CN104895210B

CN104895210B - Optimal design method of double-layer tuned mass damper based on connection stiffness

Info

Publication number: CN104895210B
Application number: CN201510306474.3A
Authority: CN
Inventors: 李春祥; 曹黎媛; 迟恩楠
Original assignee: SHANGHAI UNIVERSITY
Current assignee: SHANGHAI UNIVERSITY
Priority date: 2015-06-05
Filing date: 2015-06-05
Publication date: 2017-07-25
Anticipated expiration: 2035-06-05
Also published as: CN104895210A

Abstract

The invention discloses an optimal design method for a dual tuned mass damper based on connection stiffness. The present invention adopts the following technical solutions: 1) Establishing the structure-SDTMD system model; 2) Establishing the structure-SDTMD system and dynamic equations; 3) Using the genetic algorithm to optimize the parameters of the double tuned mass damper based on the connection stiffness; 4) Through comparison, select the optimal combination parameters to design an optimized dual tuned mass damper based on connection stiffness. The innovation of the present invention lies in the design of a new type of double tuned mass damper based on connection stiffness, which is applicable to all structures. .

Description

Optimal design method of double-layer tuned mass damper based on connection stiffness

技术领域technical field

本发明涉及一种基于连接刚度的双层调谐质量阻尼器(Stiffness based doubletuned mass dampers，SDTMD)优化设计方法。The invention relates to an optimal design method of a double-layer tuned mass damper (Stiffness based doubletuned mass dampers, SDTMD) based on connection stiffness.

背景技术Background technique

地震作为严重威胁人类生命财产安全的自然灾害，给人类造成了巨大的灾害，是众多地震多发国之一，例如近几年来发生的汶川地震、日本地震、雅安地震。这些大地震不仅造成了重大的经济损失，还给人们带来了巨大的悲痛和严重的心里伤害。21世纪，随着世界经济的高速发展，人们对工程结构的安全性和防灾性提出了越来越高的要求，要求工程结构在自然灾害(例如强震和台风)突发时能不被破坏，而且要求工程结构在其作用下能够无受损伤。于是我们对工程结构的防灾减灾提出了一些革命性的要求，而结构振动控制技术有望是实现这一防灾减灾革命性要求的根本途径。传统的结构抗震设计一般是通过增强建筑结构自身的强度与刚度来抵抗外荷载的作用，从而达到抗震的效果。所以我们在进行抗震设计时，首先需要准确估计结构所要承受的外部荷载、把握所用材料的特性，并且需要选择合理的设计及分析方法。但是地震荷载的高度不确定性、材料的非线性和使用时性能的变异以及现有结构分析和设计方法的局限性使得结构存在不满足使用功能和安全的要求的可能性。考虑到传统结构抗震设计方法的局限性，业界学者们开始对此不断探求新的方法，结构振动控制的设计方法就是在这种情况下产生并发展的。As a natural disaster that seriously threatens the safety of human life and property, earthquake has caused huge disasters to human beings. It is one of the many earthquake-prone countries, such as the Wenchuan earthquake, Japan earthquake, and Ya'an earthquake that occurred in recent years. These major earthquakes not only caused great economic losses, but also brought great grief and serious psychological damage to people. In the 21st century, with the rapid development of the world economy, people have put forward higher and higher requirements for the safety and disaster prevention of engineering structures. damage, and requires that the engineering structure can not be damaged under its action. So we put forward some revolutionary requirements for disaster prevention and mitigation of engineering structures, and structural vibration control technology is expected to be the fundamental way to realize this revolutionary requirement of disaster prevention and mitigation. The traditional anti-seismic design of structures generally resists the effect of external loads by enhancing the strength and stiffness of the building structure itself, so as to achieve the anti-seismic effect. Therefore, when we carry out seismic design, we first need to accurately estimate the external load to be borne by the structure, grasp the characteristics of the materials used, and choose reasonable design and analysis methods. However, the high uncertainty of seismic load, the nonlinearity of materials and the variation of performance during use, as well as the limitations of existing structural analysis and design methods make it possible that the structure does not meet the requirements of function and safety. Considering the limitations of traditional structural seismic design methods, scholars in the industry began to explore new methods, and the design method of structural vibration control was generated and developed under such circumstances.

