An optimization design method of an adaptive damping vibration reduction system and a damping vibration reduction system

Abstract

The application belongs to the technical field of vibration control, and discloses an optimization design method of a self-adaptive damping vibration reduction system and the damping vibration reduction system, wherein the damping vibration reduction system comprises a mass inertia unit and a plurality of branch units arranged in parallel, each branch unit comprises a damping element and a stiffness element arranged in series, and the optimization design method comprises the following steps: S1, determining the lowest damping ratio required by low-order modes and high-order modes of a controlled structure respectively; S2, setting a constraint equation according to the lowest damping ratio required by the low-order modes and the high-order modes of the controlled structure respectively; and S3, obtaining the setting parameters of the damping vibration reduction system by using an optimization algorithm according to the constraint equation. The setting parameters of the damping vibration reduction system are optimized by using the constraint equation, so that the damping vibration reduction system can meet the damping requirements of the low-order modes and the high-order modes of the controlled structure respectively, and has the self-adaptive characteristic, thereby having a good control effect on the multi-modal vibration control of the controlled structure.

Description

Technical Field

[0001] This invention belongs to the field of vibration control technology, and more specifically, relates to an optimization design method and a damping vibration reduction system for an adaptive damping vibration reduction system. Background Technology

[0002] Currently, vibration control methods for structures generally include passive and semi-active control methods. However, for multi-modal control, conventional passive control often fails to meet the requirements, while semi-active control is mainly limited by its energy requirements and large size. Taking cable vibration control as an example, as the span of cable-stayed bridges increases, the cables also become longer, with many cables exceeding 600 meters. At this point, conventional passive control methods, due to fixed damping coefficients and installation location limitations, struggle to provide effective control across a wide range of vibration modes for ultra-long cables. While semi-active control offers better control performance than passive control in cable control, it requires external power supply, necessitating sophisticated energy storage equipment, which limits its application in bridges.

[0003] Existing vibration control methods for structures have the problem that conventional passive control cannot meet the requirements for multimodal control. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides an optimized design method and a damping vibration reduction system for an adaptive damping vibration reduction system. This solves the problem that conventional passive control methods cannot meet the requirements for multi-modal control of existing structures. The aim is to achieve a semi-active control effect by using passive control methods.

[0005] To achieve the above objectives, according to one aspect of the present invention, an optimization design method for an adaptive damping vibration reduction system is provided. The damping vibration reduction system includes inertial mass units arranged in parallel and multiple branch units, each of the branch units including a damping element and a stiffness element arranged in series. The optimization design method includes:

[0006] S1, the vibration modes of the controlled structure are divided into low-order modes and high-order modes, wherein the order of the low-order modes is less than the order of the high-order modes, and the minimum damping ratio required for the low-order modes and high-order modes of the controlled structure is determined respectively;

[0007] S2, according to the minimum damping ratios required for the low-order and high-order modes of the controlled structure, set constraint equations, wherein the modal damping ratio of the controlled structure after the installation of the damping and vibration reduction system is greater than or equal to the corresponding minimum damping ratio;

[0008] S3. Based on the constraint equations, the setting parameters of the damping vibration reduction system are obtained using an optimization algorithm.

[0009] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, S2 further includes: setting an optimization objective, wherein the optimization objective is to maximize the minimum damping ratio among the modal damping ratios of the controlled structure after the installation of the damping vibration reduction system, and establishing an optimization equation based on the optimization objective;

[0010] Accordingly, S3 specifically involves: obtaining the global optimal solution for the setting parameters of the damping vibration reduction system using an optimization algorithm based on the constraint equation and the optimization equation.

[0011] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, the minimum damping ratio required for the low-order and high-order modes of the controlled structure in S1 is determined according to the specification requirements or design parameters.

[0012] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, the constraint equation in S2 is specifically as follows:

[0013]

[0014] Where p is the maximum modal order of the controlled structure; n is the order boundary point distinguishing between low-order and high-order modes; and ξ is the minimum damping ratio required for the low-order and high-order modes of the controlled structure, respectively. limit,1 and ξ limit,2 ξ j The damping ratio of the j-th mode of the controlled structure after the installation of the damping and vibration reduction system.

