非均质基础与结构共同作用的随机动力反应分析

假定基础的剪切模量随深度呈线性变化，并引入结构微分算子，利用连续线性系统的随机振动理论，研究了非均质基础地震的动力反应问题。将上部结构简化为多自由度体系，将基础简化为一剪切梁，分析了基础与结构共同作用的随机地震反应。通过进一步分析，得到了基础与结构的地震随机反应及平稳输入时土层最大位移的动力可靠性分析参数。采用模态叠加法进行反应分析，与普通的分离变量法相比较，此方法概念明确、步骤简单。

The stochastic earthquake response analysis of interaction between non-homogeneous foundation and structures

Based on the assumption that shear modulus of foundation changes linearly along depth, the dynamic response of non-homogeneous foundation is studied in this paper by introducing differentiating operator of structure and using the stochastic vibration theory for continuous linear system. Then simplifying upside structures as multi-degrees of freedom system and foundation as shear beam, the stochastic earthquake response of interaction between foundation and structures is implemented. Using those results, the dynamic reliability parameters of foundation and structural maximal displacement are obtained. The response analysis is implemented by mode superposition method, which has a definite conception and simpler calculation procedures compared with ordinary separation variable method.