Delivered by Ingenta to: Chinese University of Hong Kong IP: 5.101.220.194 On: Fri, 17 Jun 2016 07:47:21 Copyright: American Scientific Publishers RESEARCH ARTICLE Copyright © 2013 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational and Theoretical Nanoscience Vol. 10, 1408–1417, 2013 On the Initial Stress, Magnetic Field, Voids and Rotation Effects on Plane Waves in Generalized Thermoelasticity A. M. El-Naggar 1 , Z. Kishka 2 , A. M. Abd-Alla 2 5 , I. A. Abbas 2 6 , S. M. Abo-Dahab 3 5 , and M. Elsagheer 2 4 ∗ 1 Faculty of Science, Math. Department, Benha University, Egypt 2 Faculty of Science, Math. Department, Sohag University, Egypt 3 Faculty of Science, Math. Department, SVU, Qena, Egypt 4 Faculty of Science, Math. Department, Northren Border University, Arar, Saudi Arabia 5 Faculty of Science, Math. Department, Taif University, Saudi Arabia 6 Faculty of Science and Arts-Khulais, Math. Department, King Abdulaziz University, Jeddah, Saudi Arabia In this work, we study the effect of the magnetic field, rotation, thermal field, and the initial stress and also voids on the reflection of P -wave with one relaxation time. The formulation is applied to gen- eralization, the Lord–Shulman theory with one relaxation time. The electromagneto-thermoelastic interactions in perfectly conducting plane is subjected to a uniform axial magnetic field with voids and rotation. It is shown that there exist four plane waves; P 1 -, P 2 -, P 3 - and P 4 -. In addition, the reflection coefficients from insulated stress-free surface for the incident P -wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of magnetic field, initial stress, rotation, thermal relaxation time and voids param- eters and displayed graphically. In the case of neglecting the effect of the magnetic field, and made clear the impact of other variables on the reflection coefficients, which is considered a special case of this study and displayed graphically. Keywords: Magneto-Thermoelasticity, Relaxation Time, Rotation, Thermoelasticity, Reflection, Initial Stress, Voids. 1. INTRODUCTION In recent years, more attentions has been given for the rotation effect on waves with thermal field, initial stress and voids under relaxation time because of its utilitar- ian aspects on Seismic waves, Earthquakes, Aerospace, Volcanoes and Acoustics. In the classical theory of ther- moelasticity, when an elastic solid is subjected to a ther- mal disturbance, the effect is felt at a location far from the source, instantaneously. This implies that the thermal wave propagates with infinite speed, a physically impos- sible result. In contrast to conventional thermoelasticity, non-classical theories came into existence during the last part of 20th century. Thermoelasticity theories that pre- dict a finite speed for the propagation of thermal signals have aroused much interest in the last four decades. The ∗ Author to whom correspondence should be addressed. thermoelasticity theory based on a parabolic heat equa- tion, which predicts an infinite speed for the propagation of heat was putted by Ref. [4]. Reference [17] discovered the theory which determines the finite speed for the motion due to thermal field using one relaxation time by including temperature rate. Reference [35] investigated the reflec- tion of thermoelastic waves from the free surface of a solid half-space of generalized thermoelasticity with ther- mal relaxation time. Reference [10] discussed the gen- eralized thermoelasticity for anisotropic media. Effect of rotation and relaxation times on plane waves in gener- alized thermoelasticity is discussed by Ref. [29]. Refer- ence [37] investigated the reflection of thermoelastic waves at a solid half-space with two thermal relaxation times. The reflection and refraction of thermoelastic waves from the free surface of a solid half-space of with two thermal relaxation times at the interface between two semi-infinite media in welded contact of generalized thermoelasticity 1408 J. Comput. Theor. Nanosci. 2013, Vol. 10, No. 6 1546-1955/2013/10/1408/010 doi:10.1166/jctn.2013.2862