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

Khusnutdinova, K.R. and Tranter, M.R. ORCID: 0000-0002-6019-8819, 2017. On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations. Chaos: an Interdisciplinary Journal of Nonlinear Science, 27 (1): 013112. ISSN 1054-1500

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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.

Long longitudinal bulk strain solitary waves observed in elastic waveguides, such as rods, bars, plates, and shells, can be modelled with Boussinesq-type equations. Radiating solitary waves, that is solitary waves radiating a co-propagating one-sided oscillatory tail, emerge in layered elastic waveguides with soft ("imperfect") bonding between the layers. In this paper, we study the scattering of a radiating solitary wave in delaminated areas of imperfectly bonded bi-layers within the scope of the coupled Boussinesq equations. We develop direct and semi-analytical numerical approaches and demonstrate that radiating solitary waves undergo changes which could be used to control the quality of the interfaces.

Item Type: Journal article
Publication Title: Chaos: an Interdisciplinary Journal of Nonlinear Science
Creators: Khusnutdinova, K.R. and Tranter, M.R.
Publisher: AIP Publishing
Date: 2017
Volume: 27
Number: 1
ISSN: 1054-1500
Identifiers:
NumberType
10.1063/1.4973854DOI
Rights: All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Divisions: Schools > School of Science and Technology
Depositing User: Linda Sullivan
Date Added: 28 Jun 2019 10:36
Last Modified: 28 Jun 2019 10:37
URI: http://irep.ntu.ac.uk/id/eprint/36947

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