Static and dynamic stability of a spherical dielectric elastomeric membrane

Resumo

The aim of this work is to investigate the static and the nonlinear vibration responses of an inflated spherical membrane composed of an isotropic, homogeneous, incompressible, and dielectric hyperelastic material. Both geometric nonlinearity, due to finite deformations, and material nonlinearity are considered. For the same elastomeric material, three hyperelastic constitutive models—neo-Hookean, Mooney-Rivlin, and Ogden—are employed. The system is subjected to a time-dependent uniform pressure and a continuous electric voltage to describe the nonlinear equations of motion. For each constitutive model, the natural frequencies, nonlinear static equilibrium paths, and nonlinear frequency–amplitude relationships are determined. A detailed parametric analysis highlights the significant influence of internal pressure, dielectric properties, and material parameters on the static stability and nonlinear oscillations of the membrane, revealing the emergence of distinct structural stability regimes depending on the chosen constitutive model.