[0015] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, in S2, after the damping vibration reduction system is installed, the modal damping ratio of the controlled structure is determined based on the equivalent stiffness and equivalent damping of the damping vibration reduction system, the installation parameters of the damping vibration reduction system, and the vibration parameters of the controlled structure.

[0016] The equivalent stiffness and equivalent damping of the damping vibration reduction system are calculated in the following way:

[0017]

[0018]

[0019] in, and These represent the equivalent stiffness and equivalent damping of the damping and vibration reduction system, respectively; m is the number of branch units; ω is the vibration frequency of the controlled structure; k i β is the stiffness coefficient of the i-th branch element;i The stiffness coefficient and damping coefficient c of the i-th branch element i The ratio; m e is the mass coefficient of the inertial mass unit.

[0020] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, the inertial mass coefficient of the inertial mass unit is designed according to the equivalent stiffness of the damping vibration reduction system, so that the equivalent stiffness decreases as the vibration frequency of the controlled structure increases.

[0021] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, the inertial mass coefficient m of the inertial mass unit is... e Calculated in the following way:

[0022]

[0023] Where γ is the adjustment coefficient; m is the number of branch units; ω0 is the vibration frequency of the lowest-order mode of the controlled structure; k i β is the stiffness coefficient of the i-th branch element; i The stiffness coefficient and damping coefficient c of the i-th branch element i The ratio.

[0024] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, S3 specifically includes:

[0025] S31, in the j-th design loop, firstly, randomly generate the initial parameters P for optimization within the solution space. st,j ;

[0026] S32, using P st,j The constraint equations and the optimization equations are used to find P using an optimization algorithm. st,j Nearby local optimal solution P local，j ;

[0027] S33, according to P local,j Calculate the modal damping ratios of the controlled structure after installing the damping and vibration reduction system, and determine the minimum damping ratio ξ among the modal damping ratios. min,j ;

[0028] S34, if ξ min,j >ξ min,0 ξ min，0 Let ξ be the initially set minimum damping ratio. min,0 =ξ min,j And store the local optimal parameters in P. op China P op =P local,j ;

[0029] S35. If j < N, where N is the pre-set number of optimization iterations, then j = j + 1, and return to S32 to restart the loop optimization calculation using the local optimal solution until j = N, and then output the global optimal solution.

[0030] According to the optimization design method of the adaptive damping vibration reduction system provided by the present invention, after S3, it further includes:

[0031] S4. Based on the global optimal solution of the parameters of the damping vibration reduction system, eliminate the branch units in which the damping coefficient of the damping element or the stiffness coefficient of the stiffness element is less than the preset value. The remaining branch units and the inertance unit form the final damping vibration reduction system.

[0032] According to another aspect of the present invention, there is provided a damping vibration reduction system, including an inertance unit and a plurality of branch units arranged in parallel. Each branch unit includes a damping element and a stiffness element arranged in series. The setting parameters of the damping vibration reduction system are determined according to the optimization design method of the adaptive damping vibration reduction system described in any one of the above.

[0033] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the optimization design method of the adaptive damping vibration reduction system and the damping vibration reduction system provided by the present invention:

[0034] 1. By using the modal damping ratio of the controlled structure after installing the damping vibration reduction system being greater than or equal to the minimum damping ratio corresponding to the requirements as the constraint equation to optimize and obtain the setting parameters of the damping vibration reduction system, the damping vibration reduction system can meet the damping requirements for the low-order and high-order modes of the controlled structure respectively, and the equivalent stiffness and damping coefficient of the system can change with the change of the vibration frequency. Therefore, compared with the traditional passive control damper, the present invention has an adaptive characteristic and has a good control effect on the multi-modal vibration control of the controlled structure.

[0035] 2. The damping vibration reduction system essentially still belongs to a new type of passive control structure and does not require additional energy supply. Therefore, it is less restricted by the surrounding environment, and due to being a passive control, its reliability and stability are guaranteed. Therefore, it has certain advantages compared with semi-active control methods.

