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Transient Waves Due to Mechanical Loads in Elasto-Thermo-Diffusive Solids

Published online by Cambridge University Press:  03 June 2015

J. N. Sharma ,
N. K. Sharma  and
K. K. Sharma
J. N. Sharma*
Affiliation:
Department of Applied Sciences and Humanities, National Institute of Technology, Hamirpur-177 005, India
N. K. Sharma*
Affiliation:
Department of Applied Sciences and Humanities, National Institute of Technology, Hamirpur-177 005, India
K. K. Sharma*
Affiliation:
Department of Applied Sciences and Humanities, National Institute of Technology, Hamirpur-177 005, India
*
Corresponding author. Email: [email protected]
Email: [email protected]
Email: [email protected]
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Abstract

This paper deals with the study of transient waves in a homogeneous isotropic, solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion. The halfspace is assumed to be disturbed due to mechanical loads acting on its boundary. The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique. Noting that the second sound effects are short lived, the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts. In case of continuous and periodic loads acting at the boundary, the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load. The temperature and concentration fields are found to be discontinuous at all the wave fronts. The displacement, temperature change and concentration deviation due to impulsive, continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform. The computer simulated numerical results have been presented graphically in respect of displacement, temperature change and concentration deviation for brass. A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.

Keywords

76R5044A1034A4535L05DiffusionLaplace transformsmall time approximationswave fronts
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 1 , February 2011 , pp. 87 - 108
Copyright
Copyright © Global-Science Press 2011

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