建筑结构基于Clough-Penzien谱的随机地震动响应的简明解析解法  

Concise analytical solutions for random response of building subjected to Clough-Penzien seismic excitation

作　　者：王善库[1] 葛新广[2] 赵立菊[1] WANG Shanku;GE Xinguang;ZHAO Liju(College of Architectural Engineering,Xinyang Vocational and Technical College,464000 Xinyang,China;School of Civil Engineering&Architecture,Guangxi University of Science and Technology,545002 Liuzhou,China)

机构地区：[1]信阳职业技术学院建筑工程学院,信阳464000 [2]广西科技大学土木建筑学院,柳州545002

出　　处：《应用力学学报》2022年第1期96-103,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.51468005)。

摘　　要：针对建筑结构基于Clough-Penzien(C-P)谱下的结构随机地震动响应既有方法复杂的现状,提出了一种简明解析法。C-P谱是将场地的地震动看作基于白噪声激励的两个关联的滤波方程,较准确地模拟场地的平稳地震动特征。首先,提出将C-P谱滤波方程组与建筑结构的运动方程联立,实现了不易求解的非白噪声激励精确转化为简明的白噪声激励的效果;其次,基于复模态正交法对重构后的结构运动方程组进行解耦,并基于随机振动理论推导出结构响应的功率谱密度函数和0阶、1阶和2阶谱矩的简明解析式;最后,分析了基于首次超越破坏准和最弱失效模式下的结构体系动力可靠度。算例验证了所提方法的准确性和简洁性;此外,所提方法也可推广至其他复杂平稳非白噪声激励的地震动响应分析。Aiming at the inefficiency of structural response and dynamic reliability analysis under Clough-Penzien(C-P) random earthquake excitation,a simple and fast method for solving the seismic response equation of building structure by using C-P filtering equations and seismic response equation of building structure is proposed.C-P spectrum regards the ground motion of site as two filtering differential equations,which can accurately simulate the stationary ground motion characteristics of site.First,the complex ground motion excitation is transformed into the ground motion excitation based on white noise by combining filtering equations of C-P spectrum with structural dynamic equations.Second,the complex mode method is used to decouple the ground motion equations,and the concise analytical expressions of covariance,power spectral density function and 0-2 order spectral moments of structural response are obtained based on the random vibration theory.Last,the system dynamic reliability calculation of the structure based on the first passage failure criterion is analyzed.An example shows the accuracy and simplicity of the proposed method.In addition,this method can also be applied to the analysis of ground motion response subjected to other complex stationary non-white noise rand excitation.

关 键 词：Clough-Penzien(C-P)谱 谱矩 体系动力可靠度 简明解析解 复模态法 

分 类 号：TU318[建筑科学—结构工程]