Abstract
This paper investigates the nonlinear dynamics of square dielectric elastomer membranes under time-dependent, through-thickness compressive loading. The dielectric elastomer is modeled as an isotropic ideal dielectric, with mechanical stiffening at large strains captured using the Gent hyperelastic constitutive model. The equation of motion for the in-plane membrane stretch is derived using Hamilton’s principle. The static response of the membrane is first investigated, with equilibrium stretches calculated numerically for a wide range of compressive pre-loads and applied voltages. Snap-through instabilities are observed, with the critical snap-through voltage decreasing with increasing compressive pre-load. The dynamic response of the membrane is then investigated under forced harmonic excitation. Frequency response plots characterizing the steady-state vibration reveal primary, subharmonic, and superharmonic resonances. Near these resonances, two stable vibration states are possible, corresponding to upper and lower branches in the frequency response. Significant and practically meaningful differences in the dynamic response are observed when the system vibrates at a fixed frequency about the upper and lower branches, a feature not discussed in previous research.
