DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximat...

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Bibliographic Details
Published in:Acta mechanica solida Sinica 2010-10, Vol.23 (5), p.420-427
Main Authors: Niu, Datian, Yuan, Xuegang, Cheng, Changjun, Ren, Jiusheng
Format: Article
Language:English
Subjects:
Bifurcations
Classical Mechanics
Computer simulation
cylindrical membrane
Differential equations
Dynamic characteristics
dynamical characteristic
Engineering
incompressible hyperelastic material
Mathematical models
Membranes
nonlinear periodic oscillation
Nonlinearity
Oscillations
Surfaces and Interfaces
Theoretical and Applied Mechanics
Thin Films
不可压缩
二阶非线性常微分方程
动态特性
弹性圆柱
材料参数
材料组成
横观各向同性
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Summary:In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.
ISSN:0894-9166
1860-2134
DOI:10.1016/S0894-9166(10)60044-4