Analysis of Dynamic Behavior of a Pre-Stretched Circular Hyper Elastic Membrane with Finite Deformation

This paper deals with the dynamic analysis of the linear vibration response of a prestretched circular hyper elastic membrane with large deformation. Geometrical as well as material nonlinearity come together due to finite deformations and a hyper elastic constitutive relationship. The membrane material is assumed to be isotropic, homogeneous, and Neo-Hookean. A commercial finite element code ANSYS is used to perform the prestressed modal analysis as well as hyper elastic material curve fitting. The results are compared to the analytical solutions obtained from literature. The effect of stretching ratio and membrane thickness on the mode frequencies, shapes and order is studied. The increase in stretching ratio increases the concentration of in plane modes in the lower frequencies, and also decreases the frequency of the same. The out of plane modes are dominant in the lower frequencies at lower stretch ratios due to the predominance bending stiffness compared to membrane stiffness. Finally, the influence of the hyper elastic constitutive laws on linear vibrations is investigated. Results show that the selection of appropriate hyper elastic material model plays a crucial part in getting the correct results.