[0036] 3. The structure of the damping vibration reduction system is simple, and the Maxwell unit therein can be replaced by materials with damping and stiffness commonly used in engineering, with low cost, easy implementation, and has a wide engineering application prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a schematic diagram of the model of the damping vibration reduction system provided by the present invention;

[0038] Figure 2This is a flowchart of the main steps of the optimization design method for the adaptive damping vibration reduction system provided by the present invention;

[0039] Figure 3 This is a schematic diagram of the equivalent damping variation of the damping and vibration reduction system provided by the present invention;

[0040] Figure 4 This is a schematic diagram of the equivalent stiffness change of the damping vibration reduction system provided by the present invention;

[0041] Figure 5 This is a schematic diagram of the installation of the damping vibration reduction system provided by the present invention on the cable when used for cable vibration reduction control;

[0042] Figure 6 This is a schematic diagram comparing the modal damping ratios of the cable and the viscous damper after optimal design when the damping and vibration reduction system provided by this invention is used for cable installation.

[0043] Figure 7 This is a comparison diagram of the mid-span displacement of the cable with the damping and vibration reduction system provided by this invention installed and with the cable with the viscous damper installed;

[0044] Figure 8 This is a comparison diagram of the 61st-order mid-span acceleration of a cable with the damping and vibration reduction system provided by this invention installed and with a viscous damper installed. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0046] Please see Figure 1 This invention provides an optimized design method for an adaptive damping vibration reduction system. The damping vibration reduction system includes a mass unit and multiple branch units arranged in parallel. Each branch unit includes a damping element and a stiffness element arranged in series. The branch units are Maxwell elements, and the mass unit is connected in parallel with each Maxwell element. By introducing the mass unit, the dynamic stiffness of the vibration reduction system under high-frequency vibration can be effectively reduced, thereby improving its control performance in high-frequency vibration of the controlled structure.

[0047] The mass coefficient m of an inertial mass unit e The damping coefficient c of the Maxwell element damping element numbered i. i The stiffness coefficient k of the stiffness element iThe number of branch units, m, can be designed using the parameter optimization method proposed in this invention, thereby optimizing the performance of the vibration reduction system in structural multimodal vibration control; Reference Figure 2 The optimization design method includes:

[0048] S1, the vibration modes of the controlled structure are divided into low-order modes and high-order modes, wherein the order of the low-order modes is less than the order of the high-order modes, and the minimum damping ratio required for the low-order modes and high-order modes of the controlled structure is determined respectively;

[0049] S2, Based on the minimum damping ratios required for the low-order and high-order modes of the controlled structure, constraint equations are set. The constraint equations state that the modal damping ratio of the controlled structure after installing the damping and vibration reduction system is greater than or equal to the corresponding minimum damping ratio; that is, after installing the damping and vibration reduction system, the modal damping ratio of the controlled structure in the low-order mode is greater than or equal to the minimum damping ratio required for the low-order mode of the controlled structure, and the modal damping ratio of the controlled structure in the high-order mode is greater than or equal to the minimum damping ratio required for the high-order mode of the controlled structure.

[0050] S3. Based on the constraint equations, the setting parameters of the damping vibration reduction system are obtained using an optimization algorithm. This ensures that the modal damping ratio of the controlled structure satisfies the aforementioned constraint equations after the installation of the damping vibration reduction system, thereby enabling the damping vibration reduction system to meet the damping requirements of the low-order and high-order modes of the controlled structure.

[0051] The adaptive damping vibration reduction system optimization design method provided by this invention optimizes the setting parameters of the damping vibration reduction system by using the constraint equation that the modal damping ratio of the controlled structure after the installation of the damping vibration reduction system is greater than or equal to the corresponding minimum damping ratio. This enables the damping vibration reduction system to meet the vibration reduction damping requirements of the low-order and high-order modes of the controlled structure, and the equivalent stiffness and damping coefficient of the system can change with the vibration frequency. Therefore, compared with traditional passive control dampers, this invention has adaptive characteristics and has a good control effect on the multimodal vibration control of the controlled structure.

[0052] This invention is essentially a novel passive control structure that requires no additional energy, thus being less affected by the surrounding environment. Furthermore, due to its passive control nature, its reliability and stability are guaranteed, giving it advantages over semi-active control methods. The structure of this invention is extremely simple, and the Maxwell unit can be replaced with commonly used engineering materials with damping and stiffness, resulting in lower costs, easier implementation, and broad engineering application prospects.

