Elastic-wave scattering and Stoneley wave localization by anisotropic imperfect interfaces between solids

Abstract

SUMMARY In this paper, elastic scattering and localization of guided waves on a thin anisotropic imperfect interfacial layer between two solids are studied. We have proposed a second-order asymptotic boundary condition approach to model such an interfacial layer. Here, using previous results, we derive simple stiffness-matrix representations of stress-displacement relations on the interface for the decomposed symmetric and anti-symmetric elastic motions. The stiffness matrices are given for an off-axis orthotropic layer or, equivalently, for a monoclinic interfacial layer. For the problem of scattering on such a thin anisotropic layer between identical isotropic semi-spaces the scattering matrices are obtained in explicit forms. Analytical dispersion equations for Stoneley-type interfacial waves localized in such a system are also given. Additional results are included for imperfect interfaces, such as fractured interfaces, modelled by spring boundary conditions. The applicability of the stiffness-matrix approach to the layer model is analysed by numerical comparison between the approximate and exact solutions. The numerical examples, which include reflection transmission on the interphase and dispersion curves of the interfacial waves, show that the stiffness-matrix method is a simple and accurate approach to describe wave interaction with a thin anisotropic interfacial layer between two solids.