直角坐标下横观各向同性饱和半空间体动力响应问题的解析解  

Analytical Solutions of Dynamic Response of Transversely Isotropic Saturated with Media Half-space under Rectangular Coordinates

作　　者：黄义[1] 王小岗[1] 

机构地区：[1]西安建筑科技大学土木工程学院,西安710055

出　　处：《力学季刊》2003年第4期552-559,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金重点项目(56978003)

摘　　要：基于双重Fourier变换技术,成功求解了直角坐标系下,横观各向同性弹性饱和多孔介质的三维Biot动力方程,得到了以固体骨架位移分量和孔隙流体压力为基本未知量的积分形式一般解。进而,用一般解给出了饱和介质的总应力分量表达式。在此基础上,研究了在任意分布的表面竖向和水平谐振力作用下,横观各向同性饱和半空间体的动力响应问题。数值结果表明,采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的动力性能。A study of the dynamic response of half-space with transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source was presented by using the technique of Fourier expansion and Hankel transform. However, the method may not be always valid. The work is extended to the case of an general harmonic source distributing on an arbitrary surface zone of the half-space with transversely isotropic saturated poroelastic media. Based on the Biot's theory the analysis was described. By the technique of double Fourier transform, the governing differential equation for transversely isotropic saturated poroelastic media was easily solved and the cooresponding Fourier transformed stress and displacement solutions were obtained. Under the boundary conditions, the analytical solutions for half-space were presented.

关 键 词：BIOT波动方程 横观各向同性饱和弹性介质 动力响应 双重Fourier变换 

分 类 号：O357.3[理学—流体力学]