Effect of Initial Stress on the Propagation Characteristics of Waves in Fiber-Reinforced Transversely Isotropic Thermoelastic Material under an Inviscid Liquid Layer

Rajneesh Kumar,S K Garg,Sanjeev Ahuja

doi:10.1155/2014/134276

Abstract

The present investigation deals with the propagation of waves in fiber-reinforced transversely isotropic thermoelastic solid half space with initial stresses under a layer of inviscid liquid. The secular equation for surface equation in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficients of plane waves are studied numerically for a particular model. Effects of initial stress and thickness of the layer on the phase velocity, attenuation coefficient, and specific loss of energy are predicted graphically in the certain model. A particular case of Rayleigh wave has been discussed and the dispersion curves of the phase velocity and attenuation coefficients have also been presented graphically. Some other particular cases are also deduced from the present investigation.

Highlights

Fiber-reinforced materials are widely used in engineering structures due to their superiority over the structural materials in applications requiring high strength and stiffness in lightweight components
Othman and Song [22] discussed the reflection of plane waves from a thermoelastic elastic solid half-space under hydrostatic initial stress without energy dissipation
Othman et al [24] investigated the influences of fractional order, hydrostatic initial stress, and gravity field on the plane waves in a fiber-reinforced isotropic thermoelastic medium using normal mode analysis

Summary

Introduction

Fiber-reinforced materials are widely used in engineering structures due to their superiority over the structural materials in applications requiring high strength and stiffness in lightweight components. Othman and Song [22] discussed the reflection of plane waves from a thermoelastic elastic solid half-space under hydrostatic initial stress without energy dissipation. No attempt has been made to discuss the effect of hydrostatic initial stress on propagation of waves in the layer of fiberreinforced transversely isotropic thermoelastic material. Othman et al [24] investigated the influences of fractional order, hydrostatic initial stress, and gravity field on the plane waves in a fiber-reinforced isotropic thermoelastic medium using normal mode analysis. Othman and Atwa [26] studied the effect of rotation, gravity, and reinforcement on the total deformation and mutual interaction of the body in a fiber-reinforced thermoelastic solid using normal mode analysis in the context of GreenNaghdi theory of thermoelasitcity. The study of present investigation has applications in civil engineering and geophysics

Basic Equations

Formulation of the Problem

Solution of the Problem

Derivations of the Secular Equations

Numerical Results and Discussion

Conclusions