Propagation of Waves at an Interface between a Liquid Half‐Space and an Orthotropic Micropolar Solid Half‐Space

Baljeet Singh,Ritu Sindhu

doi:10.1155/2011/159437

Abstract

An inviscid liquid half‐space is considered in welded contact with a orthotropic micropolar solid half‐space. Appropriate plane harmonic solutions of equations governing a liquid half‐space and an orthotropic solid half‐space are obtained. These solutions satisfy the required boundary conditions at the interface to obtain a system of four nonhomogeneous equations in amplitude ratios for incident quasi‐longitudinal displacement wave. The amplitude ratios of various reflected and refracted waves are computed numerically for a particular example of the present model. The effect of anisotropy upon these amplitude ratios is shown graphically for a particular range of the angle of incidence.

Highlights

Material response to external stimuli depends heavily on the motions of its inner structures
Singh [13] investigated the two-dimensional plane wave propagation in an orthotropic micropolar elastic soli and showed the existence of three types of coupled plane waves in xy-plane, whose velocities depend upon the angle of propagation and material parameters
The x1-axis is along the interface between the liquid half-space and orthotropic micropolar solid half-space

Summary

Introduction

Material response to external stimuli depends heavily on the motions of its inner structures. Eringen [1] developed the linear micropolar theory of elasticity, which included the intrinsic rotations of the microstructure It provides a model which can support body and surface couples and display high frequency optical branch of the wave spectrum. Singh [13] investigated the two-dimensional plane wave propagation in an orthotropic micropolar elastic soli and showed the existence of three types of coupled plane waves in xy-plane, whose velocities depend upon the angle of propagation and material parameters. He studied the reflection of these plane waves from a stress-free free surface and obtained the reflection coefficients for various reflected waves. The reflection and transmission coefficients are computed numerically for a particular model to observe the effect of orthotropy

Formulation of the Problem and Solution

Reflection and Transmission

Numerical Example

Concluding Remarks