Nonlinear oscillation of a dielectric elastomer balloon

Much of the existing literature on dielectric elastomers has focused on quasi-static deformation. However, in some potential applications, the elastomer deforms at high frequencies and undergoes nonlinear oscillation. While nonlinear oscillation has been studied in many areas of science and engineering, we are unaware of any theoretical analysis of nonlinear oscillation of dielectric elastomers. This paper reports a theoretical study of the dynamic behavior of a dielectric elastomer balloon subject to a combination of pressure and voltage. When the pressure and voltage are static, the balloon may reach a state of equilibrium. We determine the stability of the state of equilibrium, and calculate the natural frequency of the small-amplitude oscillation around the state of equilibrium. We focus on the parametric responses of the dielectric elastomer balloon. When the voltage is sinusoidal, the balloon resonates at multiple frequencies of excitation, giving rise to superharmonic, harmonic and subharmonic responses. When the frequency of excitation varies continuously, the oscillating amplitude of the balloon may jump, exhibiting hysteresis. c © 2010 Society of Chemical Industry