Reflection and refraction of SH‐waves at a corrugated interface between two monoclinic elastic half‐spaces

Abstract

SUMMARYA problem of reflection and transmission of shear wave incident upon a corrugated interface between two monoclinic solid half-spaces have been investigated. Rayleigh's method of approximation is used to investigate the reflection and transmission coefficients for first and second approximation of the corrugation. For a special interface, closed-form expressions of these coefficients for the first order approximation of the corrugation are obtained. It is found that these coefficients are functions of amplitude of corrugation, elastic parameters of the media, frequency of the incident wave and angle of incidence. The numerical computations are performed for a specific model and the results obtained are presented graphically. It is found that the reflection and transmission coefficients are strongly influenced by the corrugation and the elastic properties of the media. Results of some earlier workers in this field have been reduced as particular case from the present formulation.

Quasi-P-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces

“…Several papers have been appeared based on Rayleigh's technique and other techniques in the problems of scattering of elastic waves from boundary surfaces e.g. Asano (1960Asano ( , 1961Asano ( , 1966, Abubakar (1962a,b,c), Rice (1951), Dunkin and Eringen (1962), Deresiewiez and Wolf (1964), Levy and Deresiewicz (1967), Kuo and Nafe (1962), Tomar and Saini (1997), Gupta (1978Gupta ( , 1987, Tomar et al (2002), Kumar et al (2003), Tomar and Kaur (2003) and Kaur and Tomar (2004). Nayfeh (1991) derived analytical expressions for the reflection and transmission coefficients from the interfaces of liquid-anisotropic half-spaces possessing up to as low as monoclinic symmetry and the expressions for the distributions of stresses and displacements throughout the fluid-solid system.…”

Effects of frequency parameter due to elastic wave in monoclinic elastic medium

“…Singh and Tomar (2007) investigated the problem of qP-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces and obtained the reflection and transmission coefficients of the irregular waves using Rayleigh's technique. Kaur and Tomar (2004) investigated the problem of reflection and transmission of shear wave incident upon a corrugated interface between two monoclinic elastic half-spaces with the help of Rayleigh's technique. But, there are many experimental evidences that the interfaces between layers are not perfectly plane, but they are of irregular in nature.…”

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

“…Rayleigh used this method, in his paper "On the dynamical theory of grating" [1907], and later, researchers in various fields applied his method to explain reflection and transmission phenomena of waves from irregular boundary surfaces. Using different techniques, many problems of reflection and refraction of elastic waves from irregular boundary surfaces have appeared in the open literature, such as [Abubakar 1962;Asano 1960;1961;1966;Dunkin and Eringen 1962;Tomar and Saini 1997;Okamoto and Takenaka 1999;Tomar et al 2002;Gupta 1987;Kumar et al 2003;Tomar and Kaur 2003;Kaur and Tomar 2004;Kaur et al 2005].…”