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International Journal of Rotating Machinery
Volume 2008, Article ID 752062, 10 pages
Research Article

Free Vibration Analysis of a Rotating Composite Shaft Using the 𝑝 -Version of the Finite Element Method

Department of Mechanical Engineering, Faculty of Sciences Engineering, Abou Bakr Belkaid University, Tlemcen 13000, Algeria

Received 19 November 2007; Accepted 24 May 2008

Academic Editor: Agnes Muszynska

Copyright © 2008 A. Boukhalfa 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.


This paper is concerned with the dynamic behavior of the rotating composite shaft on rigid bearings. A 𝑝 -version, hierarchical finite element is employed to define the model. A theoretical study allows the establishment of the kinetic energy and the strain energy of the shaft, necessary to the result of the equations of motion. In this model the transverse shear deformation, rotary inertia and gyroscopic effects, as well as the coupling effect due to the lamination of composite layers have been incorporated. A hierarchical beam finite element with six degrees of freedom per node is developed and used to find the natural frequencies of a rotating composite shaft. A program is elaborate for the calculation of the eigenfrequencies and critical speeds of a rotating composite shaft. To verify the present model, the critical speeds of composite shaft systems are compared with those available in the literature. The efficiency and accuracy of the methods employed are discussed.