中文摘要：

为设置粘弹性阻尼器的多层基础隔震结构平稳地震响应分析的扩阶复模态法。在建立了结构上、下部的运动方程以及阻尼器阻尼力的一阶微分方程基础上；将上部结构按第一振型展开，获得了含有第一振型广义位移、隔震层位移及阻尼力为未知参数的二阶方程组后，通过扩阶将原二阶方程组精确化为一阶状态方程组，运用复模态法，获得了结构位移、速度及阻尼器响应的解析解，在平稳白噪声随机激励作用下，结构及阻尼器的响应方差解析解，并给出一般性算例；最终建立了基于扩阶复模态法分析多层基础隔震结构附加粘弹性阻尼器的平稳地震响应的一整套计算方法。算例结果表明：设置粘弹性阻尼器的隔震结构比一般结构的抗震效果优越很多。

英文摘要：

Smooth earthquake response of a multi-isolated structure setting a viscoelastic damper using the expansion complex modal method is raised systematically. Firstly, equations of motion of a upper-main part and a lower isolation layer of this structure, and a first-order differential equation of a damper＇s damping force are established. Secondly, a upper-main part is expanded according to the first mode, second-order equations containing those parameters which are the first-mode generalized displacement, isolation layer-displacement and damping force are obtained. Original second-order equations are exactly converted into a first-order equation of state by expanding order, and using the complex mode method, then analytical solutions of displacement response, velocity response and damper response of this structure are obtained, in the stationary white noise as a seismic excitation model, response variance＇s analytical solutions of structure and damper are obtained, and a general example is given. Finally, a set of calculation methods of smooth earthquake response of a multi-isolated structure setting a viscoelastic damper based on the expansion complex modal method is established. Numerical results show that isolated structure setting viscoelastic dampers is superior to the general structure in seismic effects.