Applied Mathematics, 2015, 6, 793-805 Published Online May 2015 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2015.65075 How to cite this paper: Othman, M.A., Atwa, S.Y. and Elwan, A.W. (2015) Two and Three Dimensions of Generalized Ther- moelastic Medium without Energy Dissipation under the Effect of Rotation. Applied Mathematics, 6, 793-805. http://dx.doi.org/10.4236/am.2015.65075 Two and Three Dimensions of Generalized Thermoelastic Medium without Energy Dissipation under the Effect of Rotation MohamedI A. Othman 1,2 , Sarhan Y. Atwa 3 , Ahmed W. Elwan 4 1 Department of Mathematics, Faculty of Science, ZagazigUniversity, Zagazig, Egypt 2 Department of Mathematics, Faculty of Science, Taif University, Taif City, Saudi Arabia 3 Department of Engineering Mathematics and Physics, Higher Institute of Engineering, Shorouk Academy, Shorouk City, Egypt 4 Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia Email: m_i_a_othman@yahoo.com , srhan_1@yahoo.com , ahmedelwan@yahoo.com Received 29 March 2015; accepted 8 May 2015; published 12 May 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The purpose of this paper is to study the effect of rotation on the general three-dimensional model of the equations of the generalized thermoelasticity for a homogeneous isotropic elastic half-space solid. The problem is studied in the context of the Green-Naghdi theory of type II (without energy dissipation). The normal mode analysis is used to obtain the expressions for the temperature, thermal stress, strain and displacement. The distributions of variables considered are represented graphically. Keywords Generalized Thermoelasticity, Three-Dimensional Modeling, Rotation, Normal Mode Method, Green-Naghdi Theory 1. Introduction The propagation of waves in thermoelastic materials has many applications in various fields of science and technology, namely, atomic physics, industrial engineering, thermal power plants, submarine structures, pressure vessel, aerospace, chemical pipe and metallurgy. Thermoelasticity theories, which admit a finite speed for ther- mal signals, have received a lot of attention for the past four decades. In contrast to the conventional coupled thermoelasticity theory based on a parabolic heat equation by Biot [1], which predicts an infinite speed of the