[0059]

[0060] Equation (4) is essentially equivalent to assuming that α and β are in φ i The relative position in is 1 (i.e., φ) α,i -φ β,iWhen q = 1, the generalized coordinate q i The physical meaning can be interpreted as the dynamic response Δu of the relative deformation between these two degrees of freedom (i.e., Δu = q). i ). q i Defined as "master degree of freedom", a generalized single-degree-of-freedom system with master degree of freedom is defined as a master degree-of-freedom system, and thus the generalized coordinate q can be easily obtained through equation (4). i A concise mathematical expression is derived for the actual relative deformation response Δu between the two degrees of freedom at the installation location, and then the actual displacement response u of the structure is obtained through modal superposition. By selecting different mode shapes and principal degrees of freedom, specific target modal control of an inertial-capacitive system installed at any location on the structure can be effectively achieved.

[0061] (3) Select the equivalent damping ratio added to the main degree of freedom system, and determine the normalized design parameters of the inertial-capacitive system with different connection methods, such as a tuned inertial-capacitive damper or a tuned viscous mass damper, the structure of which is as follows: Figure 3 As shown, the corresponding normalized design parameter expressions are as follows:

[0062]

[0063]

[0064] Where, ζ eq The equivalent additional damping ratio of the inertial-compressive system; μ, κ, and ξ are the inertia-mass ratio, stiffness ratio, and damping ratio of the inertial-compressive system in the main degrees of freedom system, respectively, and are expressed as:

[0065]

[0066] Where c d m in k d These are the damping coefficient, apparent mass, and stiffness of an inertial-compressive system; m * k * It refers to the generalized mass and generalized stiffness of the main structure.

[0067] (4) Repeat steps 1 to 3 to design response control for all target modes.

[0068] (5) By combining the design results of all target modes, the parameters and installation locations of each inertial capacitive system are summarized.

[0069] (6) Verify the structural performance. If it does not meet the requirements, redetermine the equivalent damping ratio corresponding to the target mode and the inertial capacitive system, and repeat steps 1 to 5.

[0070] Based on the above process, a structural design for inertial-capacitive damping guided by targeted modal control can be obtained.

[0071] Function: This invention focuses on the precise control of multi-mode response of structures by inertial-capacitive systems. It proposes a design strategy guided by targeted modal control and provides closed-loop analytical design formulas for the parameters of the inertial-capacitive system. This method uses the relative deformation of the inertial-capacitive system's installation position as the principal degree of freedom and the mode shape of the targeted control mode as the structural deformation shape. It decouples the complex multi-degree-of-freedom original structure into multiple principal degree-of-freedom systems with additional inertial capacities. The required inertial-capacitive system parameters for controlling the target mode are calculated analytically, and their placement is determined. This method can accurately and efficiently reduce the response of the targeted mode without changing the period or mode shape of other modes. Compared to classic inertial-capacitive damping design methods, this method reduces the inertial-capacitive system parameters under the same performance requirements, achieving control of the structural response with smaller design parameters.

[0072] This invention proposes a design method for the master degrees of freedom of an inertial capacitive system guided by targeted modal response control. It fully considers the inertial adjustment mechanism related to the relative acceleration of the two nodes of the inertial container, utilizing the inertial capacitive system to precisely tune any multi-order modal response of the structure, achieving targeted modal control without altering the period, mode shape, and modal response information of other unrelated modes. This method significantly reduces the parameters of the inertial capacitive system, ensuring effective vibration reduction while saving costs. Furthermore, this method uses the equivalent additional damping ratio as the design index of the inertial capacitive system, providing analytical closed-form design formulas for the system parameters. This avoids extensive iterative calculations and reliance on engineering experience, significantly improving the design efficiency of inertial capacitive vibration reduction structures. It boasts advantages such as high accuracy, low computational cost, and ease of implementation.

[0073] The present invention will be described in detail with reference to specific embodiments.

