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Nonlinear Behaviors of an Isotropic Incompressible Hyperelastic Spherical Membrane Under Different Dynamic Loads

D. NIU, W. ZHAO, X. YUAN

Abstract


Some nonlinear dynamic behaviors are studied for a spherical membrane composed of a class of isotropic incompressible Ogden materials subjected to different forms of dynamic loads at its inner surface. The mathematical model is formulated and a second order nonlinear ordinary differential equation that approximately describes the radially symmetric motion of the membrane is obtained. The corresponding phase diagrams under three types of dynamic loads (i.e., constant load, isochronal step loads, and periodic load) are presented. It is shown that the ∞-type homoclinic orbit may appear under certain conditions. The effects of the dynamic loads and the thickness on the motion of the membrane are also analyzed

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