Two-dimensional interactions due to moving load in generalized thermoelastic solid with diffusion

Abstract

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically. Nomenclature λ, μ Lame's constants, ρ density of the medium, σij components of stress tensor, eij components of strain tensor, ui components of displacement vector, CE specific heat at constant strain, t time, T absolute temperature, T0 reference temperature chosen so thatδij Kronecker delta, P chemical potential per unit mass, C mass concentration, D thermodiffusion constant, τ0 thermal relaxation time, τ diffusion relaxation time, a measure of thermodiffusion effect, b measure of diffusive effects, β1 = (3λ + 2μ)αt, β2 = (3λ + 2μ)αc, αt coefficient of linear thermal expansion, αc coefficient of linear diffusion expansion, F0 intensity of the applied mechanical load, *

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