Circumferential wave propagation in nonlinear dielectric bilayer tubes under inhomogeneous biasing fields

Abstract

Dielectric elastomer structures with large deformation and electromechanical coupling are susceptible to biasing fields and show potentials in tunable elastic wave devices. This work focuses on circumferential waves in the incompressible isotropic dielectric bilayer tube subjected to an axial pre–stretch and radial voltage. Based on the nonlinear electroelasticity theory, the deformation of the structure characterized by the Gent ideal dielectric model is elaborated. The strain–stiffening enables the bilayer tube to resist large deformation and enhances the tunability under inhomogeneous biasing fields. In order to analyze the dynamic behaviors of circumferential shear horizontal (CSH) and Lamb–like (CLT) waves, the Legendre polynomial expansion method (LPEM) is combined with the linearized incremental equations to derive the dispersion relation. It overcomes the difficulties of conventional matrix methods in dealing with radial dependent electroelastic moduli and shows good convergence. Numerical results demonstrate that the pre–stretch, voltage and strain–stiffening can change the geometry and electroelastic moduli of the dielectric tube, which exhibit the potential to tune the propagation behaviors of circumferential waves. In addition, dispersion properties of circumferential waves are sensitive to the voltage change, which indicates that the dielectric bilayer tubular systems can act as voltage–controlled elastic wave actuators and sensors.