二维各向同性多孔介质的弹性动力学通解

王裕宁; 赵宝生

doi:10.21656/1000-0887.390235

二维各向同性多孔介质的弹性动力学通解

doi: 10.21656/1000-0887.390235

辽宁科技大学机械工程与自动化学院, 辽宁鞍山 114051

基金项目: 国家自然科学基金(11472299)

详细信息

作者简介:
王裕宁 (1991—)，男，硕士生（E-mail: 827489034@qq.com);赵宝生(1973—)，男，教授，博士，硕士生导师（通讯作者. E-mail: zhaobaos@pku.org.cn）.

中图分类号: O343
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- 被引次数: 0
出版历程
- 收稿日期: 2018-09-06
- 修回日期: 2019-01-17
- 刊出日期: 2019-09-01

General Solutions of Elastodynamics for 2D Isotropic Porous Media

School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan, Liaoning 114051, P.R.China

Funds: The National Natural Science Foundation of China(11472299)

摘要

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.
- 多孔介质 /
- 通解 /
- Lur’e算子矩阵 /
- 完备性 /
- 类调和函数
Abstract: With the general equations of solid displacement and fluid velocity, the general solution of elastodynamics for 2D 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 2D isotropic porous media were given, and their completeness was proved.
- porous medium /
- general solution /
- Lur’e operator matrix /
- completeness /
- quasi harmonic function

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参考文献(15)

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