Nonlinear dynamic analysis of dielectric elastomer minimum energy structures

This paper presents a theoretical study of nonlinear dynamic behavior of a dielectric elastomer minimum energy structure (DEMES). While planar Dielectric Elastomer Actuators (DEA) solely poses material nonlinearity in their model, geometrical nonlinearity imposes additional challenge to model DEMES. Considering dielectric elastomer and bending frame, respectively, as a hyper-elastic film and an elastic beam, Euler–Lagrange equation is employed to derive the equation of motion of actuator subject to a harmonic voltage. Fixed point analysis of the equation of motion demonstrates supercritical pitchfork bifurcation with respect to film pre-stretch as bifurcation parameter. It is shown by simulation results that the system possesses harmonic resonances as well as superharmonic and subharmonic resonance. Investigating Poincare map of the time response indicates that by changing excitation frequency and amplitude the response transforms from periodic to quasiperiodic and eventually aperiodic form.