Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell

YUAN Xue-gang; ZHU Zheng-you; CHENG Chang-jun

Volume 26 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(8): 892-898

Yun Tian-quan. Solution of a 2-D Weak Singular Integral Equation with Constraint[J]. Applied Mathematics and Mechanics, 1995, 16(5): 415-420.

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YUAN Xue-gang, ZHU Zheng-you, CHENG Chang-jun. Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell[J]. Applied Mathematics and Mechanics, 2005, 26(8): 892-898.

Yun Tian-quan. Solution of a 2-D Weak Singular Integral Equation with Constraint[J]. Applied Mathematics and Mechanics, 1995, 16(5): 415-420.

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Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;

Received Date: 2003-12-20
Rev Recd Date: 2005-03-22
Publish Date: 2005-08-15

Abstract

Abstract

The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained. And the first integral of the equation was then carried out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed, and the corresponding numerical examples were carried out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely. That is to say, the shell will be destroyed ultimately.
- imperfect incompressible neo-Hookean material,
- dynamical behavior,
- critical value,
- nonlinear periodic oscillation

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References(13)

References

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