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

Abstract

In this paper we have derived reflection and transmission coefficients of qP-waves at a corrugated interface between two different elastic half-spaces of monoclinic type. Using Rayleigh's method, the expressions for reflection and transmission coefficients are derived in closed form for a specific interface and for the first order approximation of the corrugation. Numerical computations are performed for a specific model and the results obtained have been shown graphically. The variation of the modulus of reflection and transmission coefficients with the angle of incidence, frequency and corrugation of the interface are shown separately. These coefficients are found to be strongly influenced by the angle of incidence, frequency, elastic parameters and amplitude of the corrugation of the interface. It is found that (i) the modulus of reflection and transmission coefficients at the plane interface are independent of corrugation of the interface and that of frequency of the incident wave, (ii) the reflection and transmission coefficients of regularly reflected and transmitted waves are found to be greater than that of irregularly reflected and transmitted waves, (iii) the coefficients of irregularly reflected and transmitted waves are found to increase and decrease with increase of corrugation and frequency parameters respectively. The results of Singh and Khurana [Singh, S.J., Khurana, S., 2001. Reflection and transmission of P-and SV-waves at the interface two between monoclinic elastic half-spaces. Proc. Natl. Acad. Sci. India 71(A) (IV), 305-319] have been reduced from the present problem.

Homogenization of an interface highly oscillating between two concentric ellipses

“…In particular, we want to find the explicit homogenized equation of the problem (1), (7) and the associate boundary conditions in terms of the variables r, θ. Note that σ and λ are defined by (3).…”

“…Boundary-value problems in domains with rough boundaries or interfaces is closely related to various practical problems such as scattering of elastic waves at rough boundaries and interfaces [1], transmission and reflection of waves on rough interfaces [2,3,4], mechanical problems concerning the plates with densely spaced stiffeners [5], flows over rough walls [6] and so on. When the amplitude (height) of the roughness is much small comparison with its period, the problems are usually analyzed by perturbation methods.…”

Homogenization of Rough Two-Dimensional Interfaces Separating Two Anisotropic Solids

“…Boundary-value problems in domains with rough boundaries or interfaces appear in many fields of natural sciences and technology such as scattering of waves on rough boundaries [1-4]; transmission and reflection of waves on rough interfaces [5][6][7]; mechanical problems concerning the plates with densely spaced stiffeners [8]; the flows over rough walls [9]; nearly circular hole, inclusion problems in plane elasticity and thermoelasticily [10][11][12]; and so on. When the amplitude (height) of the roughness is much small in comparison with its period (see, for example, Ref.…”

Effect of point source and heterogeneity on the propagation of magnetoelastic shear wave in a monoclinic medium

“…Chattopadhyay et al (1994) studied the propagation of a crack due to shear waves in a non-homogeneous medium of monoclinic. Subsequently, Singh and Tomar (2007) studied the propagation of quasi-P wave at the interface between two monoclinic half-spaces.…”