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Advances in Acoustics and Vibration
Volume 2013, Article ID 857821, 15 pages
Research Article

Three-Dimensional Investigation of the Stokes Eigenmodes in Hollow Circular Cylinder

1Arts et Métiers ParisTech, ENSAM Angers, 2 Boulevard du Ronceray, 49035 Angers, France
2IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France

Received 8 July 2013; Revised 29 August 2013; Accepted 30 August 2013

Academic Editor: K. M. Liew

Copyright © 2013 Adil El Baroudi and Fulgence Razafimahery. 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 studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced.