横观各向同性饱和半空间体上圆薄板的非轴对称振动

Non-axisymmetical harmonic responses of elastic circular plate on the transversely isotropic saturated half-space

研究了横观各向同性饱和半空间地基上弹性圆板的非轴对称振动问题。首先利用Fou rier展开和Hankel变换 ,给出了柱坐标下 ,横观各向同性饱和多孔介质Biot波动方程非轴对称形式的通解 ,然后按混合边值问题建立了饱和半空间地基上 ,弹性圆板非轴对称振动的对偶积分方程 ,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程 。

A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper by the authors based on the assumption of saturated ground and elastic circular plate excited by the axisymmetical harmonic source.However,the assumption may not always by valid.In this paper,the work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetical harmonic force.The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established by the first author of this paper.By the technique of Fourier expansion and Hankel transform,the governing different equation for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained.Then,under the contact conditions,the problem leads to a pair of dual integral equations which describing the mixed boundary-value problem.Furthermore,the dual integral equations can be reduced to the Fredholm integral equations of the second kind and solved by numerical procedure.At the end of this paper,a numerical result is presented.