Shear Waves Through Non Planar Interface Between Anisotropic Inhomogeneous and Visco-Elastic Half-Spaces

Subject Areas : Engineering

B Prasad ¹ , P Chandra Pal ² , S Kundu ³

1 - Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
2 - Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
3 - Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India

Received: 2018-06-28 Accepted : 2018-08-27 Published : 2018-09-30

Keywords: Inhomogeneity, SH-waves, Anisotropy, Visco-elastic, Corrugated boundary,

Abstract :

A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the corrugation. Further, closed form formulae of these coefficients are presented for a corrugated interface of periodic shape (cosine law interface). Numerical computations for this particular type of corrugated interface are performed and a number of graphs are plotted to illustrate the effect of different parameters of the both half-spaces on the reflection and transmission coefficients. It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave and are strongly influenced by the anisotropy, inhomogeneity and visco-elasticity of the half-spaces. Some special cases are also derived.

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