[0053] Furthermore, S2 also includes: setting an optimization objective, wherein the optimization objective is to maximize the minimum damping ratio among the modal damping ratios of the controlled structure after the installation of the damping and vibration reduction system, and establishing an optimization equation based on the optimization objective;

[0054] Accordingly, S3 specifically involves: obtaining the globally optimal solution for the setting parameters of the damping vibration reduction system using an optimization algorithm based on the constraint equations and the optimization equations. By setting the above optimization objective, and using the above optimization objective as the criterion for determining the optimal solution during the optimization calculation of the damping vibration reduction system setting parameters, it is possible to obtain the damping vibration reduction system setting parameters that satisfy the constraint equations and have the largest minimum damping ratio, i.e., to obtain the globally optimal solution, thereby optimizing the vibration control performance of the damping vibration reduction system.

[0055] Specifically, the minimum damping ratios required for the lower-order and higher-order modes of the controlled structure described in S1 are determined according to specifications or design parameters. The minimum damping ratio ξ for the lower-order modes... limit，1 and the minimum higher-order modal damping ratio ξ limit，2 The values ​​can be set according to the specifications or the designer's experience. For example, taking the ultra-long cable of a cable-stayed bridge as an example, the logarithmic decay rate of its low-order modes should be greater than 0.5% (specification). The logarithmic decay rate of the high-order modes can be taken as 0.16% according to the designer's experience. The boundary between low-order and high-order modes is 15th order, that is, modes less than 15th order are low-order modes, and modes greater than or equal to 15th order are high-order modes.

[0056] In some specific embodiments, the constraint equations in S2 are specifically as follows:

[0057]

[0058] Where p is the maximum modal order of the controlled structure; n is the order boundary point distinguishing between low-order and high-order modes; and ξ is the minimum damping ratio required for the low-order and high-order modes of the controlled structure, respectively. limit，1 and ξ limit，2 ξ j The damping ratio of the controlled structure after the installation of the damping and vibration reduction system is the j-th modal damping ratio. Taking a cable as an example, for an ultra-long cable exceeding 500 meters in length, generally p is greater than 60th order and n is around 15th order.

[0059] After the damping and vibration reduction system is installed in S2, the modal damping ratio of the controlled structure is determined based on the equivalent stiffness and equivalent damping of the damping and vibration reduction system, the installation parameters of the damping and vibration reduction system, and the vibration parameters of the controlled structure. The equivalent stiffness and equivalent damping of the damping and vibration reduction system are calculated in the following manner:

[0060]

[0061]

[0062] in, and These represent the equivalent stiffness and equivalent damping of the damping and vibration reduction system, respectively; m is the number of branch units; ω is the vibration frequency of the controlled structure; k i β is the stiffness coefficient of the i-th branch element; i The stiffness coefficient and damping coefficient c of the i-th branch element i The ratio; m e is the mass coefficient of the inertial mass unit.

[0063] In some specific embodiments, the inertial mass coefficient of the inertial mass unit is designed according to the equivalent stiffness of the damping vibration reduction system, so that the equivalent stiffness decreases as the vibration frequency of the controlled structure increases; thereby facilitating multimodal vibration control.

[0064] The mass coefficient of the mass unit can be derived from the formula for calculating equivalent stiffness, ensuring that the mass coefficient setting meets the above requirements. Specifically, the mass coefficient m of the mass unit... e Calculated in the following way:

[0065]

[0066] Where γ is the adjustment coefficient; m is the number of branch units; ω0 is the vibration frequency of the lowest-order mode of the controlled structure; k i β is the stiffness coefficient of the i-th branch element; i The stiffness coefficient and damping coefficient c of the i-th branch element i The ratio.

[0067] In some specific embodiments, S3 specifically includes:

[0068] S31, in the j-th design loop, firstly, randomly generate the initial parameters P for optimization within the solution space. st,j ;

[0069] S32, using P st，j The constraint equations and the optimization equations are used to find P using an optimization algorithm. st，j Nearby local optimal solution P local,j ;

[0070] S33, according to P local,j Calculate the modal damping ratios of the controlled structure after installing the damping and vibration reduction system, and determine the minimum damping ratio ξ among the modal damping ratios. min,j ;

[0071] S34, if ξ min,j >ξ min,0, ξ min，0 is the minimum damping ratio of the initial setting. Let ξ min，0 = ξ min,j and store the locally optimal parameters in P op in P op = P local,j ;

[0072] S35, if j < N, where N is the number of optimization times of the initial setting, then j = j + 1, and return to S32 to restart the loop optimization calculation using the locally optimal solution until j = N, and output the approximate global optimal solution.

