Modelling and analysis of imperfect and sliding interfaces on Love-type wave in non-planar non-homogeneous nearly incompressible elastic layered structure

Abstract

This work aims to develop a mathematical model for Love-type wave (LTW) propagation in non-planar non-homogeneous nearly incompressible elastic layered structure with imperfect and sliding interfaces following a geometrical model. Concretely, the geometrical model constitutes two unlike non-homogeneous nearly incompressible elastic materials forming a combination of stratum and substrate, which in turn involve imperfectness at the interface and non-planar boundaries (NPBs). With aid of applicable mathematical techniques, the expressions of displacement components (DCs) of LTW have been determined for both planar boundaries (PBs) and NPBs with imperfect interface. As a special case of the study, the expressions of DCs of LTW have also been deduced for both PBs and NPBs with sliding interface. Further, as an offshoot of the current study, dispersion relations (DRs) of LTW propagating in non-homogeneous and homogeneous nearly incompressible as well as isotropic elastic structures having imperfect, perfect and sliding interfaces have been established and validated with the results present in the literature. For graphical delineation, numerical computation of the DCs and phase velocity (PV) of LTW has been performed. The influences of non-homogeneity parameters, curvature parameters, interfacial parameter and wave number on DCs and PV of LTW have been figured out. It has been revealed that the presence of non-homogeneity in structure has substantial effect on the DCs and PV of LTW. Moreover, a comparative approach has been brought in to study the DCs and PV of LTW in non-homogeneous and homogeneous cases of nearly incompressible elastic structure (NIES) having imperfect and sliding interfaces.