Some qualitative properties of incompressible hyperelastic spherical membranes under dynamic loads  

作　　者：袁学刚 张洪武 任九生 朱正佑 

机构地区：[1]State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology [2]School of Science,Dalian Nationalities University [3]Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第7期903-910,共8页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos.10872045, 10721062,and 10772104);the Program for New Century Excellent Talents in University (No.NCET-09-0096);the Post-Doctoral Science Foundation of China (No.20070421049);the Fundamental Research Funds for the Central Universities (No.DC10030104)

摘　　要：Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic step loads at its inner and outer surfaces. A second-order nonlinear ordinary differential equation approximately describing radially symmetric motion of the membrane is obtained by setting the thick- ness of the spherical structure close to one. The qualitative properties of the solutions are discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane are proposed. In certain cases, it is proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type ＂∞＂, and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic step loads at its inner and outer surfaces. A second-order nonlinear ordinary differential equation approximately describing radially symmetric motion of the membrane is obtained by setting the thick- ness of the spherical structure close to one. The qualitative properties of the solutions are discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane are proposed. In certain cases, it is proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type ＂∞＂, and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.

关 键 词：nonlinear dynamic property hyperelastic spherical membrane periodic step loads nonlinear periodic oscillation 

分 类 号：O343[理学—固体力学]