非平稳地震激励下惯容耗能结构动力响应解析法  

Analytical solution for dynamic response of inertial energy dissipation structures under non-stationary seismic excitation

作　　者：李创第[1] 王瑞勃 葛新广 江丽富 LI Chuang-di;WANG Rui-bo;GE Xin-guang;JIANG Li-fu(School of Civil Engineering and Architecture,Guangxi University of Science and Technology,Liuzhou 545006,China;School of Civil Engineering and Architecture,Liuzhou Institute of Technology,Liuzhou 545616,China)

机构地区：[1]广西科技大学土木建筑工程学院,广西柳州545006 [2]柳州工学院土木建筑工程学院,广西柳州545616

出　　处：《振动工程学报》2024年第11期1862-1874,共13页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51468005);广西研究生教育创新计划资助项目(YCSW2022450)。

摘　　要：针对惯容减震系统在非平稳地震激励下动力响应研究不足的问题,提出设有混联Ⅰ型惯容减震系统的多自由度耗能结构动力响应时变方差的解析解法。根据惯容减震系统的本构关系、结构的动力方程及非平稳地震激励,综合利用复模态法和虚拟激励法,将惯容耗能结构解耦为一阶系统,以便获得结构位移、速度、层间剪力等响应量的统一解。采用二次式分解法将统一解的时变功率谱密度函数转化为惯容耗能结构复模态特征值、模态系数、时变模态强度系数和含有圆频率平方项的二次式乘积的线性组合。在此基础上,利用非平稳模态谱矩在无限积分区间有解析解的特征,推导出非平稳地震激励下耗能结构响应时变方差的解析解。通过采用突加型白噪声激励对结构动力响应进行分析,验证了所提动力响应功率谱和时变方差的正确性。同时,基于突加型Kanai-Tajimi模型的框架结构动力响应研究,分析了惯容系统参数对减震效果的影响。所提方法可适用于线性结构在其他非平稳调制函数的地震动下的响应分析。Due to the lack of research on the dynamical response of the inerter system based on non-stationary seismic excitation,an analytical solution for the time-varying variance of the dynamical response of a multi-degree-of-freedom energy-consuming structure with series-parallel layoutⅠinerter system(SPIS-Ⅰ)is proposed.According to the constitutive relationship of the SPIS-Ⅰ,the dynamic equations of the energy dissipation structure,and the impulsive non-stationary seismic excitation,we decouple the inertial energy dissipation structure into first-order systems using complex modal analysis and the virtual excitation method.It is convenient to obtain the unified solution of the structural response quantities such as displacement,velocity,inter-story shear force,etc.The quadratic decomposition method is used to transform the time-varying power spectral density function of the unified solution into a linear combination of the complex modal eigenvalues of the inertial-capacitated energy-consuming structure,the modal coefficients,the time-varying modal strength coefficients,and the quadratic product containing the squared term of the circular frequency.On this basis,an analytical solution for the time-varying variance of the response of the energy-consuming structure under non-stationary seismic excitation is derived by utilizing the characteristics that the non-stationary modes spectral moments have an analytical solution in the infinite integration interval.The accuracy of the proposed dynamic response power spectrum and timevarying variance is verified by using the sudden white noise excitation to analyze the dynamic response of the structure.At the same time,the dynamic response of the frame structure based on the sudden Kanai-Tajimi model is studied,and the influence of the parameters of the inertial system on the damping effect is analyzed.The proposed method can be applied to analyze the seismic response of linear structures under other non-stationary modulation functions.

关 键 词：惯容减震系统 非平稳地震激励 功率谱二次式分解法 时变方差 解析解法 

分 类 号：TU311.3[建筑科学—结构工程] O324[理学—一般力学与力学基础]