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Effects of voids and rotation on plane waves in generalized thermoelasticity

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Abstract

In the present paper, we study the influence of rotation, thermal and voids parameters on the reflection phenomenon of plane waves in generalized thermoelastic solid with one relaxation time. The governing field equations for isotropic and homogeneous thermoelastic half-space with voids and rotation are formulated in the context of Lord and Shulman theory of generalized thermoelasticity. The solutions of these governing equations indicate the existence of four coupled plane waves, namely; P1; P; P3 and P4 waves in the thermoelastic medium. The boundary conditions at stress-free thermally insulated surface are satisfied to obtain the system of four nonhomogenous equations in the reflection coefficients of various reflected waves for the incidence of P1 wave. A particular material is modeled as the thermoelastic solid half-space to compute the complex absolute values of speeds and reflection coefficients. The speeds and reflection coefficients are shown graphically to observe the influences of rotation, thermal relaxation time and voids parameters.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taif University, 888, Taif, Saudi Arabia

    S. M. Abo-Dahab & A. M. Abd-Alla

  2. Mathematics Department, Faculty of Science, SVU, Qena, 83523, Egypt

    S. M. Abo-Dahab

  3. Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    S. R. Mahmoud

  4. Mathematics Department, Faculty of Science, Sohag University, Sohag, Egypt

    A. M. Abd-Alla & S. R. Mahmoud

Authors
  1. S. M. Abo-Dahab
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  2. A. M. Abd-Alla
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  3. S. R. Mahmoud
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Correspondence to S. M. Abo-Dahab.

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Recommended by Associate Editor Jun-Sik Kim

El-Sayed Mohamed Abo-Dahab Khedary is Associate Professor in SVU, Egypt and currently an Associate Professor in Applied Mathematics (Continuum Mechanics), Taif University, Saudi Arabia. He was born in Egypt-Sohag-Elmaragha-Ezbet Bani-Helal in 1973. He received his Master’s degree in Applied Mathematics in 2001 from SVU, Egypt. He then received his Ph.D. in 2005 from Assiut University, Egypt. In 2012 he received the Assistant Professor Degree in Applied Mathematics. He is the author or coauthor of over 60 scientific publications. His research interests include elasticity, thermoelasticity, fluid mechanics, fiber-reinforced, and magnetic field. He published a lot of new papers in science, engineering, biology, geology, acoustics, physics, plasma, etc. He authorized many books in mathematics, he is research papers have been cited by many articles or textbooks.

Abdelmooty Mohamed Abd-Alla is currently a Professor in Applied Mathmatics (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. He is the author or coauthor of over 100 scientific publications, reviewer of many international journals in solid mechanics and applied mathematics. His research papers have been cited in many articles and textbooks. He authored many books in mathematics.

S. R. Mahmoud was born in Sohag, Egypt, in 1971. He received his B. Sc. Degree from Assiut University, in 1994 with honors degree. He received his M. Sc. and Ph.D. degree in mathematics from Sohag University, in 2004. Now he is working as an Assistant professor of Mathematics, in faculty of Science, King Abdulaziz University, Saudi Arabia. His research interests include Theory of elasticity, Thermoelasticity, Fuid mechanics, Vibration, Biomechanics, Diffusion mass, A voids, and Fiber-reinforced. He is the author or co-author of over 60 scientific publications, reviewer of many international journals in solid mechanics and applied mathematics. His research papers have been cited in many articles and textbooks. He authored many books in mathematics.

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Abo-Dahab, S.M., Abd-Alla, A.M. & Mahmoud, S.R. Effects of voids and rotation on plane waves in generalized thermoelasticity. J Mech Sci Technol 27, 3607–3614 (2013). https://doi.org/10.1007/s12206-013-0903-3

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  • DOI: https://doi.org/10.1007/s12206-013-0903-3

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