Stability analysis of radial inflation of incompressible compositerubber tubes  

作　　者：袁学刚 张文正 张洪武 朱正佑 

机构地区：[1]School of Science,Dalian Nationalities University,Dalian 116600,Liaoning Province,P. R. China [2]State Key Laboratory of Structural Analysis for Industrial Equipment,Departmentof Engineering Mechanics,Dalian University of Technology [3]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第3期301-308,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 and10721062);the Program for New Century Excellent Talents in University (No. NCET-09-0096);the Fundamental Research Funds for the Central Universities (No. DC10030104)

摘　　要：The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.

关 键 词：composite rubber tube radial inflation stability nonlinearly periodic oscillation 

分 类 号：O317[理学—一般力学与力学基础]