YUAN Xue-gang, ZHANG Hong-wu, REN Jiu-sheng, ZHU Zheng-you. Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads[J]. Applied Mathematics and Mechanics, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011
Citation: YUAN Xue-gang, ZHANG Hong-wu, REN Jiu-sheng, ZHU Zheng-you. Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads[J]. Applied Mathematics and Mechanics, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011

Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads

doi: 10.3879/j.issn.1000-0887.2010.07.011
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-05-12
  • Publish Date: 2010-07-15
  • The nonlinear dynamic properties of axisymm etric deformation were examined for a sphericalm embrane composed of a transversely isotropic incompressible Rivlin-Saundersmaterial, where the membrane was subjected to periodic step loads at its inner and outer surfaces. A second order nonlinear ordinary differential equation that approxmiately describes the radially symmetric motion of the membrane was obtained by setting the thickness of the spherical structure close to 1 and the qualitative properties of the solutions were discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane were proposed. Under certain cases, it was proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type "∞" and that the growth of the amplitude of the periodic oscillation was discontinuous, and numerical results were also provided.
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