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Mathematical Problems in Engineering
Volume 2013, Article ID 250567, 11 pages
Research Article

On Free Vibrations of Elastodynamic Problem in Rotating Non-Homogeneous Orthotropic Hollow Sphere

1Department of Mathematics, Science Faculty, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Mathematics Department, Science Faculty, Sohag University, Sohag 82524, Egypt
3Mathematics Department, Faculty of Mathematics, Brasov University, Brasov, Romania
4Department of Mathematics, Science Faculty, Hail University, Saudi Arabia
5Department of Mathematics, Science Faculty, Al-Azhar University, Nassr City, Egypt

Received 30 April 2013; Accepted 23 June 2013

Academic Editor: Abdelouahed Tounsi

Copyright © 2013 S. R. Mahmoud 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 effect of non-homogenity and rotation on the free vibrations for elastodynamic problem of orthotropic hollow sphere is discussed. The free vibrations are studied on the basis of the linear elasticity. The determination is concerned with the eigenvalues of the natural frequency for mixed boundary conditions. The numerical results of the frequency equations are discussed in the presence and absence of non-homogenity and rotation. The computer simulated results indicate that the influence of non-homogenity and rotation in orthotropic material is pronounced.