Propagation of transverse waves in a bilayer with initial stress

Abstract

The propagation of waves in a bilayer without stress was studied in [6]. Wave propagation in a bilayer with initial stresses has been considered in a simplified formulation in [I, 8] and elsewhere, where the treatment was mainly limited to deriving the dispersion relations. In [4, 7] wave propagation was considered in a multiple-layered medium with initial stress. In the present paper we consider the propagation of transverse waves in a bilayer subjected to finite, static, uniform deformations. It is assumed that in thenatural (undeformed) state the layer is isotropic. The dispersion ~e!ations are derived for SH waves and Love waves for a body with an arbitrary potential. Numerical results are presented for the Murnaghan potential. The no=ation of [3, 5] is followed, i. The propagation of small-amplltude waves in a body with initial stresses is studied using the three-dimensional linearized theory of elasticity [2, 5]. In the case when the initial stress-deformed state is uniform u~ = 8m~ (~i-l)x~ (~: = const), (i.!) the linearized equations of motion in terms of the displacements have the following form in the absence of body forces and for an initially isotropic body: