Dynamics of a thick-walled dielectric elastomer spherical shell

The nonlinear vibration response of a thick-walled spherical shell subjected to the mechanical pressure and electric field is studied in this paper. When subject to an electric field through the thickness of the spherical shell, the material expands in plane and contracts in thickness. The dielectric elastomer is assumed to be isotropic and neo-Hookean. Based on simple geometrical and spherical capacitor assumptions, we deduce an explicit analytical equation of motion of the dielectric elastomer spherical shell. The dynamic behaviors of the spherical shell under a constant electric loading and periodic electric loading are analyzed. In addition, the critical voltage is calculated in terms of various loading.