[0073] Furthermore, after S3, it further includes:

[0074] S4, based on the global optimal solution of the parameters of the damping and vibration reduction system, eliminate the branch unit whose damping coefficient of the damping element or the stiffness coefficient of the stiffness element is less than the preset value. The remaining branch units and the inertance unit form the final damping and vibration reduction system. For the Maxwell unit with a very small stiffness or damping coefficient, since the stiffness and damping are in series, any one of the coefficients being too small will make the output of this unit extremely small. Therefore, for the simplicity of the structure, this unit branch can be eliminated. Specifically, when the damping coefficient of the damping element or the stiffness coefficient of the stiffness element is less than 10 -1 , eliminate the branch unit where it is located.

[0075] The present invention also provides a damping and vibration reduction system, which includes an inertance unit and multiple branch units arranged in parallel. Each branch unit includes a damping element and a stiffness element arranged in series. The setting parameters of the damping and vibration reduction system are determined according to the optimization design method of the adaptive damping and vibration reduction system described in any one of the above.

[0076] Specific example

[0077] Based on the problems existing in the prior art, this embodiment proposes a passive control method with a damping coefficient that can change with the vibration frequency. Due to its variable damping coefficient characteristics, it has a certain adaptive characteristic and has broad application prospects. This embodiment specifically provides a damping and vibration reduction system with adaptive damping and adaptive stiffness and a parameter optimization method, aiming to approximately achieve the semi-active control effect by passive control means. Refer to Figure 2 , this damping and vibration reduction system includes:

[0078] It is composed of an inertance unit and m branch units in parallel. Each branch unit consists of a Maxwell unit; the Maxwell unit is composed of a viscous damper and a stiffness element in series, and in engineering, it can be replaced by common materials with damping and stiffness properties; refer to Figure 2The steps of the parameter optimization method for the damped vibration reduction system with adaptive damping and adaptive stiffness include:

[0079] (1) Determine the minimum damping ratio ξ required for the lower-order and higher-order modes of the controlled structure. limit,1 and ξ limit,2 ;

[0080] (2) Set the initial values ​​for the solution: number of optimization attempts N, initial minimum damping ratio ξ min,0 And the number of Maxwell cells, m;

[0081] (3) Using ξ limit,1 and ξ limit,2 Write the constraint equations f cons And based on the optimization objective of maximizing the minimum damping ratio within the controlled modal range, the optimization equation f is written. op ;

[0082] (4) Using f cons and f op Two equations are used, and the global optimal solution P for the system parameters is found by performing an optimization loop using the Optimization Toolbox in Matlab. op ;

[0083] (5) In P op After removing branches whose parameters approach zero and contribute little to vibration control, the remaining branches form the optimized damping vibration reduction system.

[0084] The number of optimization attempts, N, should be large enough so that the final result is closer to the true global optimum. Specifically, N can be 8000 or more.

[0085] The sub-steps for writing constraint equations and optimization equations are as follows:

[0086] First, the equivalent stiffness and equivalent damping of the damping vibration reduction system are obtained according to the relevant calculation formulas;

[0087] Then, the modal damping ratio expression is calculated based on the equivalent stiffness and equivalent damping.

[0088] Then, constraint equations are constructed based on the expressions for equivalent stiffness, equivalent damping, and modal damping ratio.

[0089] The expressions for the modal damping ratio differ depending on the controlled structure after installing a damping and vibration reduction system. The expression for the modal damping ratio in cables is listed here:

[0090]

[0091] Where ξ j ω is the damping ratio of the j-th mode; jLet be the j-th modal vibration frequency of the controlled structure; is the equivalent installation position of the damping vibration reduction system; l is the cable length; T is the axial cable force.

[0092] Construct the optimization objective equation f op :

[0093] f op =max(ξ min );

[0094] Where ξ min It is the minimum damping ratio within the modal range of the controlled structure.

