The effect of shear on the propagation of elastic surface waves

Abstract

The propagation of surface waves on a half-space of a pre-stressed incompressible elastic material is discussed. In contrast to previous studies, in which the pre-stress is associated with a pure homogeneous strain with one principal axis normal to the surface of the half-space, this paper examines the influence of an underlying deformation which corresponds to a homogeneous simple shear, so that no principal axis of the deformation is along the surface normal. For a particular class of strain-energy functions an explicit secular equation for the wavespeed is obtained and then analysed to provide necessary and sufficient conditions for the existence and uniqueness of surface waves and quasi-static deformations. Numerical calculations are used to illustrate the dependence of the results on the amount of shear and on the hydrostatic stress.