横观各向同性饱和弹性半空间地基上圆环板的简谐振动  

Harmonic Vibration of Annular Plates on Transversely Isotropic Saturated Porous Half Space

作　　者：何芳社[1] 黄义[1] 郭春霞[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《力学季刊》2010年第1期124-130,共7页Chinese Quarterly of Mechanics

基　　金：陕西省教育厅自然科学研究项目(08JK342)

摘　　要：本文基于在L^2[a,b]上的完备正交函数组,通过将板的挠度、荷载、地基反力及板下地基表面的沉降展开为Fourier-Bessel级数,利用解析法对横观各向同性饱和弹性半空间地基上圆环板的简谐振动进行了系统分析。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圆环板的动力相互作用问题转化为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。Based on the complete orthogonal function systems in L^2[a, b] and general Fourier-Bessel series, the harmonic vibration of annular plates on transversely isotropic saturated porous half-space were investigated by analytic method. The deflection of plate, the load, the reactive force of soil ground, and the settlement of half space＇s surface under the plate were all expanded to the double Fourier-Bessel series. The unknown coefficients in those series were ascertained by the boundary conditions of plate, the governing equation of plate, and the continuous condition of plate ground. The problems of dynamic interaction between plate and half space were changed to the problems of solving algebraic equations. In the end, the numerical calculation were accomplished and the results indicate that the series are of quick convergence rate.

关 键 词：圆环板 饱和多孔半空间 横观各向同性 简谐振动 Fourier—Bessel级数 

分 类 号：TU435[建筑科学—岩土工程] TU471.2[建筑科学—土工工程]