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

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