# On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations

## TL;DR

This paper develops a semi-analytical method to study the scattering of radiating solitary waves in layered elastic structures with delamination, providing insights into wave dynamics and potential structural integrity control.

## Contribution

A semi-analytical approach using matched asymptotic expansions to analyze radiating solitary waves in bi-layered structures with delamination, validated against numerical simulations.

## Key findings

- Semi-analytical method agrees well with numerical simulations.
- Radiating solitary waves influence the integrity of layered structures.
- Wave dynamics can be controlled through understanding of scattering processes.

## Abstract

We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft (`imperfect') bonding between the layers within the scope of the coupled Boussinesq equations. The direct numerical modelling of this and similar problems is challenging and has natural limitations. We develop a semi-analytical approach, based on the use of several matched asymptotic multiple-scale expansions and averaging with respect to the fast space variable, leading to the coupled Ostrovsky equations in bonded regions and uncoupled Korteweg-de Vries equations in the delaminated region. We show that the semi-analytical approach agrees well with direct numerical simulations and use it to study the nonlinear dynamics and scattering of the radiating solitary wave in a wide range of bi-layers with delamination. The results indicate that radiating solitary waves could help us to control the integrity of layered structures with imperfect interfaces.