结构振动控制是通过采取一定的控制措施以调整建筑结构自身的动力特性或是通过施加外部能量来抵消外荷载作用，从而达到抗震减灾性能。根据是否需要外界能源，结构控制一般可分为以下四类：(1)被动控制系统，一种不需要外部能源的结构控制技术，一般是指在结构的某个部位附加一个子系统，或对结构自身的某些构件做构造上的处理以改变结构体系的动力特性(如，调谐质量阻尼器(TMD)和多重调谐质量阻尼器(MTMD))；(2)主动控制系统，一种需要外部能源的结构控制技术，通过施加与振动方向相反的控制力来实现结构控制，控制力由前馈外激励和(或)反馈结构的动力响应决定；(3)半主动控制系统，一般以被动控制为主，当结构动力反应开始越限时，利用控制机构来主动调节结构内部的参数，使结构参数处于最优状态，所需的外部能量较小；(4)混合控制系统，主动控制和被动控制的联合应用，使其协调起来共同工作，这种控制系统充分利用了被动控制与主动控制各自的优点，既可以通过被动控制系统大量耗散振动能量，又可以利用主动控制系统来保证控制效果，例如主被动调谐质量阻尼器(active-passive tuned mass damper，APTMD)。Structural vibration control is to adjust the dynamic characteristics of the building structure itself by taking certain control measures or offset the external load by applying external energy, so as to achieve the performance of earthquake resistance and disaster reduction. According to whether external energy is needed, structural control can generally be divided into the following four categories: (1) Passive control system, a structural control technology that does not require external energy, generally refers to attaching a subsystem to a certain part of the structure, or Some components of the structure itself are structurally processed to change the dynamic characteristics of the structural system (such as tuned mass dampers (TMD) and multiple tuned mass dampers (MTMD)); (2) active control systems, a type that requires external The energy structure control technology realizes structure control by applying a control force opposite to the vibration direction, and the control force is determined by the dynamic response of the feed-forward external excitation and/or feedback structure; (3) semi-active control system, generally passive control Mainly, when the structural dynamic response begins to exceed the limit, the control mechanism is used to actively adjust the internal parameters of the structure, so that the structural parameters are in the optimal state, and the required external energy is small; (4) Hybrid control system, active control and passive control The combined application of the control system makes it coordinate and work together. This control system makes full use of the respective advantages of passive control and active control. It can not only dissipate a large amount of vibration energy through the passive control system, but also use the active control system to ensure the control effect. Such as active-passive tuned mass damper (active-passive tuned mass damper, APTMD).

发明内容Contents of the invention

针对现有技术存在的缺陷，本发明的目的是提供一种基于连接刚度的双层调谐质量阻尼器(SDTMD)优化设计方法For the defects existing in the prior art, the object of the invention is to provide a kind of double-layer tuned mass damper (SDTMD) optimal design method based on connection stiffness

为达到上述目的，本发明采用如下述技术方案：To achieve the above object, the present invention adopts the following technical solutions:

一种基于连接刚度的双层调谐质量阻尼器优化设计方法，其特征在于：操作步骤如下：A method for optimal design of a double-layer tuned mass damper based on connection stiffness, characterized in that the operation steps are as follows:

1)建立结构—基于连接刚度的双层调谐质量阻尼器SDTMD系统力学模型：由结构自身的质量m_s、阻尼c_s和刚度k_s，在单个调谐质量阻尼器TMD的基础上又串联增加一个小质量块，在结构质量块与小质量块之间添加一个附加弹簧。然后建立结构—基于连接刚度的双层调谐质量阻尼器SDTMD系统的力学模型；1) Establish structure-mechanical model of double-layer tuned mass damper SDTMD system based on connection stiffness: from the structure's own mass m _s , damping c _s and stiffness k _s , a single tuned mass damper TMD is added in series For the small mass, an additional spring is added between the structural mass and the small mass. Then the structure-mechanical model of the double-layer tuned mass damper SDTMD system based on the connection stiffness is established;

2)建立结构—基于连接刚度的双层调谐质量阻尼器SDTMD系统动力学方程：根据结构动力学原理，对结构及第一个调谐质量阻尼器TMD1、第二个调谐质量阻尼器TMD2进行受力分析，建立结构—基于连接刚度的双层调谐质量阻尼器SDTMD系统方程；2) Establish structure—dynamic equation of double-layer tuned mass damper SDTMD system based on connection stiffness: According to the principle of structural dynamics, the structure and the first tuned mass damper TMD1 and the second tuned mass damper TMD2 are stressed Analysis and establishment of structure-SDTMD system equation of double-layer tuned mass damper based on connection stiffness;

3)对基于连接刚度的双层调谐质量阻尼器SDTMD进行参数优化计算；3) Perform parameter optimization calculation on the double-layer tuned mass damper SDTMD based on connection stiffness;

4)设计出优化的基于连接刚度的双层调谐质量阻尼器SDTMD：通过比较，选取最优组合参数，设计出优化的基于连接刚度的双层调谐质量阻尼器，用于对结构进行振动控制。4) Design an optimized double-layer tuned mass damper SDTMD based on connection stiffness: Through comparison, select the optimal combination parameters, and design an optimized double-layer tuned mass damper based on connection stiffness for vibration control of the structure.

