不可压缩柱形弹性动力学方程的解的定性分析

Qualitative Analyses of Solutions of Incompressible Cylindrical Elastic Dynamical Equations

本文研究了轴对称变形假设下的不可压缩超弹性柱形结构的动力学稳定性问题.利用材料的不可压缩条件将描述圆柱形结构径向对称运动的弹性动力学方程约化为二阶非线性常微分方程.特别地,针对圆柱体、含有微孔的圆柱体、圆柱壳以及柱形薄膜等结构的径向对称运动问题,分别给出了一些具有共性的结论,如圆柱体轴线上空穴生成的条件、圆柱壳或薄膜产生非线性周期振动以及破裂的条件等.

Abstract： In this paper, dynamic stability problems are examined for cylindrical structures composed of incompressible hyper- elastic materials under the assumption of axially syrmnetric deformation. The elastic dynamical equationthat describes the radially symmetric motion of the cylindrical structures is reduced to a second order nonlinear ordinary differential equation by using the incompressible condition. In particular, some common conclusions are presentedfor the radially symmetric motion problems of a cylinder, a cylinder with a micro - void, a cylindrical shell and a cylindrical membrane, such as, conditions of cavity formation at the axial line of the cylinder, conditions of presenting nonlinearly periodic oscillation and fracture of a cylindrical shell or a cylindrical membrane.