饱和弹性半空间地基与中厚圆板的动力相互作用

DYDAMIC INTERACTIONS BETWEEN MODERATELY THICK CIRCULAR PLATES AND TRANSVERSLY ISOTROPIC SATURATED POROELASTIC HALF-SPACE

利用Fourier-Bessel级数,对横观各向同性饱和弹性半空间地基与中厚圆板的动力相互作用问题进行了系统地分析。板的位移函数、荷载、地基反力及板下地基表面的沉降均被展开为二重Fourier-Bessel级数,这些级数中的待定系数由板的边界条件、板的控制方程及板-地基的相容条件加以确定,从而将饱和弹性半空间地基与中厚圆板的动力相互作用问题转化为数值积分和代数方程组的求解问题。数值计算表明,该级数解答具有较快的收敛速度。可以将该方法推广到弹性半空间与梁、矩形板相互作用问题的分析。

Basing on Fourier-Bessel series, the dynamic interactions between moderately thick circular plates and transversely isotropic saturated poroelastic half-space are investigated. The displacement functions of plate, the loads, the reactive force of soil ground, and the settlement of half-space＇s surface under the plate are all expanded to the double Fourier-Bessel series. The unknown coefficients in those series are determined by the boundary conditions of plate, the governing equations of plate, and the continuous condition of plate-ground. The problems of dynamic interaction between plate and half-space are reduced to the problems of calculating numerical integral and solving algebraic equations. The numerical calculations are accomplished and the results indicate that the series are of fast convergence rate. The solving methods can be generalized to the interaction analysis of elastic half-space and beam or half-space and rectangular plate.