所述步骤1)中建立结构—SDTMD系统的力学模型：将结构作为一个单自由度质点，根据其材料特点确定其阻尼c_s和刚度k_s，将TMD1装置在结构上，再将TMD2装置在TMD1上，在TMD2与结构之间添加一个刚度为k_L的附加弹簧；以此构成结构—SDTMD系统。In the step 1), the mechanical model of the structure-SDTMD system is established: the structure is regarded as a single-degree-of-freedom mass point, and its damping c _s and stiffness k _s are determined according to its material characteristics, TMD1 is installed on the structure, and TMD2 is installed on the structure On TMD1, an additional spring with stiffness k _L is added between TMD2 and the structure; in this way, the structure-SDTMD system is formed.

所述步骤2)中建立结构—SDTMD系统的动力方程：分别对结构、TMD1、TMD2进行受力分析，根据结构动力学理论，列出其系统方程为：Described step 2) in setting up the dynamic equation of structure-SDTMD system: structure, TMD1, TMD2 are carried out stress analysis respectively, according to structural dynamics theory, list its system equation as:

式中，为地震地面运动加速度；y_s为结构相对于基底的位移；y_T为TMD1(即大质量块)相对于结构的位移；y_t为TMD2(即小质量块)相对于结构的位移；m_s、c_s和k_s分别为结构的受控振型质量、阻尼和刚度；m_T、c_T和k_T分别为TMD1质量、阻尼和刚度；m_t、c_t和k_t分别为TMD2质量、阻尼和刚度；k_L为附加弹簧的刚度。In the formula, is the seismic ground motion acceleration; y _s is the displacement of the structure relative to the base; y _T is the displacement of TMD1 (ie the large mass) relative to the structure; y _t is the displacement of TMD2 (ie the small mass) relative to the structure; m _s , c _s and k _s are the controlled modal mass, damping and stiffness of the structure respectively; m _T , c _T and k _T are the mass, damping and stiffness of TMD1 respectively; m _t , c _t and k _t are the mass, Damping and stiffness; k _L is the stiffness of the additional spring.

所述步骤3)中对基于连接刚度的双层调谐质量阻尼器进行参数优化设计为：In the step 3), the parameter optimization design of the double-layer tuned mass damper based on the connection stiffness is:

结构—SDTMD系统的位移(y_s)动力放大系数：Structure—displacement (y _s ) dynamic amplification factor of SDTMD system:

TMD1冲程(y_T)的动力放大系数为：The power amplification factor of TMD1 stroke (y _T ) is:

TMD2冲程(y_t)的动力放大系数为：The power amplification factor of TMD2 stroke (y _t ) is:

式中：In the formula:

R_eT(λ)＝D₁₁R_e(λ)-D₁₂I_m(λ)R _eT (λ)＝D ₁₁ R _e (λ)-D ₁₂ I _m (λ)

I_mT(λ)＝D₁₂R_e(λ)+D₁₁I_m(λ)I _mT (λ)＝D ₁₂ R _e (λ)+D ₁₁ I _m (λ)

R_et(λ)＝D₂₁R_e(λ)-D₂₂I_m(λ)R _et (λ)＝D ₂₁ R _e (λ)-D ₂₂ I _m (λ)

I_mt(λ)＝D₂₂R_e(λ)+D₂₁I_m(λ)I _mt (λ)＝D ₂₂ R _e (λ)+D ₂₁ I _m (λ)

C₁₂＝-2(1+η)ξ_tf_tλC ₁₂ ＝-2(1+η)ξ _t f _t λ

C₂₂＝2ξ_Tf_TλC ₂₂ =2ξ _T f _T λ

式中：λ为主结构的频率比；f_T为TMD1的频率比；f_t为TMD2的频率比；f_L为附加弹簧的频率比；ξ_s为主结构的阻尼比；ξ_T为TMD1的阻尼比；ξ_t为TMD2的阻尼比；μ_T为TMD1与结构的质量比；μ_t为TMD2与结构的质量比；η为TMD2与TMD1的质量比。In the formula: λ is the frequency ratio of the main structure; f _T is the frequency ratio of TMD1; f _t is the frequency ratio of _TMD2 ; f _L is the frequency ratio of the additional spring; ξ _s is the damping ratio of the main structure; Damping ratio; ξ _t is the damping ratio of TMD2; μ _T is the mass ratio of TMD1 to the structure; μ _t is the mass ratio of TMD2 to the structure; η is the mass ratio of TMD2 to TMD1.

优化过程中，根据实际工程，设定λ、μ_T、η的值，对f_T、f_t、f_L、ξ_T、ξ_t进行参数优化。During the optimization process, according to the actual project, set the values of λ, μ _T , η, and optimize the parameters of f _T , f _t , f _L , ξ _T , ξ _t .

