线性结构基于Kanai-Tajimi谱的随机地震动响应分析的新解法  

Novel method for the random seismic response analysis of linear structures subjected to Kanai-Tajimi excitation

作　　者：葛新广 龚景海[1] 李创第[1,2] GE Xinguang;GONG Jinghai;LI Chuangdi(School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;School of Civil Engineering&Architecture,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240 [2]广西科技大学土木建筑学院,广西柳州545006

出　　处：《振动与冲击》2020年第22期60-66,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(51468005);广西科技大学创新团队支持计划项目。

摘　　要：针对当前分析Kanai-Tajimi谱地震动作用下结构分析比较繁杂的问题,提出了计算单自由度结构响应的简明解法。基于Kanai-Tajimi谱的滤波振动方程,将地面运动表示成白噪声激励,并与结构的运动方程组成非经典阻尼结构的地震动系统;运用复模态方法获得结构相对位移、相对速度基于白噪声激励的协方差的解析表达式;利用白噪声激励的谱矩与协方差的简明关系,获得单自由线性结构响应的谱矩简明解析表达式。基于首超破坏准则和Markov分布假定,获得结构的动力可靠度。通过算例,验证了该方法的正确性和简洁性。In view of the operational complexity of current methods for analyzing responses of structures excited by the Kanai-Tajimi spectrum earthquake,a novel and simple method for calculating the structural response of a single-degree-of-freedom(SDOF)system was proposed.The ground motion of Kanai-Tajimi spectrum was expressed as white noise excitation by using a filter vibration equation,so the non-classical damped structural system was composed of the SDOF dynamic equation and the filter vibration equation.Then,the analytic expressions for the covariance of relative displacement and relative velocity of the structure under white noise excitation were derived by the complex mode method.Considering the simple relationship between the spectral moment and covariance of the white noise excitation,a concise analytical expression of spectral moments for the response of SDOF structures subjected to Kanai-Tajimi excitation was obtained.Finally,based on the first-pass failure criterion and Markov distribution assumption,the dynamic reliability of the structure was achieved.The correctness and simplicity of the proposed method were verified by an example.

关 键 词：Kanai-Tajimi谱 白噪声激励谱 谱矩 复模态法 动力可靠度 Markov分布假设 

分 类 号：TU318[建筑科学—结构工程]