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Wave Propagation of Generalized Magneto-Thermoelastic Interactions in an Elastic Medium Under Influence of Initial Stress

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Abstract

Magneto-thermoelastic interactions in an isotropic homogeneous elastic half-space with two temperatures are studied using mathematical methods under the purview of the Lord–Şhulman (LS) and Green–Lindsay (GL) theories, as well as the classical dynamical coupled theory (CD). The medium is considered to be permeated by a uniform magnetic field. The general solution obtained is applied to a specific problem of a half-space and the interaction between them under the influence of magnetic field subjected to one type of heating the thermal shock type. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature and couple stress distribution. The variations in the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results.

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Abbreviations

\(\lambda,\mu\) :

Counterparts of Lame’s parameters

p :

Initial pressure

η :

Initial stress parameter

a :

Two-temperature parameter

\(\alpha_{t}\) :

Coefficient of linear thermal expansion

\(\theta = T - T_{0}\) :

Thermodynamic temperature

\(\phi = \phi_{0} - T\) :

Conductive heat temperature (thermal temperature)

T :

Absolute temperature

T 0 :

Temperature of the medium in its natural state assumed to be \(\left| {\frac{{T - T_{0} }}{{T_{0} }}} \right| < 1\)

\(\sigma_{{ij}}\) :

Components of the stress tensor

u i :

Components of the displacement vector

\(\rho\) :

Density of the medium

e ij :

Components of the strain tensor

e :

Cubical dilatation

C E :

Specific heat at constant strain

K :

Thermal conductivity

\(\tau_{0}\) :

Thermal relaxation time

\(\mu_{0}\) :

Magnetic permeability

\(\varepsilon_{0}\) :

Electric permittivity

F i :

Lorentz force

\(\delta_{ij}\) :

Kronecker delta function

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Taibah University, Madina, Kingdom of Saudi Arabia

    Kh. Lotfy

  2. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    Kh. Lotfy

  3. Basic and Applied Science Department, Arab Academy of Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

    A. A. El-Bary

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  1. Kh. Lotfy
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  2. A. A. El-Bary
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Correspondence to Kh. Lotfy.

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Lotfy, K., El-Bary, A.A. Wave Propagation of Generalized Magneto-Thermoelastic Interactions in an Elastic Medium Under Influence of Initial Stress. Iran J Sci Technol Trans Mech Eng 44, 919–931 (2020). https://doi.org/10.1007/s40997-019-00315-x

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  • DOI: https://doi.org/10.1007/s40997-019-00315-x

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