[0095] In step (4), when performing optimization calculations using optimization algorithms from software such as Matlab, the parameter that needs to be optimized is the stiffness coefficient k of each Maxwell element. i Damping coefficient c i and inertia coefficient m e , where m e Satisfy the following formula:

[0096]

[0097] Where γ is the adjustment coefficient, β i stiffness divided by damping k i / c i Therefore, the parameters that need to be optimized become γ and β. i and k i .

[0098] Furthermore, in step (4), the specific parameter design process is as follows:

[0099] In the j-th design loop, the initial parameters P for optimization are first randomly generated within the solution space. st,j =[k j β j γ j ]; where k j =[k1k2…k m And β j =[β1β2…β m ];

[0100] Using P st，j and f cons and f op Use Matlab's Optimization Toolbox to find P st，j Nearby local optimal solution P local，j ;

[0101] According to P local,jCalculate the modal damping ratios of each order of the controlled structure and find the minimum value ξ min，j ;

[0102] If ξ min，j >ξ min，0 , let ξ min，0 =ξ min,j and store the local optimal parameters in P op where P op =P local,j ;

[0103] If j < N, then j = j + 1 and return to the start of the loop again, otherwise jump out of the loop.

[0104] At this time, after N loops, when N is large enough, P op will be very close to the theoretically optimal parameters.

[0105] The parameter settings of the damping and vibration reduction system obtained according to the described optimization method can make the equivalent damping decrease with the increase of frequency, and at the same time make the equivalent stiffness small enough or even generate negative equivalent stiffness in the high-order vibration modes, which is beneficial to multi-modal vibration control.

[0106] Through the research on the damping and vibration reduction system with adaptive damping and adaptive stiffness and the parameter optimization method proposed in this embodiment, it is found that the equivalent damping coefficient of the system is approximately inversely proportional to the cable vibration frequency, and the equivalent stiffness also decreases monotonically after exceeding a certain frequency range. These characteristics are very beneficial to the multi-modal vibration control of the structure. Therefore, the multi-modal vibration of the controlled structure can be effectively controlled by this new damping and vibration reduction system.

[0107] As Figure 3 and Figure 4 shown, through numerical analysis, it can be found that the equivalent damping of the present invention decreases continuously with the increase of the vibration frequency, and at the same time its equivalent stiffness also decreases continuously in the high-frequency region, so the present invention has certain adaptive characteristics;

[0108] According to Figure 5 shown, a numerical simulation was carried out on the installation of a damping and vibration reduction system with adaptive damping and adaptive stiffness proposed in the present invention on a 609-meter ultra-long cable, and the installation position was at 2.2%l from the left end point of the cable.

[0109] The modal damping ratios of each order are as Figure 6 shown, and it can be found that the modal damping ratio of the present invention after optimal design can not only meet the requirements of the lowest damping ratio of the low order, but also the damping ratio of the high order is large enough. Compared with the viscoelastic damper (VD) with the same optimal design, it has better multi-modal control performance;

[0110] The control effect of the high order of the present invention is as Figure 7 and Figure 8 As shown, these two figures compare the displacement and acceleration time history curves at the mid-span of the cable under high-frequency load (61st stage) with the present invention and conventional VD, respectively. It can be seen from the figures that the present invention has better displacement and acceleration control effects compared to VD. Figure 6 The conclusions in the text are largely consistent.

[0111] This invention enables a damping vibration reduction system to adaptively adjust its equivalent damping coefficient and equivalent stiffness based on the vibration frequency of the controlled structure, thus exhibiting adaptive characteristics. Therefore, this method offers better control performance in multimodal vibration control of structures compared to traditional passive dampers. Furthermore, this invention is essentially a novel passive control method, requiring no energy input, minimally affected by environmental constraints, and possessing a simple structure. Maxwell elements can be approximated using materials with common engineering properties exhibiting stiffness and damping characteristics. Additionally, due to the adaptive characteristics of this damping model, its equivalent coefficient decreases with increasing vibration frequency, which is beneficial for vibration control over a wide frequency range. In conclusion, this novel damping vibration reduction system has significant engineering application prospects.