所述步骤4)通过比较选取最优组合参数，设计出优化的SDTMD：定义最优参数评价准则：设置基于连接刚度的双层调谐质量阻尼器的结构最大动力放大系数的最小值的最小化，即越小，则装置振动控制有效性就约佳；利用基因遗传算法进行参数优化，并与TMD、DTMD、DDTMD进行比较。Said step 4) by comparing and selecting the optimal combination parameters, design the optimized SDTMD: define the optimal parameter evaluation criteria: set the minimum value of the minimum value of the structure maximum dynamic amplification factor of the double-layer tuned mass damper based on the connection stiffness, which is The smaller the value, the better the vibration control effectiveness of the device; use the genetic algorithm to optimize the parameters, and compare with TMD, DTMD, and DDTMD.

与现有技术相比，本发明具有如下突出的实质性特点和显著的优点：Compared with the prior art, the present invention has the following prominent substantive features and remarkable advantages:

本发明方法设计一种适用于所有结构的基于连接刚度的双层调谐质量阻尼器，优越之处在于能够有效地控制地震作用下结构的位移响应，且优于TMD、DTMD、DDTMD。The method of the present invention designs a double-layer tuned mass damper based on connection stiffness applicable to all structures, which has the advantage of being able to effectively control the displacement response of the structure under earthquake action, and is superior to TMD, DTMD, and DDTMD.

附图说明Description of drawings

图1是基于连接刚度的双层调谐质量阻尼器(SDTMD)优化设计方法程序框图。Figure 1 is a block diagram of an optimal design method for a double-layer tuned mass damper (SDTMD) based on connection stiffness.

图2是基于连接刚度的双层调谐质量阻尼器(SDTMD)系统模型结构示意图。Fig. 2 is a schematic diagram of the structural model of a double-layer tuned mass damper (SDTMD) system based on connection stiffness.

图3是TMD、DTMD、SDTMD的f_T随η变化关系曲线图。Fig. 3 is a graph showing the relationship between f _T and η of TMD, DTMD and SDTMD.

图4是DTMD、SDTMD的f_t随η变化关系曲线图。Fig. 4 is a graph showing the relationship between f _t and η of DTMD and SDTMD.

图5是SDTMD的f_L随η变化关系曲线图。Fig. 5 is a graph showing the relationship between f _L and η of SDTMD.

图6是TMD、DTMD、SDTMD的ξ_T随η变化关系曲线图。Fig. 6 is a graph showing the relationship between ξ _T and η of TMD, DTMD, and SDTMD.

图7是DTMD、SDTMD的ξ_t随η变化关系曲线图。Fig. 7 is a graph showing the relationship between ξ _t and η of DTMD and SDTMD.

图8是TMD、DTMD、DDTMD、SDTMD的随η变化关系曲线图。Figure 8 is the TMD, DTMD, DDTMD, SDTMD Variation curve with η.

图9是TMD、DTMD、SDTMD的随η变化关系曲线图。Figure 9 is the TMD, DTMD, SDTMD Variation curve with η.

图10是DTMD、基SDTMD的随η变化关系曲线图。Figure 10 is the DTMD, base SDTMD Variation curve with η.

具体实施方式detailed description

下面结合附图，对本发明的具体实施例作详细说明。The specific embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

实施例一：Embodiment one:

如图1所示，本基于连接刚度的双层调谐质量阻尼器优化设计方法，包括如下步骤：As shown in Figure 1, the optimization design method of double-layer tuned mass damper based on connection stiffness includes the following steps:

如图2所示，所述步骤1)中建立结构—SDTMD系统的力学模型：将结构作为一个单自由度质点，根据其材料特点确定其阻尼c_s和刚度k_s，将TMD1装置在结构上，再将TMD2装置在TMD1上，在TMD2与结构之间添加一个刚度为k_L的附加弹簧；以此构成结构—SDTMD系统。As shown in Figure 2, the mechanical model of the structure-SDTMD system is established in the step 1): the structure is regarded as a single-degree-of-freedom mass point, and its damping c _s and stiffness k _s are determined according to its material characteristics, and TMD1 is installed on the structure , and then install TMD2 on TMD1, and add an additional spring with a stiffness of k _L between TMD2 and the structure; this constitutes the structure-SDTMD system.

