饱和地基上条形弹性基础的摇摆振动

Rocking vibration of an elastic strip footing on saturated soil

基于Biot动力方程,研究了饱和均质弹性半空间上弹性条形基础的摇摆振动问题。通过Fourier积分变换求解了饱和土的动力控制方程,然后结合基础底部为混合边界的条件得到了弹性条形基础的摇摆振动对偶积分方程,利用正交多项式将对偶积分方程转化为求解一组线性代数方程组,同时利用复合Simpson法则,得到了动力柔度系数的表达式,通过算例得出了不同参数时地基动力柔度系数随无量纲频率的关系曲线。

In order to delineate the complex coupling behavior of the soil under the rocking loading, the analytical solution for an elastic strip foundation on saturated soil under a rocking moment is developed under the framework of the Biot＇s coupling theory. By employing the method of Fourier transform, the dynamic governing differential equations for saturated poroelastic medium are solved. Considering the mixed boundary-value conditions at the bottom of the foundation, a pair of dual integral equations governing the rocking vibration of an elastic strip footing are then derived, which are further converted to linear equations by means of infinite series of orthogonal functions--the Jacobi polynomials. A numerical procedure is proposed to solve the equations. The dynamic compliance functions for rocking vibration are also derived. The effects of plate flexibility, ground permeability and Poisson＇s ratio on the dynamic compliance are investigated; and some meaningful conclusions are drawn.