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

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.

arXiv comment17 pages, 10 figures. Accepted for publication in Chaos (2017)

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• Parametric excitation of multiple resonant radiations from localized wavepackets
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• Radiating solitary waves in coupled Boussinesq equations
• Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities
• Solitary Wave Propagation in Elastic Bars with Multiple Sections and Layers
• Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction
• D'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation
• Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Wavegudes