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Propagation of p- and T-waves in solid-liquid of thermoelastic media subjected to initial stress and magnetic field in the context of CT-theory

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Abstract

The effect of magnetic field and initial stress on plane wave propagation is discussed. We have investigated the problem of reflection and refraction of the thermoelastic wave at a magnetized solid-liquid interface in presence of initial stress. In the context of the CT-theory (Classical dynamical theory) of thermoelasticity, the problem has been solved. The boundary conditions at the interface for (i) displacement continuity, (ii) vanishing the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) tangential force per unit initial area must vanish, and (v) continuity of temperature are applied. The amplitude ratios for the incident p- and T-waves have been obtained. The reflection and transmitted coefficients for the incident waves are computed numerically, considering the initial stress and magnetic field effect and presented graphically. Comparisons are made with the results in the absence and presence of initial stress and magnetic field. The results indicate that the effect of initial stress and magnetic field on wave propagation are very pronounced.

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Author information

Authors and Affiliations

  1. Math. Dept., Faculty of Science, Taif University, 888, Taif, Saudi Arabia

    S. M. Abo-Dahab & A. M. Abd-Alla

  2. Math. Dept., Faculty of Science, SVU, Qena, 83523, Egypt

    S. M. Abo-Dahab

  3. Math. Dept., Faculty of Science, Sohag University, Cairo, Egypt

    A. M. Abd-Alla

  4. Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, UPM, 43400, Serdang, Selangor, Malaysia

    A. Kilicman

Authors
  1. S. M. Abo-Dahab
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  2. A. M. Abd-Alla
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  3. A. Kilicman
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Corresponding author

Correspondence to A. M. Abd-Alla.

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Recommended by Chief-in-Editor Maenghyo Cho

El-Sayed Mohamed Abo-Dahab Khedary is an Associate Professor in SVU, Egypt and currently an Associate Professor in Applied Mathematics (Continuum Mechanics), Taif University, Saudi Arabia. He received his Master’s degree in Applied Mathematics in 2001 from SVU, Egypt and his Ph.D. in 2005 from Assiut University, Egypt. In 2012 he received the Assistant Professor Degree in Applied Mathematics. His research interests include elasticity, thermoelasticity, fluid mechanics, fiber-reinforced, and magnetic field.

Abdelmooty Mohamed Abd-Alla is currently a Professor in Applied Mathematics (Continuum Mechanics), Taif University, Saudi Arabia. He was born in Egypt-Assuit in 1956. Now he is working as professor of Mathematics, in Faculty of Science, Sohag University, Egypt. His research interests include theory of elasticity, vibration, thermoelasticity and fluid mechanics.

Adem Kilicman serves as a Full Professor at the Department of Mathematics, Faculty of Science, University Putra, Serdang, Selangor, Malaysia. He received his B.S. and M.S. degrees from the Department of Mathematics, Hacettepe University, Turkey, and Ph.D. from the University of Leicester, UK.

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Abo-Dahab, S.M., Abd-Alla, A.M. & Kilicman, A. Propagation of p- and T-waves in solid-liquid of thermoelastic media subjected to initial stress and magnetic field in the context of CT-theory. J Mech Sci Technol 29, 579–591 (2015). https://doi.org/10.1007/s12206-015-0118-x

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  • DOI: https://doi.org/10.1007/s12206-015-0118-x

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