Unusual nonlinear frequency response in circular dielectric elastomer membranes excited by fluctuating through-thickness voltages

Abstract

This work demonstrates novel nonlinear vibration behavior in circular dielectric elastomer membranes that are excited by low nominal voltages with moderate-to-large-amplitude sinusoidal fluctuations. Low nominal voltages are those where the membrane has only one equilibrium stretch, and snap-though instability is not possible. The dynamic stretches therefore can be extremely large, and are limited only by the locking stretch of the elastomer. Because extremely large stretches are possible without snap-through instability, resonances in the frequency response transition from softening nonlinearity at moderate stretches to hardening nonlinearity at large stretches. Two types of atypical frequency response that depend on the amplitude of voltage fluctuations that dynamically excite the membrane are reported here for the first time. First, for moderate-amplitude voltage fluctuations, three steady-state vibrations (corresponding to small, moderate, and extreme stretches) are possible within a frequency band near resonance. Second, for large-amplitude voltage fluctuations, a frequency band occurs near resonance where only one steady-state vibration is possible, and this vibration corresponds to extreme dynamic stretches. Because of these unique steady-state solutions near resonance, new atypical jump-phenomenon may occur during frequency sweeps through resonance. The new, previously unreported vibration and jump phenomena demonstrated in this paper may be leveraged for improved performance in applications like resonators, energy harvesters, actuators, and sensors.