Nonlinear vibration of dielectric elastomer incorporating strain stiffening

Due to the strain-stiffening of polymer chains, a membrane of dielectric elastomer (DE) can reach two different stable equilibrium states under a static electrical load. In this paper, a theoretical model is developed to investigate the strain-stiffening effect on the nonlinear vibration of a circular DE membrane subjected to electro-mechanical loading. Free vibration, steady parametric excitation and chaos of the DE membrane undergoing large deformation are studied respectively. We find that after a small perturbation the DE membrane vibrates steadily around the two stable stretches and two natural frequencies exist for the same loading condition. With the increase of initial perturbation energy, the amplitude–frequency response of free vibration shows a transition from behaving like a soft spring to a hard spring attributed to strain-stiffening effect. When driven by a sinusoidal voltage, the DE membrane can resonate at multiple frequencies of excitation around small and large stable equilibrium states respectively. Variation of the sinusoidal voltage may induce a sudden change from steady vibration to chaos and the critical conditions for the transition are numerically calculated.