Dynamic behavior of multi-layer heterogeneous composite magneto-elastic structures for surface wave scattering

Abstract

The paper is focused on the surface wave field in functionally graded multi-layer transversely isotropic heterogeneous magneto-elastic reinforced media. The Geometry of the problem is formulated by considering the (n−1) finite layer composite structure over a semi-infinite substance, occupying the domain: −∞<x,y<∞,hi−1≤z≤hi,i=1,2,⋯n−1,h0=0 and hn−1≤z≤∞. Mechanical properties of magneto-elastic heterogeneous reinforced media in wave scattering are an essential part of this study. A generalized Haskell’s [1] technique has been applied to obtain the wave scattering relation in multi-layer heterogeneous magneto-elastic media using suitable boundary conditions. Estimated wave scattering relation is in affirmation with the general Love-type surface wave relation in case of a single layered medium over a semi-infinite substance as well as multi-layered media over the semi-infinite substance. A finite difference technique is derived to obtain the group and phase velocities with shear deformation in the magneto-elastic heterogeneous reinforced media. To study the group and phase velocity in a square grid, stability conditions for introducing finite difference techniques have been derived. Using graphical representation, it has been examined that phase velocity, group velocity, and wave scattering in the layered media are affected by heterogeneity, reinforced, magneto-elastic coupling parameters, and stability ratio.