横观各向同性饱和介质非轴对称动力响应分离变量解  

Separation of variables solution of non-axisymmetrical dynamic response of transversely isotropic saturated porous media

作　　者：王春玲[1] 黄必成[1] 刘俊卿[1] 

机构地区：[1]西安建筑科技大学理学院,西安710055

出　　处：《计算力学学报》2016年第3期399-404,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金面上项目(51178387);陕西省自然科学基金(2014JM7015)资助项目

摘　　要：首先将横观各向同性饱和弹性多孔介质非轴对称问题的Biot波动方程,变换为适宜于进行分离变量法求解的形式;然后在非轴对称简谐激励下,用分离变量法得到Biot方程的一般解,即用分离变量法求得了多孔介质位移和应力分量的解析表达式;并给出了半空间横观各向同性饱和弹性多孔介质在表面竖向简谐荷载作用下表面竖向位移的数值分析结果,得出载荷对30倍受载半径以外的区域几乎无影响的结论。同时表明了本文的分析方法是切实可行的。Firstly, this paper transforms the Blot ~s wave equations of transversely isotropic saturated elastic media under the excitation of non-axisymmetrical simple harmonic into a form which can be solved suitably by separation of variables. Secondly,the general solutions of Blot＇s equations and the analytical expression of porous media displacement and stress components can be derived using the separation of variables. Finally, it also gives numerical results of the surface vertical displacement of half-space trans- versely isotropie and poroelastic media under the surface vertical harmonic loads. It also comes to a con- clusion that the load has no effect on the area outside 30 times the radius of the loading area. It demon- strates the accuracy and applicability of the present approach.

关 键 词：BIOT波动方程 横观各向同性饱和弹性多孔介质 非轴对称动力响应 分离变量法 解析解 

分 类 号：O357.3[理学—流体力学]