[0074] This example is a 7-story reinforced concrete frame structure (structural damping ratio = 0.05), with a basic seismic intensity of 8 degrees and a seismic fortification category of Class C. According to the "Code for Seismic Design of Buildings" GB50011-2010, the site soil is Class II, and the design seismic group is Group II (Tg = 0.4s). The basic structural information is shown in Table 1.

[0075] Table 1 Basic Structural Information

[0076] Floor number Floor height h / (m) Layer mass (ton) Layer stiffness (kN / mm) 7 3.6 779 365 6 3.6 699 368 5 3.6 699 364 4 3.6 708 416 3 3.6 721 428 2 4.2 737 387 1 4.6 765 650

[0077] The calculation process in this embodiment is as follows:

[0078] By modal decomposition, the original structure is equivalent to a system with 7 decoupled master degrees of freedom, and the frequency of the system is the frequency ω of the structure. i The specific deformation shape of the system is the mode shape φ of each order. i The floor with the largest relative deformation in each mode shape is selected as the principal degree of freedom q. iTherefore, an equivalent single-degree-of-freedom system with tuning and vibration reduction requirements is established for targeted modal response control of the structure. The modal participation factor of the first mode accounts for more than 50%, and the modal participation factors of other modes decrease accordingly. Therefore, in this example, the control of the first modal response of the structure is the primary consideration, while the control of other modes is also considered. Considering the contribution and control requirements of each modal response, the dimensionless design parameters are shown in Table 2. The actual parameters of the inertial-compressive system can be calculated using the dimensionless design parameters. The installation position of the inertial-compressive system is determined according to the location of the maximum relative deformation of each mode. The design results are shown in Table 3.

[0079] Table 2 Dimensionless Standardized Design Parameters for Inertial Capacitance Systems

[0080] Control Mode Inertia-mass ratio stiffness ratio Damping ratio 1 0.65 1.82 0.65 2-4 0.50 1.00 0.35 5-7 0.32 0.45 0.15

[0081] Table 3 Summary of Inertial Capacitance System Specifications

[0082]

[0083] Table 4 compares the periods of the uncontrolled structure and the inertial-compressive damping structure. Each installation of an inertial-compressive system adds one degree of freedom to the structure, thus increasing the original 7 modes to 14. According to the results in Table 4, the periods of adjacent modes in the inertial-compressive damping structure are quite close, roughly distributed on both sides of the original period of the uncontrolled structure, indicating that each mode of the uncontrolled structure is precisely tuned by the corresponding inertial-compressive system.

[0084] Table 4. Period of Uncontrolled Structures and Inertial Compressed Vibration Reduction Structures

[0085]

[0086] Figure 4 The power spectral density of the top-level displacement response under different orders of controlled modes in this embodiment of the invention is shown on the vertical axis, which represents the power spectral density of the top-level displacement response of the main structure under white noise excitation. Figure 4 (a)~(d) represent controlling the peak value of each modal response individually; Figure 5 This is a comparison diagram of the vibration modes of the uncontrolled structure and the controlled structure at the fundamental frequency of the vibration reduction structure according to an embodiment of the present invention.

[0087] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for designing an inertial-capacitive damping structure, characterized in that, The method includes: Step S1: Based on the dynamic characteristic analysis of the original multi-degree-of-freedom structure, determine the controlled target mode of the structure and the installation position of the inertial-capacitive system; Step S2: Using the relative deformation at the installation location of the inertial-capacitive system as the main degree of freedom, decouple the original structure into an equivalent main degree of freedom system with a specific frequency and deformation shape; Step S3: Select the equivalent damping ratio added to the main degree of freedom system and determine the normalized design parameters of the inertial-capacitive system with different connection methods. Step S4: Repeat steps S1 to S3 to design response control for all target modes; Step S5: Integrate the design results of all target modes, allocate the design parameters to each floor, and obtain the summary results of the specifications, quantity and installation location of the inertial capacity system on each floor; Step S6: Verify the structural performance. If it does not meet the requirements, repeat steps S1 to S5 to redetermine the equivalent damping ratio corresponding to the target mode and the inertial capacitive system.

