隔震结构系统线性黏弹性液体阻尼器非平稳响应分析法

Non stationary response analysis of isolated structures with linear viscoelastic liquid dampers

为建立线性黏弹性阻尼器抗震动力可靠度分析法和基于反应谱的模态叠加抗震设计法,对隔震系统线性黏弹性液体阻尼器时域瞬态响应的模态叠加解析解和非平稳随机地震响应分析法进行了系统研究。采用最一般的线性黏弹性阻尼器的积分型分析模型,用非对称微分积分方程组实现设置线性黏弹性液体阻尼器的隔震结构系统的时域非扩阶建模;采用传递矩阵法,直接获得隔震结构系统及其一般线性黏弹性液体阻尼器在任意激励和非零初始条件下时域瞬态响应的非扩阶模态叠加解析解;应用此解析解和快速虚拟激励法,建立隔震系统及其线性黏弹性液体阻尼器在均匀与非均匀调幅滤过白噪声非平稳地震激励下的非平稳响应分析法。所获得的时域瞬态响应解析解以及所建立的一般非平稳随机地震响应分析法,将为建立整体隔震系统各构件抗震动力可靠度和基于反应谱的模态叠加抗震设计法提供分析路径。

In order to establish an analytical method for seismic dynamic reliability analysis and a modal superposition seismic design method based on response spectrums for viscoelastically damped linear structures,the modal superposition solutions of transient responses and the analytical method for non stationary random seismic responses of isolated structures with linear viscoelastic liquid dampers were studied systematically.Using the general integral analytical model for linear viscoelastic dampers,the non-symmetric integral-differential dynamic response equations for the structures were established.By using the transfer matrix method,the modal superposition solutions in original structural space for the transient responses of the isolated structures and its general linear viscolastic liquid dampers under arbitrary exterior forcing loadings and non-zero initial conditions were obtained.By virtue of these analytical solutions and the fast pseudo excitation method,a non stationary response analytical method for isolated structures with linear viscoelastic liquid dampers under uniform or non-uniform amplitude modulated filtered white noise seismic excitation was established.The obtained transient response solutions and the established general non stationary response analytical method can provide a path for establishing the analytical method for seismic dynamic reliability analysis and the modal superposition seismic design method based on response spectrums of the components of isolated structures.