带TMD结构随机地震响应分析的复模态法

本文对多自由度带TMD结构的随机地震响应问题进行了系统研究。首先将结构简化成多层剪切型模型。然后建立运动方程，根据结构的振动反应以第一振型为主，将结构按第一振型展开，针对所得方程为非经典阻尼，非对称质量和非对称刚度情况，运用复模态理论进行解耦，获得了以第一振型表示的结构地震响应的解析解，对单自由度体系，此解即为结构响应的精确解，从而建立了两自由度体系在任意非经典阻尼，非对称质量和刚度情况下随机地震响应解析解分析的一般方法。本文方法也可用于基础隔震结构和无损伤“加层减震”加固结构的随机地震响应分析与优化设计。

The Complex Modal Methods for Analysis of Random Earthquake Response of Structures with TMD

In the paper,the random earthquake response of multi_degrees of freedom structures with TMD is studied systematicaly.Firstly,the structure is simplified to a multi_story shear type mode and then the dynamic equations are established.According to the fact that the first mode is contributed to be the main part of the total motion,the structure is unfolded through the first mode.Because of the situation that the damping is non_classical and the structure is non_symmetr ical the complex modal method is used to decouple the equations,and the precise solution of earthquake respons,which is expressed by first mode,is obtained.The method of the paper can be used to random response analysis and optimization design of the structure with base isolation.