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Modelling of nonlinear wave scattering in a delaminated elastic bar

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journal contribution
posted on 17.11.2015 by Karima Khusnutdinova, Matt Tranter
Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of the structure. Can nonlinear waves help us to control the quality of layered structures? In this paper, we numerically model the dynamics of a long longitudinal strain solitary wave in a split, symmetric layered bar. The recently developed analytical approach, based on matching two asymptotic multiple-scales expansions and the integrability theory of the Korteweg–de Vries equation by the inverse scattering transform, is used to develop an effective semi-analytical numerical approach for these types of problems. We also employ a direct finite-difference method and compare the numerical results with each other, and with the analytical predictions. The numerical modelling confirms that delamination causes fission of an incident solitary wave and, thus, can be used to detect the defect.

Funding

This work was supported by the Engineering and Physical Sciences Research Council (EPSRC). M.R.T. is supported by an EPSRC studentship.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of the Royal Society A

Volume

471

Issue

2183

Citation

KHUSNUTDINOVA, K.R. and TRANTER, M., 2015. Modelling of nonlinear wave scattering in a delaminated elastic bar. Proceedings of the Royal Society A, 471 (2183)

Publisher

The Royal Society (© The authors)

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Publication date

2015

Notes

This is an Open Access article published under the Creative Commons Attribution licence (CC BY 4.0).

ISSN

1364-5021

eISSN

1471-2946

Language

en

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