2. The inertial-capacitive damping structure design method according to claim 1, characterized in that, Step S1 specifically involves: performing dynamic characteristic analysis on the original structure, evaluating the contribution of each modal response to the actual response of the structure, selecting the target mode to be controlled, and analyzing the floor with the largest relative deformation in the target mode shape as the installation location of the inertial capacitance system.

3. The inertial-capacitive damping structure design method according to claim 1, characterized in that, Step S2 specifically involves: establishing a master degree-of-freedom system through modal decomposition. For the target mode, the mode shape is taken as the structural deformation shape, and the relative deformation at the installation position of the inertial-capacitive system is taken as the master degree of freedom. The original structure is decoupled into an equivalent master degree-of-freedom system with a specific circular frequency and deformation shape.

4. The inertial-compression damping structure design method according to claim 3, characterized in that, In step S2, the original structure is decoupled into an equivalent master degree-of-freedom system with a specific circular frequency and deformation shape. When the relative deformation of any two degrees of freedom in a specific mode shape is 1, the physical meaning of the generalized coordinates is interpreted as the dynamic response of the relative deformation between the selected two degrees of freedom. This generalized coordinate is defined as the master degree of freedom to represent the relative deformation response of the inertial-capacitive system's installation position. Specifically, the equivalent single-degree-of-freedom system with master degrees of freedom is defined as the master degree-of-freedom system. 1) For a specific mode shape , For any two degrees of freedom and In a specific vibration mode The position in the middle, the corresponding displacement response and The expressions are as follows: （1） Among them, subscript The corresponding mode number; For a specific vibration mode Generalized coordinates; 2) Calculate the degrees of freedom and Relative deformation between The expression is: （2） 3) Specific vibration modes Standardization yields specific vibration modes ; 4) Calculate the degrees of freedom and Dynamic response of relative deformation between ; 5) Obtain the actual displacement response of the structure through modal superposition. .

5. The inertial-capacitive damping structure design method according to claim 4, characterized in that, The specific vibration mode Standardization, specifically, means: defining a specific mode shape. Divide by Standardization yields the standardized mode shape. The expression is: （3） in, ; Substituting equation (3) into equation (2) yields the degrees of freedom. and Dynamic response of relative deformation between: （4）。 6. The inertial-capacitive damping structure design method according to claim 1, characterized in that, In step S3, the additional equivalent damping ratio is determined. To calculate the normalized design parameters of an inertial-capacitive system, including the damping ratio. Inertia-mass ratio Stiffness ratio .

7. The inertial-capacitive damping structure design method according to claim 6, characterized in that, Step S3 specifically involves: using an inertial-capacitive system with a tuned viscous mass damper, i.e., an inertial-capacitive system in which the inertial-capacitive element and the damping element are connected in parallel and then in series with the stiffness element, selecting the equivalent damping ratio added to the main degrees of freedom system. Determine the normalized design parameters: （5） in, The equivalent damping ratio added to the inertial-capacitive system; , , These represent the inertia-mass ratio, stiffness ratio, and damping ratio of the inertial-compressive system in the main degree of freedom system, respectively.

8. The inertial-capacitive damping structure design method according to claim 6, characterized in that, Step S3 specifically involves: using an inertial capacitive system with a tuned inertial capacitive damper, i.e., an inertial capacitive system in which stiffness elements and damping elements are connected in parallel and then in series with inertial capacitive elements, and selecting the equivalent damping ratio added to the main degrees of freedom system. Determine the normalized design parameters: （6） in, The equivalent damping ratio added to the inertial-capacitive system; , , These represent the inertia-mass ratio, stiffness ratio, and damping ratio of the inertial-compressive system in the main degree of freedom system, respectively.

9. The inertial-capacitive damping structure design method according to claim 1, characterized in that, Step S4 specifically involves repeating steps S1 to S3, selecting different mode shapes and master degrees of freedom, performing specific target mode control by installing an inertial-capacitive system at any location on the structure, and designing response control for all target modes.

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