Parametric vibration of a dielectric elastomer microbeam resonator based on a hyperelastic cosserat continuum model

Abstract

Dielectric elastomers are smart soft systems that belong to electroactive polymers. Microbeam resonators have been introduced as a new application of the dielectric elastomers. In this paper, the nonlinear size-dependent vibration of a dielectric elastomer microbeam resonator was analyzed. The constitutive model of the system was considered based on a hyperelastic Cosserat continuum model. The equation of transverse motion was derived and discretized through the use of Hamilton’s principle and the Galerkin method, respectively. The resulting ordinary differential equation was solved numerically in time domain via the Runge-Kutta method. The influence of the system’s parameters -e.g., the length-scale parameter, polarization voltage, amplitude of AC voltage, and Lame’s modulus on the dynamic response of the system was analyzed. The outcome of the numerical results indicates that both the chaos and quasiperiodicity arise in the micro reasoner. Taking the size effect into account, decreases the response amplitude. The DC and AC voltages can control the chaos phenomenon. Besides, the Lame’s modulus could harness the occurrence of the chaotic motion in the system.