Asymptotic analysis of the dispersion relation of an incompressible elastic layer of uniform thickness

Abstract

This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform hydrostatic stress. In respect of a general form of incompressible,isotropic elastic strain-energy function, the dispersion equation for infinitesimal waves is obtained asymptotically for incremental traction boundary conditions on the faces of the layer. Two sets of wavespeeds as a function of wave number, layer thickness and material parameter are obtained and the numerical results are illustrated for two different classes of strain-energy functions. For a particular class of strain energy functions, it is shown that wave speeds don't depend upon the amount of shear and the material parameters. For materials not in this special class velocities do depend upon the shear deformation.