所述步骤2)中建立结构—SDTMD系统的动力学方程：分别对结构、TMD1、TMD2进行受力分析，根据结构动力学理论，列出其系统方程为：Described step 2) in setting up the kinetic equation of structure-SDTMD system: structure, TMD1, TMD2 are carried out stress analysis respectively, according to structural dynamics theory, list its system equation as:

式中：In the formula:

C₁₂＝-2(1+η)ξ_tf_tλC ₁₂ ＝-2(1+η)ξ _t f _t λ

C₂₂＝2ξ_Tf_TλC ₂₂ =2ξ _T f _T λ

运用基因遗传算法进行优化计算，在结构中装备基于连接刚度的双层调谐质量阻尼器时得出在结构中装备基于连接刚度的双层调谐质量阻尼器时，大质量块和原结构频率f_T、小质量块和原结构频率比f_t、TMD1的阻尼比ξ_T、TMD2的阻尼比ξ_t、附加弹簧的频率比f_L、位移动力放大系数TMD1冲程的动力放大系数TMD2冲程的动力放大系数随η的变化关系曲线，如图3至10所示。Using the genetic algorithm for optimization calculation, when the structure is equipped with a double-layer tuned mass damper based on the connection stiffness, it is obtained that when the structure is equipped with a double-layer tuned mass damper based on the connection stiffness, the large mass and the original structure frequency f _T , small mass and original structure frequency ratio f _t , TMD1 damping ratio ξ _T , TMD2 damping ratio ξ _t , additional spring frequency ratio f _L , displacement dynamic amplification factor Power amplification factor of TMD1 stroke Power amplification factor of TMD2 stroke With the change relationship curve of η, as shown in Figure 3 to 10.

由图8可以看出，基于连接刚度的双层调谐质量阻尼器的振动控制的有效性比单个调谐质量阻尼器(TMD)、双层调谐质量阻尼器(DTMD)和基于阻尼连接的双层调谐质量阻尼器(DDTMD)好，且随着η的增大，有效性越来越好。From Fig. 8, it can be seen that the vibration control of the double-layer tuned mass damper based on the connection stiffness is more effective than a single tuned mass damper (TMD), a double-layer tuned mass damper (DTMD) and a double-layer tuned mass damper based on damping connection The mass damper (DDTMD) is good, and the effectiveness gets better and better as η increases.

由图9可以看出，装有基于连接刚度的双层调谐质量阻尼器的阻尼系统的TMD1的冲程相对于装有单个调谐质量阻尼器(TMD)和双层调谐质量阻尼器(DTMD)的明显减小。当η≥0.75时随着TMD2与TMD1的质量比η的增大，冲程减小的不明显。It can be seen from Fig. 9 that the stroke of TMD1 of the damping system equipped with a double-layer tuned mass damper based on connection stiffness is significantly larger than that of a single tuned mass damper (TMD) and a double-layer tuned mass damper (DTMD). decrease. When η≥0.75, as the mass ratio η of TMD2 and TMD1 increases, the stroke does not decrease significantly.

由图3至图10综合看出，装有基于连接刚度的双层调谐质量阻尼器的阻尼系统的ξ_t相对于双层调谐质量阻尼器(DTMD)有明显减小，小于0.6；基于连接刚度的双层调谐质量阻尼器的阻尼的f_t随着TMD2与TMD1的质量比η的增大而减小，小于或接近于0.35，不适于实际工程运用；而当η≥0.75时随着TMD2与TMD1的质量比η的增大，有效性提高不明显，且TMD1的冲程与TMD2的冲程相差太大，故实际运用中可考虑0.25<η<0.75的情况。From Figure 3 to Figure 10, it can be seen that the ξ _t of the damping system equipped with a double-layer tuned mass damper based on the connection stiffness is significantly lower than that of the double-layer tuned mass damper (DTMD), which is less than 0.6; based on the connection stiffness The damping f _t of the double-layer tuned mass damper decreases with the increase of the mass ratio η of TMD2 and TMD1, which is less than or close to 0.35, which is not suitable for practical engineering applications; while when η≥0.75, as TMD2 and The increase of the mass ratio η of TMD1 does not improve the effectiveness significantly, and the stroke of TMD1 is too different from that of TMD2, so the situation of 0.25<η<0.75 can be considered in practical application.

比较图3至图10，考虑有效性的因素，选取μ_T＝0.01，η＝0.5，f_T＝1.021，f_t＝0.429，f_L＝0.751，ξ_T＝0，ξ_t＝0.219，这一组数据设计SDTMD装置，该SDATMD装置的有效性较TMD、DTMD、DDTMD好，且参数均在合理范围内，能够更好的控制减小振动对结构的损坏。Comparing Fig. 3 to Fig. 10, considering the factor of effectiveness, select μ _T = 0.01, η = 0.5, f _T = 1.021, f _t = 0.429, f _L = 0.751, ξ _T = 0, ξ _t = 0.219, This set of data designs the SDTMD device. The effectiveness of the SDATMD device is better than that of TMD, DTMD, and DDTMD, and the parameters are all within a reasonable range, which can better control and reduce the damage to the structure due to vibration.

