This paper analyzes a membrane of a dielectric elastomer, prestretched and mounted on a rigid circular ring, and then inflated by a combination of pressure and voltage. Equations of motion are derived from a nonlinear field theory, and used to analyze several experimental conditions. When the pressure and voltage are static, the membrane may attain a state of equilibrium, around which the membrane can oscillate. The natural frequencies can be tuned by varying the prestretch, pressure, or voltage. A sinusoidal pressure or voltage may excite superharmonic, harmonic, and subharmonic resonance. Several modes of oscillation predicted by the model have not been reported experimentally, possibly because these modes have small deflections, despite large stretches.

International Journal of Solids and Structures. In press.

This paper studies 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.  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 hyste