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Analysis of Vibrations in Fractional Order Magneto-Thermo-Viscoelasticity with Diffusion

Published online by Cambridge University Press:  05 June 2014

K. K. Kalkal  and
S. Deswal
K. K. Kalkal
Affiliation:
Department of Mathematics, G. J. University of Science and Technology, Hisar-125001, Haryana, India
S. Deswal*
Affiliation:
Department of Mathematics, G. J. University of Science and Technology, Hisar-125001, Haryana, India
*
*[email protected]
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Abstract

Present paper is aimed at studying the effects of fractional order parameter, magnetic field, viscosity and diffusion on the thermoelastic interactions in an infinite body whose surface suffers a mechanical load. Body is assumed to be unstrained and unstressed initially and has uniform temperature. Formulation is applied to the fractional generalization of Lord-Shulman theory and the equations are tackled by employing Laplace and Fourier transforms. Expressions for different fields such as displacement, temperature, stress, concentration and chemical potential in physical domain are obtained using a numerical inversion technique. Finally, numerical solution is carried out for copper material and corresponding graphs are plotted to illustrate and compare theoretical results. Some particular cases of interest have also been deduced from the present study. Numerical results predict finite speeds of propagation for thermoelastic and diffusive waves.

Keywords

Fractional order theoryMagneto-thermo-viscoelasticityDiffusionLaplace-Fourier transformsRamp parameter
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 4 , August 2014 , pp. 383 - 394
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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