成层地基一维土层对地震的随机反应分析

首先基于改进的一维剪切梁模型，对成层土层推导了确定自振频率、振型函数、参与系数及稳态动力响应的封闭型解析表达式，首次证明了成层土层振型函数的正交性，然后在此基础上，利用随机振动理论，研究了成层土层对地震的随机动力反应问题，关于基岩输入地震加速度的功率谱密度函数，考虑了两种形式：白噪声谱和过滤白噪声谱。数值计算结果表明：对这两种谱，土层的最大期望反应是不相同的；平稳输入与输出过高估计了土层的随机反应。

Random response analysis of stratified foundations to earthquakes

First,based on a generalized non-homogeneous shear-beam model of stratified soil, closed-form analytical expressions are derived for natural frequencies,modal displacements,participation factors and steady state response function.The orthogonality of the modal displacements is proved for the first time, and then,the dynamic response of the stratified foundations to earthquakes is studied by the theory of random vibration.Two cases of power spectral density function for the earthquake acceleration imput at the base rock are considered, namely the white noise spectrum and filtered white noise spectrum.The numerical calculation results show that the maximum espected responses of the soil layer are different each orther for the two spectra and that results of the random respons of the soil layer obtained from both the stationary input and output are over-estimated.