Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave

Shishir Gupta,Dinesh K Majhi,Sumit K Vishwakarma,Amares Chattopadhyay

doi:10.4236/am.2011.25078

Shishir Gupta, Dinesh K Majhi + Show 2 more

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https://doi.org/10.4236/am.2011.25078

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Journal: Applied mathematics	Publication Date: Jan 1, 2011
Citations: 11	License type: CC BY 4.0

Affiliation: Indian Institute of Technology Dhanbad

Abstract

In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.

Highlights

The earth is a non-homogeneous medium with variations in density and rigidity in constituent layer
In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density
It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space

Summary

Introduction

The earth is a non-homogeneous medium with variations in density and rigidity in constituent layer. Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium is studied by Abd-Alla and Ahmed [8]. References to be made to Das and Dey [11,12], Dey [13], Dey and Addy [14], Chattopadhyay and De [15], Chattopadhyay and Kar [16] and others They suggested that the studies on the problem of elastic wave inside the earth deserve the consideration of initial stresses present in the medium. These stresses might exert significant influence on the elastic. The upper boundary plane of the layer is assumed to be rigid, and both the rigidity and the mass density of the underlying half space are assumed to increase linearly with depth

Formulation and Solution of the Problem

Solution for the Half-Space

L0 K c2 0 N0

Particular Cases

Numerical Computation and Discussion