Nonlinear bifurcations of a circular dielectric-elastomer resonator based on a modified incremental harmonic balance method

Abstract

When dielectric-elastomer (DE) resonators are operated under large alternating voltage excitations, strong geometric and material nonlinearities can significantly affect the dynamic performance. Based on the virtual work principle, a dynamic model of a circular DE resonator is established in this work. Static analysis is conducted to study the impacts of the control voltage on the strain and natural frequency of the DE resonator at equilibrium. A modified Incremental Harmonic Balance and arc-length methods are used to obtain dynamic responses of the system excited by alternating voltages, and stability analysis is conducted using the Floquet theory. The effects of the mechanical parameters are studied, and period-doubling bifurcations are observed, which are produced by the parametric excitation of the voltage. The bifurcation phenomenon is comprehensively investigated through analysis of the voltage, stress, and damping coefficient, which provides design guidance for DE resonators.