Localisation effect during wave pulse propagation in randomly stratified elastic medium

Abstract

In this paper the propagation of the planar wave pulses in a two-dimensional randomly stratified elastic medium is considered. The waves propagate in the plane (x₁, x₂) and are independent of the third variable z. The problem is described by means of the transition matrix method. The transition matrix and the wave equation for a homogeneous layer is presented. The equations for the wave fields reflected from and transmitted through the randomly stratified elastic slab are derived. The theoretical results are illustrated by graphically presented numerical calculations. A possibility of application of the wave analysis to modelling of the fatigue crack propagation initiated at the interfaces and continued due to sequences of the reflected and transmitted stress waves is discussed.