Scattering of anti-plane surface wave due to irregularity in hyperelastic imperfectly bonded bi-material structure

Abstract

The crux of this work is to investigate the scattering phenomena of Love-type wave due to irregularity on the upper surface of a layered structure. This structure basically incorporates two unlike nearly incompressible elastic materials which are bonded to each other imperfectly at the common interface between layer and half-space. The imperfect interface is described by linear spring model. The analytical methods which are applied, in order to derive the solution of displacement components and obtain the dispersion relations of Love-type wave, include variable separable method and substitution method along with perturbation technique. The dispersion relations and the expressions of displacement components of Love-type wave are obtained for both the incident and the scattered wave fields. Further, the expressions of reflected displacement fields of Love-type wave for distinct cases of irregularity, viz., rectangular shaped, parabolic shaped and triangular shaped irregularities, at the free surface are also determined. The derived results of dispersion relations and reflected displacement fields of Love-type wave, as particular case, concur well with the results existing in the literature. By means of numerical simulation, the influences of irregularity shapes and involved parameters, viz., irregularity depth, irregularity width and imperfect bonding parameter, on reflected displacement field of Love-type wave are manifested graphically. The impacts of imperfect bonding parameter and wave number on phase velocity of Love-type wave are also depicted. The computational results signify the substantial effects of irregularity at the free surface and imperfectness at the interface on the characteristics of Love-type wave in the considered nearly incompressible elastic structure. The reported results of the study may play pivotal role in the realm of civil, mechanical and earthquake engineering for the purpose of vibration isolation, shock absorber, flex-joints, engine mounts, and so forth.