Nonlinear dynamic characteristics of a dielectric elastomer membrane undergoing in-plane deformation

This paper proposes a free energy model to study the dynamic characteristics of a dielectric elastomer membrane undergoing in-plane deformation, subject to the combined loads of a mechanical press and an electric field. The natural frequency of the small-amplitude perturbation around the state of equilibrium is calculated with focus on the damping effects and the resonance phenomenon. The numerical results, such as the oscillation, phase diagrams and Poincaré maps, are presented to show the influence of the damping on the nonlinear dynamic characteristics of the dielectric elastomer. The numerical results indicate that pre-stresses, damping effects and applied voltages could tune the natural frequency and modify the dynamic behavior of the dielectric elastomer. There is a stability transition when taking the damping effect into account. The damping effect could cause the dynamic responses to constant vibration and decrease the amplitude. These conclusions may guide the exploration of high-performance dielectric elastomers under dynamic mechanical and electrical loads.