Periodic and chaotic vibrations of dielectric elastomer spherical shells considering structural damping

Dielectric elastomers (DEs) have attracted significant attention in many engineering fields due to their excellent deformation capabilities and mechanical properties. In this work, the nonlinear vibrations of the DE spherical shell characterized by the third-order Ogden model are investigated. The governing equation describing the radially symmetric motions of the shell is derived by the incompressibility constraint and the variational method. Through the qualitative and quantitative analyses, the nonlinear dynamical behaviors are discussed, along with the parameter analyses of the structural damping, pressure, direct current (DC) voltage and alternating current (AC) voltage. It is shown that with the increasing pressure and voltage, the vibrations transition from periodic vibrations to chaotic vibrations via the period-doubling bifurcation. Particularly, the self-similar structure of the system is found.