Magnetoelastic Wave Propagation

Abstract

In this chapter we analyze incremental small amplitude motions and magnetic fields superimposed on an underlying finite deformation and magnetic field with a particular interest in the effect of the underlying configuration on the propagation of small amplitude waves. First we examine the propagation of homogeneous plane waves in an infinite medium of an incompressible magnetoelastic material where the underlying configuration corresponds to a homogenous deformation with a uniform magnetic field; no restriction is placed on the material symmetry. This involves an extension of the notion of strong ellipticity to the magnetoelastic context. The theory is then applied to a prototype model of a neo-Hookean magnetoelastic material. Following this we specialize to increments in two dimensions in a principal plane of an isotropic magnetoelastic material. This specialization is then applied to the study of surface wave propagation, first for Rayleigh-type waves on a half-space with the magnetic field either parallel to or perpendicular to the surface and then to Love-type waves with a layer of different material bonded to the half-space. Finally, we investigate the propagation of Bleustein–Gulyaev-type waves on a half-space without a layer. For each type of surface wave numerical results are obtained for the speed of wave propagation in terms of parameters associated with the underlying configuration and illustrated graphically, while for the Bleustein–Gulyaev-type waves some closed-form expressions are obtained for the wave speed in particular cases.