指数阻尼模型多自由度系统振型分解反应谱法  

Mode-superposition response spectrum methods for exponentially damped MDOF systems

作　　者：肖诗颖 汪梦甫[1] XIAO Shiying;WANG Mengfu(School of Civil Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学土木工程学院,湖南长沙410082

出　　处：《地震工程与工程振动》2020年第4期155-163,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(51578225,51278181)。

摘　　要：讨论了指数阻尼体系地震反应的振型分解方法,基于复模态叠加法与状态空间法给出了地震作用下的动力反应计算的实数形式一般解答;同时,为了方便抗震设计计算,以上述实数形式一般解答为基础,推导了指数阻尼系统以反应谱表示的地震作用计算公式,从而使指数阻尼系统的抗震设计与一般黏滞阻尼系统的抗震设计的过程相吻合;最后基于Matlab平台以两个案例分别验证了阻尼矩阵非奇异与部分奇异的情况下计算方法的正确性与有效性,并与常用时程积分方法计算结果对比,说明可以满足工程计算的需要。In this paper,the mode-superposition method of exponentially damped system is discussed.A delicate general solution,completely in real value form,for calculating seismic time history response of the exponentially damped MDOF system,is deduced based on the algorithms of the complex superposition method and the state-space method.In order to meet the practical needs of seismic design based on code design spectra,a new response spectrum method is developed for seismic analysis of exponentially damped system subjected to ground motion,based on the general solution in real form mentioned above.As a result,the seismic design of exponentially damped system is consistent with that of general viscously damped system.Finally,the correctness and effectiveness of these formulas in the case of all damping matrices are non-singular and some damping matrices are singular are verified by two examples with Matlab.And the method is compared to the results of time history analyses in the two numerical examples,which shows that it can which could meet the requirements of engineering calculation.

关 键 词：指数阻尼系统 复模态叠加 时程分析 反应谱法 地震效应 

分 类 号：TU311[建筑科学—结构工程] P315.9[天文地球—地震学]