Shear wave propagation due to point source in hyperelastic layered structure with tangential resistance at the discontinuous interface: Green's function approach

In this work, the dispersive behavior of horizontally polarised shear wave is manifested under the influence of a point source at the discontinuous interface of hyperelastic layered structure. Essentially, this structure is comprised of homogeneous nearly incompressible elastic layer overlying non-homogeneous nearly incompressible elastic half-space having tangential resistance at the discontinuous interface between layer and half-space. The formulated mathematical model, based on geometry of the problem, is solved analytically by means of Fourier transform and Green's function to derive the dispersion relation of shear wave. The derived dispersion relation, as particular case of the study, leads to the deduction of various analytical results corresponding to distinct structures of interest, which are also validated with the results existing in the literature. Numerical computation is performed to trace out the effects of associated affecting parameters, viz., tangential frictional resistance parameter, functional non-homogeneity parameter, magnifying non-homogeneity parameters and wave number, on phase velocity of shear wave that are illustrated graphically. Also, dispersion curves are depicted for the case when layer and half-space are in sliding contact to each other. Further, a comparative approach is brought in to look into the impacts of aforementioned parameters on phase velocity of shear wave by considering distinct nearly incompressible elastic materials, viz., Varga material and Neo-Hookean material. The computational results quite evidently shed light on how the affecting parameters and distinct materials influence the propagation characteristics of shear wave in the considered structure under the effect of point source.