Scattering of an Ostrovsky wave packet in a delaminated waveguide

Abstract

We examine the scattering of an Ostrovsky wave packet, generated from a solitary wave, in a two layered waveguide with a delamination in the centre and soft (imperfect) bonding either side of the centre. The lower layer of the waveguide is assumed to be significantly denser than the upper layer, leading to a system of Boussinesq–Klein–Gordon (BKG) equations. Direct numerical modelling is difficult and so a semi-analytical approach consisting of several matched asymptotic multiple-scale expansions is used, which leads to Ostrovsky equations in soft bonded regions and Korteweg–de Vries equations in the delaminated region. The semi-analytical approach and direct numerical simulations are in good agreement with each other and theoretical estimates. The dispersion relations are used to estimate the wave speed and hence classify the length of the delamination, in addition to changes in the amplitude of the wave packet. We also show how to scale the non-dimensional results to material variables and an example for PMMA is presented. These results can provide a tool to control the integrity of layered structures.