一类不可压缩超弹性球壳的动力学稳定性分析  

Dynamics Stability Analysis of a Class of Incompressible Hyperelastic Spherical Shells

作　　者：袁学刚[1] 张奇[1] 张若京[1] 

机构地区：[1]同济大学航空航天与力学学院

出　　处：《同济大学学报（自然科学版）》2007年第5期654-658,共5页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(10272084;10626045)

摘　　要：研究了一类横观各向同性不可压缩的修正Varga材料组成的超弹性球壳在其内外表面分别受突加的恒定载荷作用时的动力学稳定性问题.求得了描述球壳内表面运动的二阶非线性常微分方程;讨论了方程的平衡点的存在条件及其解的定性性质.对于给定的材料和结构参数,存在一个临界载荷,证明了当突加的恒定载荷未超过这个临界值时,球壳内表面随时间的演化是非线性的周期振动;当载荷超过这个临界值时,球壳随时间的演化最终会破裂,同时给出了相应的数值算例.A dynamics stability problem is examined for a hyperelastic spherical shell composed of a class of transversely isotropic incompressible modified Varga materials, where the inner and the outer surfaces of the shell are subjected to different suddenly applied constant loads. A second-order nonlinear ordinary differential equation that describes the motion of the inner-surface of the shell is presented. For the differential equation, the existence conditions of equilibrium points and the qualitative properties of the solutions are discussed. For the given material and structure parameters, there exists a critical load. It is proved that the motion of the inner-surface of the shell presents a nonlinear periodic oscillation as the suddenly applied constant load does not exceed the critical value, and that the shell will be destroyed ultimately with time as the load exceeds the critical value. The corresponding numerical examples are given simultaneously.

关 键 词：不可压缩超弹性材料 球壳 动力学稳定性 非线性周期振动 

分 类 号：O343[理学—固体力学] O175[理学—力学]