Claims

1. a double-layer tuned mass damper optimization design method based on connection stiffness, is characterized in that, comprises the steps:

1) Establish structure-mechanical model of double-layer tuned mass damper SDTMD system based on connection stiffness: from the structure's own mass m _s , damping c _s and stiffness k _s , a single tuned mass damper TMD is added in series For the small mass, an additional spring is added between the structural mass and the small mass, and then the structure-mechanical model of the double-layer tuned mass damper SDTMD system based on the connection stiffness is established;

2) Establish structure—dynamic equation of double-layer tuned mass damper SDTMD system based on connection stiffness: According to the principle of structural dynamics, the structure and the first tuned mass damper TMD1 and the second tuned mass damper TMD2 are stressed Analyze and establish the structure-based SDTMD system equation of the double-layer tuned mass damper based on the connection stiffness, which is expressed as the following formula:

{m m}_{s the s} [[{\overset{\cdot\cdot \cdot\cdot}{x x}}_{g g} ((t t)) + + {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{S S}]] + + {c c}_{s the s} {\overset{\cdot &Center Dot;}{y the y}}_{s the s} + + {k k}_{s the s} {y the y}_{s the s} - - {c c}_{T T} {\overset{\cdot \cdot}{y the y}}_{T T} - - {k k}_{T T} {y the y}_{T T} - - {k k}_{L L} (({y the y}_{T T} + + {y the y}_{t t})) = = 00 - - - - - - ((11))

{m m}_{T T} [[{\overset{\cdot\cdot \cdot\cdot}{x x}}_{g g} ((t t)) + + {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{s the s} + + {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{T T}]] + + {c c}_{T T} {\overset{\cdot \cdot}{y the y}}_{T T} + + {k k}_{T T} {y the y}_{T T} - - {c c}_{t t} {\overset{\cdot \cdot}{y the y}}_{t t} - - {k k}_{t t} {y the y}_{t t} = = 00 - - - - - - ((22))

{m m}_{t t} [[{\overset{\cdot\cdot \cdot\cdot}{x x}}_{g g} ((t t)) + + {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{s the s} + + {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{T T} + + {\overset{\cdot\cdot \cdot\cdot}{y the y}}_{t t}]] + + {c c}_{t t} {\overset{\cdot &Center Dot;}{y the y}}_{t t} + + {k k}_{t t} {y the y}_{t t} + + {k k}_{L L} (({y the y}_{T T} + + {y the y}_{t t})) = = 00 - - - - - - ((33))

In the formula, is the earthquake ground motion acceleration; y _s is the displacement of the structure relative to the base; y _T is the displacement of TMD1, that is, the large mass block, relative to the structure; y _t is the displacement of TMD2, that is, the small mass block, relative to the structure; m _s , c _s and k _s are the controlled modal mass, damping and stiffness of the structure respectively; m _T , c _T and k _T are the mass, damping and stiffness of TMD1 respectively; m _t , c _t and k _t are the mass, Damping and stiffness; k _L is the stiffness of the additional spring;

3) Carry out parameter optimization calculation for the double-layer tuned mass damper SDTMD based on the connection stiffness;

4) Design an optimized double-layer tuned mass damper SDTMD based on connection stiffness: Through comparison, select the optimal combination parameters, and design an optimized double-layer tuned mass damper based on connection stiffness for vibration control of the structure.

2. the double-layer tuned mass damper optimization design method based on connection stiffness according to claim 1, is characterized in that, described step 1), sets up the mechanical model of structure-SDTMD system: structure is regarded as a single-degree-of-freedom mass point , determine its damping c _s and stiffness k _s according to its material characteristics, set TMD1 on the structure, then set TMD2 on TMD1, add an additional spring with a stiffness of k _L between TMD2 and the structure; thus constitute the structure —SDTMD system.

3. the double-layer tuned mass damper optimization design method based on connection stiffness according to claim 1, is characterized in that, described step 3), carries out parameter optimization design to the double-layer tuned mass damper SDTMD based on connection stiffness as :

Structural displacement (y _s ) dynamic amplification factor:

\begin{matrix} {DMF DMF}_{{H h}_{s the s}} = = | | \frac{{ω ω}_{s the s}^{22} {H h}_{s the s} ((- - i i ω ω))}{{\overset{\cdot\cdot \cdot\cdot}{X x}}_{g g}} | | \\ = = | | \frac{{\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ)) i i}{{R R}_{e e} ((λ λ)) + + {I I}_{m m} ((λ λ)) i i} | | \\ = = \frac{\sqrt{{[[{\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ))]]}^{22} + + {[[{\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ))]]}^{22}}}{\sqrt{{[[{R R}_{e e} ((λ λ))]]}^{22} + + {[[{I I}_{m m} ((λ λ))]]}^{22}}} \end{matrix} - - - - - - ((66))

