Propagation of plane waves at the interface of an elastic solid half-space and a microstretch thermoelastic diffusion solid half-space

Rajneesh Kumar,Sanjeev Ahuja,S.K Garg

doi:10.1590/s1679-78252013000600002

Rajneesh Kumar, Sanjeev Ahuja + Show 1 more

Open Access

https://doi.org/10.1590/s1679-78252013000600002

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Abstract

The problem of reflection and refraction phenomenon due to plane waves incident obliquely at a plane interface between uniform elastic solid half-space and microstretch thermoelastic diffusion solid half-space has been studied. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the microstretch thermoelastic diffusion properties of the media. The expressions of amplitude ratios and energy ratios are obtained in closed form. The energy ratios have been computed numerically for a particular model. The variations of energy ratios with angle of incidence are shown for thermoelastic diffusion media in the context of Lord-Shulman (L-S) (1967) and Green-Lindsay (G-L) (1972) theories. The conservation of energy at the interface is verified. Some particular cases are also deduced from the present investigation.

Highlights

Theory of microstretch continua is a generalization of the theory of micropolar continua.The theory of microstretch elastic solids has been introduced by Eringen [7,8,9,10]
The Matlab software 7.04 has been used to determine the values of energy ratios Ei, i = 1,2 and energy matrix Eij, i, j = 1,2,3,4,5,6 defined in the previous section for different values of incident angle (θ ) o ranging from to for fixed frequency ω
In all figures of microstretch thermoelastic diffusion medium the graphs for L-S and G-L theories are represented by the word MDLS and MDGL respectively

Summary

INTRODUCTION

Theory of microstretch continua is a generalization of the theory of micropolar continua.The theory of microstretch elastic solids has been introduced by Eringen [7,8,9,10]. Kumar et al / Propagation of waves at the interface of an elastic solid half-space and a microstretch thermoelastic diffusion solid half-space find applications in the treatment of the mechanics of composite materials reinforced with chopped fibers and various porous materials. Dudziak and Kowalski [6] and Olesiak and Pyryev [23], respectively, discussed the theory of thermodiffusion and coupled quasi-stationary problems of thermal diffusion for an elastic layer. Uniqueness and reciprocity theorems for the equations of generalized thermoelastic diffusion problem, in isotropic media, was proved by Sherief et al [24] on the basis of the variational principle equations, under restrictive assumptions on the elastic coefficients. The law of conservation of energy at the interface is verified

BASIC EQUATIONS

FORMULATION OF THE PROBLEM

REFLECTION AND REFRACTION

BOUNDARY CONDITIONS

NUMERICAL RESULTS AND DISCUSSION

CONCLUSION