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.
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Abbreviations
- λ, µ :
-
Lame’s constants
- ρ :
-
density of the medium
- σ ij :
-
components of stress tensor
- e ij :
-
components of strain tensor
- u i :
-
components of displacement vector
- C E :
-
specific heat at constant strain
- t :
-
time
- T :
-
absolute temperature
- T 0 :
-
reference temperature chosen so that \(\tfrac{{\left| {T - T_0 } \right|}}{{T_0 }} \ll 1\)
- Θ:
-
T − T 0
- K :
-
thermal conductivity
- e kk :
-
dilatation
- δ ij :
-
Kronecker delta
- P :
-
chemical potential per unit mass
- C :
-
mass concentration
- D :
-
thermodiffusion constant
- τ 0 :
-
thermal relaxation time
- τ :
-
diffusion relaxation time
- a :
-
measure of thermodiffusion effect
- b :
-
measure of diffusive effects
- β 1 :
-
= (3λ + 2µ)α t
- β 2 :
-
= (3λ + 2µ)α c
- α t :
-
coefficient of linear thermal expansion
- α c :
-
coefficient of linear diffusion expansion
- F 0 :
-
intensity of the applied mechanical load
- u :
-
displacement vector
- ϕ :
-
scalar potential
- ψ :
-
vector potential
- δ(.):
-
Dirac delta function
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Communicated by CHENG Chang-jun
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Deswal, S., Choudhary, S. Two-dimensional interactions due to moving load in generalized thermoelastic solid with diffusion. Appl. Math. Mech.-Engl. Ed. 29, 207–221 (2008). https://doi.org/10.1007/s10483-008-0208-5
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DOI: https://doi.org/10.1007/s10483-008-0208-5
Key words
- Eigen value approach
- vector matrix differential equation
- thermoelastic diffusion
- generalized thermoelasticity
- moving load
- Laplace and Fourier transforms