[0112] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimization design method for an adaptive damping vibration reduction system, characterized in that, The damping vibration reduction system includes parallel-connected inertial mass units and multiple branch units. Each branch unit includes a damping element and a stiffness element connected in series. The optimization design method includes: S1, the vibration modes of the controlled structure are divided into low-order modes and high-order modes, wherein the order of the low-order modes is less than the order of the high-order modes, and the minimum damping ratio required for the low-order modes and high-order modes of the controlled structure is determined respectively; S2, according to the minimum damping ratios required for the low-order and high-order modes of the controlled structure, set constraint equations, wherein the modal damping ratio of the controlled structure after the installation of the damping and vibration reduction system is greater than or equal to the corresponding minimum damping ratio; S3. Based on the constraint equations, the setting parameters of the damping vibration reduction system are obtained using an optimization algorithm. S2 further includes: setting an optimization objective, wherein the optimization objective is to maximize the minimum damping ratio in the modal damping ratio of the controlled structure after the installation of the damping and vibration reduction system, and to establish an optimization equation based on the optimization objective; Accordingly, S3 specifically involves: obtaining the global optimal solution of the setting parameters of the damping vibration reduction system using an optimization algorithm based on the constraint equation and the optimization equation; After the damping and vibration reduction system is installed in S2, the modal damping ratio of the controlled structure is determined based on the equivalent stiffness and equivalent damping of the damping and vibration reduction system, the installation parameters of the damping and vibration reduction system, and the vibration parameters of the controlled structure. The equivalent stiffness and equivalent damping of the damping vibration reduction system are calculated in the following way: ； ； in, and These are the equivalent stiffness and equivalent damping of the damping and vibration reduction system, respectively. m The number of the branch units; The vibration frequency of the controlled structure; For the first The stiffness coefficient of each of the branch units; For the first The stiffness coefficient and damping coefficient of each of the branch units The ratio; The mass coefficient of the inertial mass unit; The inertial coefficient of the inertial unit Calculated in the following way: ； in, For adjustment coefficients; m The number of the branch units; The vibration frequency of the lowest-order mode of the controlled structure; For the first The stiffness coefficient of each of the branch units; For the first The stiffness coefficient and damping coefficient of each of the branch units The ratio.

2. The optimization design method for the adaptive damping vibration reduction system as described in claim 1, characterized in that, The minimum damping ratios required for the low-order and high-order modes of the controlled structure described in S1 are determined according to the specifications or design parameters.

3. The optimization design method for the adaptive damping vibration reduction system as described in claim 1 or 2, characterized in that, The constraint equations described in S2 are as follows: ； in, The maximum modal order of the controlled structure; To distinguish the order boundary between low-order and high-order modes; the minimum damping ratios required for the low-order and high-order modes of the controlled structure are respectively: and ; For the controlled structure after the installation of the damping vibration reduction system j First-order mode damping ratio.

4. The optimization design method for the adaptive damping vibration reduction system as described in claim 1 or 2, characterized in that, The inertial mass coefficient of the inertial mass unit is designed according to the equivalent stiffness of the damping vibration reduction system, so that the equivalent stiffness decreases as the vibration frequency of the controlled structure increases.

5. The optimization design method for the adaptive damping vibration reduction system as described in claim 1, characterized in that, S3 specifically includes: S31, in the j In each design cycle, initial parameters for optimization are first randomly generated within the solution space. ; S32, utilizing The constraint equations and the optimization equations are used to find the optimal solution using an optimization algorithm. Local optimal solutions nearby ; S33, according to Calculate the modal damping ratios of the controlled structure after installing the damping and vibration reduction system, and determine the minimum damping ratio among the modal damping ratios. ; S34, if , Let the initial minimum damping ratio be set. And store the local optimal parameters to middle ; S35, if , N For the initial number of optimization attempts, then Then return to S32 and restart the iterative optimization calculation using the local optimum until... Output the globally optimal solution.

6. The optimization design method for the adaptive damping vibration reduction system as described in claim 1, characterized in that, S3 is followed by: S4. Based on the global optimal solution of the damping and vibration reduction system setting parameters, the branch units whose damping coefficient of the damping element or the stiffness coefficient of the stiffness element is less than the preset value are eliminated, and the remaining branch units and the inertial mass unit form the final damping and vibration reduction system.

7. A damping vibration reduction system, characterized in that, It includes inertial mass units arranged in parallel and multiple branch units, each of the branch units including damping elements and stiffness elements arranged in series, and the setting parameters of the damping vibration reduction system are determined according to the optimization design method of the adaptive damping vibration reduction system according to any one of claims 1-6.

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