The power amplification factor of TMD1 stroke (y _T ) is:

\begin{matrix} {DMF DMF}_{{H h}_{T T}} = = | | \frac{{ω ω}_{s the s}^{22} {H h}_{T T} ((- - i i ω ω))}{{\overset{\cdot\cdot \cdot\cdot}{X x}}_{g g}} | | \\ = = | | \frac{{\overset{&OverBar; &OverBar;}{R R}}_{e e T T} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m T T} ((λ λ)) i i}{{R R}_{e e T T} ((λ λ)) + + {I I}_{m m T T} ((λ λ)) i i} | | \\ = = \frac{\sqrt{{[[{\overset{&OverBar; &OverBar;}{R R}}_{e e T T} ((λ λ))]]}^{22} + + {[[{\overset{&OverBar; &OverBar;}{I I}}_{m m T T} ((λ λ))]]}^{22}}}{\sqrt{{[[{R R}_{e e T T} ((λ λ))]]}^{22} + + {[[{I I}_{m m T T} ((λ λ))]]}^{22}}} \end{matrix} - - - - - - ((77))

The power amplification factor of TMD2 stroke (y _t ) is:

\begin{matrix} {DMF DMF}_{{H h}_{t t}} = = | | \frac{{ω ω}_{s the s}^{22} {H h}_{t t} ((- - i i ω ω))}{{\overset{\cdot\cdot \cdot\cdot}{X x}}_{g g}} | | \\ = = | | \frac{{\overset{&OverBar; &OverBar;}{R R}}_{e e t t} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m t t} ((λ λ)) i i}{{R R}_{e e t t} ((λ λ)) + + {I I}_{m m t t} ((λ λ)) i i} | | \\ = = \frac{\sqrt{{[[{\overset{&OverBar; &OverBar;}{R R}}_{e e t t} ((λ λ))]]}^{22} + + {[[{\overset{&OverBar; &OverBar;}{I I}}_{m m t t} ((λ λ))]]}^{22}}}{\sqrt{{[[{R R}_{e e t t} ((λ λ))]]}^{22} + + {[[{I I}_{m m t t} ((λ λ))]]}^{22}}} \end{matrix} - - - - - - ((88))

In the formula:

{\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ)) = = {D D.}_{1111} + + [[{C C}_{1111} (({μ μ}_{T T} {f f}_{T T}^{22} + + {μ μ}_{t t} {f f}_{L L}^{22})) + + 22 {C C}_{1212} {μ μ}_{T T} {ξ ξ}_{T T} {f f}_{T T} λ λ]] + + {C C}_{21 twenty one} {μ μ}_{t t} {f f}_{L L}^{22}

{\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ)) = = {D D.}_{1212} - - [[- - {C C}_{1212} (({μ μ}_{T T} {f f}_{T T}^{22} + + {μ μ}_{t t} {f f}_{L L}^{22})) + + 22 {C C}_{1111} {μ μ}_{T T} {ξ ξ}_{T T} {f f}_{T T} λ λ]] + + {C C}_{22 twenty two} {μ μ}_{t t} {f f}_{L L}^{22}

{R R}_{e e} ((λ λ)) = = [[{D D.}_{1111} ((- - {λ λ}^{22} + + 11)) + + 22 {D D.}_{1212} {ξ ξ}_{s the s} λ λ]] - - [[{C C}_{1111} (({μ μ}_{T T} {f f}_{T T}^{22} + + {μ μ}_{t t} {f f}_{L L}^{22})) + + 22 {C C}_{1212} {μ μ}_{T T} {ξ ξ}_{T T} {f f}_{T T} λ λ]] {λ λ}^{22} - - {C C}_{21 twenty one} {μ μ}_{t t} {f f}_{L L}^{22} {λ λ}^{22}

{I I}_{m m} ((λ λ)) = = [[{D D.}_{1212} ((- - {λ λ}^{22} + + 11)) - - 22 {D D.}_{1111} {ξ ξ}_{s the s} λ λ]] + + {{[[- - {C C}_{1212} (({μ μ}_{T T} {f f}_{T T}^{22} + + {μ μ}_{t t} {f f}_{L L}^{22})) + + 22 {C C}_{1111} {μ μ}_{T T} {ξ ξ}_{T T} {f f}_{T T} λ λ]] - - 22 {C C}_{21 twenty one} {μ μ}_{t t} {f f}_{L L}^{22}}} {λ λ}^{22}

{\overset{&OverBar; &OverBar;}{R R}}_{e e T T} ((λ λ)) = = {C C}_{1111} [[{R R}_{e e} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ)) {λ λ}^{22}]] - - {C C}_{1212} [[{I I}_{m m} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ)) {λ λ}^{22}]]

{\overset{&OverBar; &OverBar;}{I I}}_{m m T T} ((λ λ)) = = {C C}_{1212} [[{R R}_{e e} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ)) {λ λ}^{22}]] + + {C C}_{1111} [[{I I}_{m m} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ)) {λ λ}^{22}]]

