Table of Contents Author Guidelines Submit a Manuscript
Advances in Acoustics and Vibration
Volume 2013, Article ID 857821, 15 pages
http://dx.doi.org/10.1155/2013/857821
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.

Linked References

  1. F. Razafimahery, “Ecoulements externes de Stokes dans des domaines non réguliers et condition de Kutta-Joukowski généralisée,” Zeitschrift für Angewandte Mathematik und Physik, vol. 54, pp. 125–148, 2003. View at Google Scholar
  2. H. Bruus, Theoretical Microfluidics, Oxford University Press, New York, NY, USA, 2008.
  3. G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, 2005.
  4. S. Childress, Mechanics of Swimming and Flying, Cambridge University Press, 1981.
  5. A. S. Ashour, “Propagation of guided waves in a fluid layer bounded by two viscoelastic transversely isotropic solids,” Journal of Applied Geophysics, vol. 44, no. 4, pp. 327–336, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. A. S. Ashour, “Wave motion in a viscous fluid-filled fracture,” International Journal of Engineering Science, vol. 38, no. 5, pp. 505–515, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. I. Edelman, “On the existence of the low-frequency surface waves in a porous medium,” Comptes Rendus, vol. 332, no. 1, pp. 43–49, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. W. Seemann and J. Wauer, “Fluid-structural coupling of vibrating bodies in a surrounding confined liquid,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 76, no. 2, pp. 67–79, 1996. View at Google Scholar · View at Scopus
  9. S. G. Kadyrov, J. Wauer, and S. V. Sorokin, “A potential technique in the theory of interaction between a structure and a viscous, compressible fluid,” Archive of Applied Mechanics, vol. 71, no. 6-7, pp. 405–417, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Leriche and G. Labrosse, “Vector potential-vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain,” Theoretical and Computational Fluid Dynamics, vol. 21, no. 1, pp. 1–13, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Rodríguez and J. E. Solomin, “The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems,” Mathematics of Computation, vol. 65, no. 216, pp. 1463–1475, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Bermúdez and R. Rodríguez, “Modelling an numerical solution of elastoacoustic vibrations with interface damping,” International Journal for Numerical Methods in Engineering, vol. 46, no. 10, pp. 1763–1779, 1999. View at Google Scholar
  13. G. G. Stokes, “On the effect of the internal friction of fluids on the motion of pendulums,” Transactions of the Cambridge Philosophical Society, vol. 9, pp. 8–106, 1851. View at Google Scholar
  14. H. Lamb, Hydrodynamics, Cambridge University Press, 1932.
  15. D. D. Joseph, “Potential flow of viscous fluids: historical notes,” International Journal of Multiphase Flow, vol. 32, no. 3, pp. 285–310, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. R. Kidambi, “Oscillatory stokes flow in a cylindrical container,” Fluid Dynamics Research, vol. 38, no. 4, pp. 274–294, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. P. N. Shankar, “Three-dimensional eddy structure in a cylindrical container,” Journal of Fluid Mechanics, vol. 342, pp. 97–118, 1997. View at Google Scholar · View at Scopus
  18. G. Pontrelli and A. Tatone, “Wave propagation in a fluid flowing through a curved thin-walled elastic tube,” Journal of FluidMechanics, vol. 5, pp. 113–133, 1971. View at Google Scholar
  19. B. Sweetman, M. Xenos, L. Zitella, and A. A. Linninger, “Three-dimensional computational prediction of cerebrospinal fluid flow in the human brain,” Computers in Biology and Medicine, vol. 41, no. 2, pp. 67–75, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Gupta, M. Soellinger, P. Boesiger, D. Poulikakos, and V. Kurtcuoglu, “Three-dimensional computational modeling of subject-specific cerebrospinal fluid flow in the subarachnoid space,” Journal of Biomechanical Engineering, vol. 131, no. 2, 11 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. V. V. Mokeyev, “On a method for vibration analysis of viscous compressible fluid-structure systems,” International Journal for Numerical Methods in Engineering, vol. 59, no. 13, pp. 1703–1723, 2004. View at Google Scholar · View at Scopus
  22. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, NY, USA, 1946.
  23. R. Ohayon and C. Soize, Structural Acoustics and Vibration, Academic Press, 1997.
  24. M. P. Paidoussis, Fluid-Structure Interactions Slender Structures and Axial Flow, vol. 1, London Academic Press, 1997.
  25. M. P. Paidoussis, Fluid-Structure Interactions Slender Structures and Axial Flow, vol. 2, Elsevier Academic Press, London, UK, 2004.
  26. “Comsol Multiphysics 3.5a,” User's Guide, 2008.
  27. “Comsol Multiphysics 3.5a,” Reference Guide, 2008.
  28. T. A. Davis, “Algorithm 832: UMFPACK V4.3: an unsymmetric-pattern multifrontal method,” ACM Transactions on Mathematical Software, vol. 30, no. 2, pp. 196–199, 2004. View at Publisher · View at Google Scholar · View at Scopus