# Stability analysis of radial inflation of incompressible composite rubber tubes

Stability analysis of radial inflation of incompressible composite rubber tubes

Abstract：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.

Author：

Xue-gang YUAN[1] Wen-zheng ZHANG[2] Hong-wu ZHANG[2] Zheng-you ZHU[3]

School of Science, Dalian Nationalities University, Dalian 116600, Liaoning Province, P. R. China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province,P.R.ChinaState Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. ChinaShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

Journal：

APPLIED MATHEMATICS AND MECHANICS

2011, 32(3)

O343

Keywords：

composite rubber tube

stability

nonlinearly periodic oscillation

P44 O4

ordinary differential equation periodic oscillation material parameters boundary conditions mathematical model governing equation first integral structure materials dynamic stress means two

the National Natural Science Foundation of China，the Program for New Century Excellent Talents in University，the Fundamental Research Funds for the Central Universities

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