Abstract
In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.
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Project supported by the National Natural Science Foundation of China (Nos. 10872045 and 10772104), the Program for New Century Excellent Talents in University (No. NCET-09-0096) and the Fundamental Research Funds for the Central Universities (No. DC10030104).
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Niu, D., Yuan, X., Cheng, C. et al. Dynamic Characteristics in Incompressible Hyperelastic Cylindrical Membranes. Acta Mech. Solida Sin. 23, 420–427 (2010). https://doi.org/10.1016/S0894-9166(10)60044-4
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DOI: https://doi.org/10.1016/S0894-9166(10)60044-4