Response analysis of the Duffing oscillator in dielectric elastomer transducers

Abstract

To elucidate the nonlinear oscillations inherent to dielectric elastomer transducers (DETs), this study delves into the dynamic behaviour exhibited by a one-dimensional asymmetric Duffing oscillator, which may exhibit either hardening or softening stiffness. The investigation utilizes hyperelastic and visco-hyperelastic constitutive models to capture the nonlinear stiffness properties of dielectric elastomers within compliant transducers. The canonical Duffing equation is employed to articulate the oscillator’s motion, complemented by both asymptotic and quantitative analyses of unforced vibrations and harmonic excitation. Our results reveal that the distinctive stiffness characteristics observed in DETs arise from the complex interplay among hyperelasticity, rheology and applied electric fields. Contrary to conventional oscillators, Maxwell stress substantially modifies the nonlinear dynamics of DETs, an aspect that has been quantitatively dissected in this study. Furthermore, the influence of additional system parameters on forced oscillation has also been meticulously evaluated.