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Indexed by:期刊论文

Date of Publication:2010-07-01

Journal:APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION

Included Journals:SCIE、EI

Volume:31

Issue:7

Page Number:903-910

ISSN No.:0253-4827

Key Words:nonlinear dynamic property; hyperelastic spherical membrane; periodic step loads; nonlinear periodic oscillation

Abstract:Some nonlinear dynamic properties of axisymmetric deformation are examined 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 thickness 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 "aaEuroe, and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.