Some qualitative properties of incompressible hyperelastic spherical membranes under dynamic loads |
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Authors: | Xue-gang Yuan Hong-wu Zhang Jiu-sheng Ren Zheng-you Zhu |
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Institution: | 1. State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,P.R.China;School of Science,Dalian Nationalities University,Dalian 116600,P.R.China 2. State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,P.R.China 3. Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics,Shanghai University,Shanghai 200072,P.R.China |
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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 “∞”, and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided. |
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Keywords: | nonlinear dynamic property hyperelastic spherical membrane periodic step loads nonlinear periodic oscillation |
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