Axisymmetric wave propagation in finitely deformed dielectric elastomer tubes

Abstract

Wave propagation in hollow dielectric elastomer cylinders is studied. The quasi-static deformation of the tube owing to a combination of radial electric field and mechanical loading is determined first. Two combinations are accounted for, one at which the tube is free to expand in the axial direction, and another at which the tube is axially pre-stretched and restricted from elongating. Subsequently, longitudinal axisymmetric incremental motions are superposed on the underlying state. The governing equations in the tube and in the surrounding space are formulated and a numerical procedure is used in order to solve the resulting set of equations. The fundamental mode in the frequency spectrum is determined for thin, intermediate and thick wall tubes. The influences of the tube geometry, the mechanical pre-stretch and particularly the electric bias field are examined. An important observation is the ability to manipulate the propagation of the waves by adjusting the electromechanical bias field. This infers the use of dielectric elastomers in tubular configurations as active waveguides or isolators by a proper tuning of the electrostatic stimuli.