基于Kanai-Tajimi谱卷积型非粘滞阻尼多自由度结构地震动响应的简明闭式解  

Concise closed-form solution for ground motion response of convolutional non-viscous damped multi-degree-of-freedom structure based on Kanai-Tajimi spectrum

作　　者：李创第[1] 贺王涛 葛新广[1,2] LI Chuangdi;HE Wangtao;GE Xinguang(College of Civil and Architectural Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China;College of Civil and Architectural Engineering,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：《地震工程与工程振动》2022年第3期34-42,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(51468005);广西科技大学创新团队支持计划项目(2016);广西重点研发计划(桂科AB19259011)。

摘　　要：针对非粘滞阻尼结构基于Kanai-Tajimi谱的卷积-微分混合动力方程解法比较繁琐的问题,给出了一种新的简明封闭解法。非粘滞阻尼模型常以指数型核函数的卷积形式表示,不易求解,文中给出其精确等效的微分型本构关系。Kanai-Tajimi地震动激励模型的功率谱表达式较为复杂,不易于获得结构动力响应的封闭解,但其可精确转化为易于获得封闭解的白噪声激励的滤波方程。利用非粘滞阻尼结构的微分型本构关系和Kanai-Tajimi谱的滤波方程,文中将基于复杂地震动激励卷积-微分型动力方程转换为基于白噪声激励的全微分型动力方程组,然后运用复模态法及白噪声激励的简明特性,给出了结构位移、速度的方差和0~2阶谱矩的简明封闭解,并研究了耗能结构的动力可靠度。算例对一多自由度结构进行分析,与虚拟激励法进行对比,验证文中所提分析响应0~2阶谱矩的封闭解法的正确性和高效性。Aiming at the cumbersome solution of the convolution-differential hybrid dynamic equation based on Kanai-Tajimi spectrum for non-viscous damping structures,a new concise closed-form solution method is presented.The non-viscous damping model is often expressed in the convolution form of an exponential kernel function,which is not easy to solve.This paper gives its exact equivalent differential constitutive relationship.The expression of the power spectrum of the Kanai-Tajimi ground motion excitation model is more complicated,and it is not easy to obtain a closed solution of the structural dynamic response,but it can be accurately transformed into a filter equation for white noise excitation that is easy to obtain a closed solution.Using the differential constitutive relationship of the non-viscous damping structure and the filtering equation of the Kanai-Tajimi spectrum,this paper converts the convolution-differential dynamic equation based on complex ground motion excitation to the fully differential dynamic equation system based on white noise excitation.Using the complex modal method and the concise characteristics of white noise excitation,the concise closed solutions of the variance of the structural displacement and velocity and the 0~2th order spectral moment are given,and the dynamic reliability of the energy-dissipating structure is studied.The calculation example analyzes a multi-degree-of-freedom structure and compares it with the virtual excitation method to verify the correctness and efficiency of the closed solution method proposed in this paper for analyzing response 0~2 order spectral moments.

关 键 词：Kanai-Tajimi谱 非粘滞阻尼 多自由度结构 简明封闭解 谱矩 

分 类 号：TU318[建筑科学—结构工程]