R _eT (λ)＝D ₁₁ R _e (λ)-D ₁₂ I _m (λ)

I _mT (λ)＝D ₁₂ R _e (λ)+D ₁₁ I _m (λ)

{\overset{&OverBar; &OverBar;}{R R}}_{e e t t} ((λ λ)) = = {C C}_{21 twenty one} [[{R R}_{e e} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ)) {λ λ}^{22}]] - - {C C}_{22 twenty two} [[{I I}_{m m} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ)) {λ λ}^{22}]]

{\overset{&OverBar; &OverBar;}{I I}}_{m m t t} ((λ λ)) = = {C C}_{22 twenty two} [[{R R}_{e e} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{R R}}_{e e} ((λ λ)) {λ λ}^{22}]] + + {C C}_{21 twenty one} [[{I I}_{m m} ((λ λ)) + + {\overset{&OverBar; &OverBar;}{I I}}_{m m} ((λ λ)) {λ λ}^{22}]]

R _et (λ)＝D ₂₁ R _e (λ)-D ₂₂ I _m (λ)

I _mt (λ)＝D ₂₂ R _e (λ)+D ₂₁ I _m (λ)

{C C}_{1111} = = - - {λ λ}^{22} + + {f f}_{L L}^{22} + + ((11 + + η η)) {f f}_{t t}^{22}

C ₁₂ =-2(1+η)ξ _t f _t λ

{D D.}_{1111} = = ((- - {λ λ}^{22} + + {f f}_{T T}^{22})) ((- - {λ λ}^{22} + + {f f}_{t t}^{22} + + {f f}_{L L}^{22})) - - 44 {ξ ξ}_{T T} {ξ ξ}_{t t} {f f}_{T T} {f f}_{t t} {λ λ}^{22} + + {ηf ηf}_{t t}^{22} ((- - {λ λ}^{22} + + {f f}_{L L}^{22}))

{D D.}_{1212} = = - - 22 {ξ ξ}_{t t} {f f}_{t t} λ λ ((- - {λ λ}^{22} + + {f f}_{T T}^{22})) - - 22 {ξ ξ}_{T T} {f f}_{T T} λ λ ((- - {λ λ}^{22} + + {f f}_{t t}^{22} + + {f f}_{L L}^{22})) - - 22 {ηξ ηξ}_{t t} {f f}_{t t} λ λ ((- - {λ λ}^{22} + + {f f}_{L L}^{22}))

{C C}_{21 twenty one} = = {f f}_{L L}^{22} - - {f f}_{T T}^{22}

C ₂₂ =2ξ _T f _T λ

{D D.}_{21 twenty one} = = - - {ηf ηf}_{t t}^{22} ((- - {λ λ}^{22} + + {f f}_{L L}^{22})) - - ((- - {λ λ}^{22} + + {f f}_{L L}^{22})) ((- - {λ λ}^{22} + + {f f}_{t t}^{22} + + {f f}_{L L}^{22})) + + 44 {ξ ξ}_{T T} {ξ ξ}_{t t} {f f}_{T T} {f f}_{t t} {λ λ}^{22}

{D D.}_{22 twenty two} = = 22 {ηξ ηξ}_{t t} {f f}_{t t} λ λ ((- - {λ λ}^{22} + + {f f}_{L L}^{22})) + + 22 {ξ ξ}_{t t} {f f}_{t t} λ λ ((- - {λ λ}^{22} + + {f f}_{T T}^{22})) + + 22 {ξ ξ}_{T T} {f f}_{T T} λ λ ((- - {λ λ}^{22} + + {f f}_{t t}^{22} + + {f f}_{L L}^{22}))

In the formula: λ is the frequency ratio of the main structure; f _T is the frequency ratio of TMD1; f _t is the frequency ratio of _TMD2 ; f _L is the frequency ratio of the additional spring; ξ _s is the damping ratio of the main structure; Damping ratio; ξ _t is the damping ratio of TMD2; μ _T is the mass ratio of TMD1 to the structure; μ _t is the mass ratio of TMD2 to the structure; η is the mass ratio of TMD2 to TMD1; during the optimization process, according to the actual project, set The values of λ, μ _T , η are used to optimize the parameters of f _T , f _t , f _L , ξ _T , ξ _t .

4. the double-layer tuned mass damper optimization design method based on connection stiffness according to claim 1, characterized in that, said step 4), design an optimized double-layer tuned mass damper based on connection stiffness: define the most Optimal parameter evaluation criterion: setting the minimum value of the minimum value of the maximum dynamic amplification factor of the double-layer tuned mass damper structure based on the connection stiffness, that is, The smaller the value, the better the effectiveness of device vibration control; use genetic algorithm to optimize parameters, and compare with TMD, DTMD, DDTMD.