Resonant behavior of a membrane of a dielectric elastomer

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.