Nonlinear dynamic analysis and active control of visco-hyperelastic dielectric elastomer membrane

Dynamic analysis and active control are important bases for dielectric elastomer (DE) applications. Most of the DE materials exhibit significant viscoelasticity. Although the visco-hyperelastic constitutive relations of DEs have been studied before, the dynamic analysis of the DEs with the consideration of viscoelasticity has rarely been explored. In this study, we lay out the dynamic equations for the visco-hyperelastic DE structures. The Gent hyperelastic model is applied to take into account the strain-stiffening effect of the elastomer. Based on the model, we derive an analytical solution for the dynamic DE under homogeneous in-plane deformation. We show that the model can capture the nonlinear oscillation of the DE and allows us to investigate how the viscoelasticity and strain-stiffening effect influence the resonant frequencies and oscillation amplitudes of the system. Given the nonlinear and viscoelastic nature of the material, its dynamic response could be complicated and deviate from the desired harmonic oscillation pattern. To achieve precise control over the outputs, we employ a PID controller to build a closed-loop feedback control and demonstrate its feasibility to correct most of the undesired outputs such as nonlinear oscillation, beating phenomenon, phase lag and so on.