二维各向同性多孔介质的弹性动力学通解  

General Solutions of Elastodynamics for 2D Isotropic Porous Media

作　　者：王裕宁 赵宝生[1] WANG Yuning;ZHAO Baosheng(School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan, Liaoning 114051, P.R.China)

机构地区：[1]辽宁科技大学机械工程与自动化学院

出　　处：《应用数学和力学》2019年第9期1025-1034,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11472299)~~

摘　　要：在二维直角坐标系下,从固体位移和流体流速满足的基本方程出发,研究了二维各向同性多孔介质的弹性动力学通解.首先引入4个物理量,对固体骨架的运动方程、流体流速运动方程、连续性方程进行整理,将方程组分解成膨胀波和扭转波两部分,并利用Lur’e算子矩阵理论,获得由3个类调和函数表示的动力学通解,该通解满足全部基本方程.最后将时间项退化获得稳态通解,并证明了稳态通解的完备性.With the general equations of solid displacement and fluid velocity, the general solution of elastodynamics for 2 D isotropic porous media were studied. Through introduction of 4 undetermined functions, the equations of motion, fluid velocity and continuity were formulated and divided into 2 parts of expansion wave and torsion wave. Thus, the general solutions expressed with 3 quasi harmonic functions were obtained under the Lur’e operator theory. With the solid displacement and fluid velocity independent of the time, the general steady-state solutions for 2 D isotropic porous media were given, and their completeness was proved.

关 键 词：多孔介质 通解 Lur’e算子矩阵 完备性 类调和函数 

分 类 号：O343[理学—固体力学]