Acceleration waves in elastic dielectrics with polarization gradient effects

Abstract

In this paper the propagation of acceleration waves arbitrary form propagating into a deformed eleastic dielectric with polarization effect is investigated. An acceleration wave is defined as a second order propagating surface of discontinuity on which the position vector, the polarization vector and Maxwell potential, and their first order derivatives with respect to time and space coordinates are continuous while the second order derivatives of these quantities may suffer jumps but are continuous everywhere else. By computing the jumps of the balance equations on the singular surface, implicit equations for wave speeds corresponding to non-zero amplitudes of the acceleration wave are obtained. It is noteworthy that the second order derivatives of Maxwell potential are also continuous across the acceleration wave. The same equation for wave speeds are also derived for isotropic elastic dielectrics. The wave speeds for longitudinal and transverse waves are obtained in explicit forms and the conditions of existence for real wave speeds are investigated.