多自由度混联I型惯容减震系统地震响应分析

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摘要针对惯容系统在多自由度结构中的应用和布置方案研究不足的问题，提出多自由度惯容系统响应频域解及谱矩的计算方法，并基于响应频域解及谱矩表达式确定了惯容系统的布置方案。通过引入状态变量将结构运动方程和混联Ⅰ型惯容系统的微分型本构关系转化为用矩阵形式表示的状态方程，进而推导了结构位移、速度、层间位移角等系列响应的频域统一解。然后运用功率谱二次分解法将响应功率谱转化为二次分解式(圆频率与复特征值平方和倒数的线性组合形式)，并将其代入谱矩的定义式，获得了位移、速度等系列响应的0-2阶谱矩。最后，以一栋18层的结构为例，验证了所提封闭解的正确性；分析了复特征值个数对结构响应精度的影响；确定并探究了惯容系统在多层结构中布置方案的可行性。结果表明：所提谱矩的封闭解正确适用；高阶振型对结构响应的影响较弱，考虑前若干振型可达到较高的计算精度；所提惯容系统布置方案具有简单易行且效果良好的特点。

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	李创第1
	王瑞勃1
	江丽富1
	葛新广2

关键词 ：混联Ⅰ型惯容系统, 随机地震响应, 功率谱二次分解法, 0-2阶谱矩, 布置方案

Abstract：Aiming at the problem of insufficient research on the application and arrangement scheme of inertial-capacity system in multi-degree-of-freedom structures, the calculation method of response frequency domain solution and spectral moment of multi-degree-of-freedom inertial capacitance system is proposed. And the arrangement scheme of inertial capacitance system is determined based on the response frequency domain solution and spectral moment expression. By introducing state variables to transform the structural equations of motion and the differential-type intrinsic structure relations of the series–parallel layout I inerter system (SPIS-I) into state equations expressed in matrix form. Then, we derive a unified solution in the frequency domain for the series response of structural displacements, velocities, and interstory displacement angles. Next, the quadratic orthogonalization method(QOM) is used to convert the response power spectrum into quadratic decomposition formula (linear combination form of the inverse of the sum of the square of the circular frequency and the square of the complex eigenvalue). Immediately after substituting the power spectral equation into the defining equation of the spectral moment, the 0-2nd order spectral moment of the series response of displacement, velocity, etc. is obtained. Finally, an 18-story structure is used as an example to verify the correctness of the proposed closure solution; the influence of the number of complex eigenvalues on the accuracy of the structural response is analyzed; the feasibility of the arrangement scheme of the inertial capacity system in a multi-story structure is explored. The results show that: the proposed closed solution for the spectral moments is correct and applicable; the influence of higher-order vibration patterns on the structural response is weak, and a high calculation accuracy can be achieved by considering the first few vibration patterns.The arrangement scheme of the inertial capacitance system proposed in this paper has the characteristics of simple and easy implementation and good effect.

Key words： series–parallel layout I inerter system (SPIS-I) random earthquake response the quadratic orthogonalization method(QOM) 0-2 order spectral moment layout plan

收稿日期: 2022-09-20 出版日期: 2023-11-28

引用本文:

李创第1，王瑞勃1，江丽富1，葛新广2. 多自由度混联I型惯容减震系统地震响应分析[J]. 振动与冲击, 2023, 42(22): 19-28.
LI Chuangdi1，WANG Ruibo1，JIANG Lifu1，GE Xinguang2. Seismic response analysis of multi-degree-of-freedom structures with a series-parallel layout Ⅰ inerter system. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(22): 19-28.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I22/19

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