Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 827901, 30 pages
Research Article

Homotopy Perturbation Method and Variational Iteration Method for Harmonic Waves Propagation in Nonlinear Magneto-Thermoelasticity with Rotation

1Math. Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2Math. Department, Faculty of Science, Taif University, Saudi Arabia
3Math. Department, Faculty of Science, SVU, Qena 83523, Egypt
4Math. Department, Faculty of Science, El-Minia University, Egypt

Received 17 August 2011; Accepted 3 October 2011

Academic Editor: Cristian Toma

Copyright © 2012 Khaled A. Gepreel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The homotopy perturbation method and variational iteration method are applied to obtain the approximate solution of the harmonic waves propagation in a nonlinear magneto-thermoelasticity under influence of rotation. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The displacement and temperature are calculated for the methods with the variations of the magnetic field and the rotation. The results obtained are displayed graphically to show the influences of the new parameters and the difference between the methods' technique. It is obvious that the homotopy perturbation method is more effective and powerful than the variational iteration method.