单层饱和地基上刚性圆板的扭转振动

运用Hankel变换求解了饱和土的动力控制方程,结合上边界为混合边界和下边界为不透水基岩的边界条件得出了单层饱和地基上刚性基础的扭转对偶积分方程,并将对偶积分方程转化为第二类Fredholm积分方程,同时给出了基础的动力柔度系数和角位移幅值的表达式.数值分析结果表明:当层厚>5倍基础半径时,可以把下卧基岩的饱和地基近似为半空间;基础的质量惯性矩越大,其共振振幅也越大,并且发生共振时的频率越小.

Torsional vibrations of a rigid disk on single-layered saturated soil

An analytical method was presented for the torsional vibration of a rigid disc resting on single-layered saturated soil.By employing the technique of Hankel transform,the dynamic governing differential equations for saturated poroelastic medium were solved.Considering the mixed boundary at the upper surface and the fixed boundary at the lower surface,the dual integral equations were established,which were further converted to a Fredholm integral equation of the second kind.Subsequently,the dynamic compliance coefficients and the angular amplitude of the foundation were presented explicitly.Selected numerical results indicate that,when height of the stratum is bigger than 5 times the radius of the foundation,single-layered saturated soil with subjacent rock-stratum can be treated as saturated half space approximately.Furthermore,the resonant amplitudes and frequencies of vibration are shown to depend on the mass inertia moment of the foundation.