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Propagation of Rayleigh waves in a rotating orthotropic material elastic half-space under initial stress and gravity

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Abstract

This paper aims to investigate the influence of rotation, initial stress and gravity field on the propagation of Rayleigh waves in a homogeneous orthotropic elastic medium. The government equations and Lame’s potentials are used to obtain the frequency equation which determines the velocity of Rayleigh waves, including rotation, initial stress and gravity field, in a homogeneous, orthotropic elastic medium has been investigated. The numerical results analyzing the frequency equation are discussed and presented graphically. It is important to note that the Rayleigh wave velocity in an orthotropic elastic medium increases a considerable amount in comparison to the Rayleigh wave velocity in an isotropic material. The results indicate that the effects of rotation, initial stress and gravity field on Rayleigh wave velocity are very pronounced.

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Authors and Affiliations

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

    A. M. Abd-Alla, S. M. Abo-Dahab & T. A. Al-Thamali

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

    S. M. Abo-Dahab

Authors
  1. A. M. Abd-Alla
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  2. S. M. Abo-Dahab
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  3. T. A. Al-Thamali
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Additional information

Recommended by Associate Editor Kyeongsik Woo

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 co-author 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.

El-Sayed Mohamed Abo-Dahab Khedary is 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. 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.

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Abd-Alla, A.M., Abo-Dahab, S.M. & Al-Thamali, T.A. Propagation of Rayleigh waves in a rotating orthotropic material elastic half-space under initial stress and gravity. J Mech Sci Technol 26, 2815–2823 (2012). https://doi.org/10.1007/s12206-012-0736-5

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  • DOI: https://doi.org/10.1007/s12206-012-0736-5

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