Nonlinear dynamic responses of electrically actuated dielectric elastomer-based microbeam resonators

Abstract

This paper aims to investigate the chaotic and nonlinear resonant behaviors of a dielectric elastomer-based microbeam resonator, incorporating material and geometric nonlinearities. The von Kármán strain-displacement equation is utilized to model the geometric nonlinearity. Material nonlinearity is described via the hyperelastic Gent model and Neo-Hookean constitutive law. The applied electrical loading to the elastomer includes both static and sinusoidal voltages. The governing equations of motion are formulated based on an energy approach and generalized Hamilton’s principle. Employing a single-mode Galerkin technique, the governing equations are obtained only in terms of time derivatives. The governing ordinary differential equations are solved by means of the multiple scale method and a time-integration-based solver. The nonlinear resonance characteristics are explored through the frequency-amplitude plots. The nonlinear oscillations of the system are analyzed making use of visual techniques such as phase plane diagram, Poincaré section and time history, and fast Fourier transform. Based on the results obtained, the resonant behavior is the hardening type. The vibration of the dielectric elastomer based-microbeam is the quasiperiodic response.