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Some Quandaries and Paradoxes in Fluid-Structure Interactions with Axial Flow

  • Michael P. PaïDoussis
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 75)

Abstract

A number of interesting quandaries and paradoxes, some resolved and some not, are reviewed briefly; they all involve axial flow over generally slender structures, as follows, (i) For pipes and shells conveying fluid, does post-divergence flutter occur or not? (ii) Do aspirating pipes and shells lose stability at infinitesimally small flow rates? (iii) Do pipes and shells with different kinds of end-support (e.g., clamped at one end and simply supported at the other) experience flow-induced damping, positive or negative, at arbitrarily small flows? (iv) In view of the similarity in the equations of motion of cylindrical structures subjected to (a) internal and (b) external axial flow, in their simplest form, how far can the analogy between internal and external flow be carried in assessing the dynamical behaviour of such systems, and what real physical effects intervene to break it down? (v) Should convective fluid-acceleration terms be taken into account in the analysis of the dynamics of strings or beams undergoing extrusion or deployment in dense fluid, and similarly for traveling web? (vi) Taking annular fluidelastic systems as an example, is the precise specification of boundary conditions on the fluid at the upstream and downstream ends essential in the determination of system stability? These are described in greater detail and clarified to the extent possible in the body of the paper.

Keywords

Axial Flow Internal Flow External Flow Annular Flow Pitchfork Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. Amabili, M., Pellicano, F. & Païdoussis, M.P. 1999 Nonlinear dynamics and stability of circular cylindrical shells containing flowing fluid. I. Stability. Journal of Sound and Vibration 225, 655–699.CrossRefGoogle Scholar
  2. Benjamin, T.B. 1961 Dynamics of a system of articulated pipes conveying fluid. II. Experiments. Proceedings of the Royal Society (London) A 261, 487–499.MathSciNetCrossRefGoogle Scholar
  3. Bertram, C.D. 1995 The dynamics of collapsible tubes. In Biological Fluid Dynamics (eds C.P. Ellington & T.J. Pedley), pp. 253–264.Google Scholar
  4. Bourrières, F.-J. 1939 Sur un phénomène d’oscillation auto-entretenue en mécanique des fluides réels. Publications Scientifiques et Techniques du Ministère de l’Air, No. 147.Google Scholar
  5. Dodds, H.L. Jr. & Runyan, H.L. 1965 Effect of high velocity fluid flow on the bending vibrations and static divergence of a simply supported pipe. NASA Technical Note D-2870.Google Scholar
  6. Done, G.T.S. & Simpson, A. 1977 Dynamic stability of certain conservative and non-conservative systems. I. Mech. E. Journal of Mechanical Engineering Science 19, 251–263.CrossRefGoogle Scholar
  7. Feodos’ev, V.P. 1951 Vibrations and stability of a pipe when liquid flows through it. Inzhenernyi Sbornik 10, 169–170.Google Scholar
  8. Gregory, R.W. & Païdoussis, M.P. 1966 Unstable oscillation of tubular cantilevers conveying fluid. II. Experiments. Proceedings of the Royal Society (London) A 293, 528–542.CrossRefGoogle Scholar
  9. Hobson, D.E. 1982 Fluid-elastic instabilities caused by flow in an annulus. Proceedings of 3rd International Conference on Vibration in Nuclear Plant, Keswick, pp. 440–463. London: BNES.Google Scholar
  10. Holmes, P.J. 1977 Bifurcations to divergence and flutter in flow-induced oscillations: a finite-dimensional analysis. Journal of Sound and Vibration 53, 471–503.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Holmes, P.J. 1978 Pipes supported at both ends cannot flutter. Journal of Applied Mechanics 45, 619–622.zbMATHCrossRefGoogle Scholar
  12. Horáček, J. & Zolotarev, I. 1984 Influence of fixing the edges of a shell conveying fluid on its dynamic characteristics. Soviet Applied Mechanics 20, 756–765.CrossRefGoogle Scholar
  13. Horáček, J. & Zolotarev, I. 2002 Free vibration and stability of cylindrical shells in interaction with flowing fluid. In NATO CLG Grant Report No. PST.CLF.977350 (eds F. Pellicano, Y. Mikhlin & I. Zolotarev), pp. 45–82. Prague: Institute of Thermomechanics (ISBN 80-85918–76-5).Google Scholar
  14. Housner, G.W.1952 Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics 19, 205–208.Google Scholar
  15. Karagiozis, K.N., Grinevich, E., Païdoussis, M.P., Misra, A.K. & Amabili, M. 2003 Stability and non-linear dynamics of clamped circular cylindrical shells containing flowing fluid. Proceedings IUTAM Symposium on Integrated Modeling of fully Coupled Fluid-Structure Interactions (eds H. Benaroya & T. Wei), Rutgers University, U.S.A.Google Scholar
  16. Katz, J. & Plotkin, A. 1991 Low-Speed Aerodynamics: from Wing Theory to Panel Methods. New York: McGraw-Hill.Google Scholar
  17. Lighthill, M.J. 1969 Hydromechanics of aquatic animal propulsion. Annual Review of Fluid Mechanics 1, 413–446.CrossRefGoogle Scholar
  18. Lighthill, M.J. 1975 Mathematical Biofluiddynamics. Philadelphia, PA: SIAM.Google Scholar
  19. Miller, D.R. 1970 Generation of positive and negative damping with a flow restrictor in axial flow. In Proceedings of the Conference on Flow-Induced Vibrations in Reactor System Components (eds G.S. Rosenberg, M.W. Wambsganss & R.P. Carter), Report ANL-7685, pp. 304–311, Argonne National Laboratory, Argonne, IL, U.S.A.Google Scholar
  20. Misra, A.K., Wong, S.S.T. & Païdoussis, M.P. 2001 Dynamics and stability of pinned-clamped and clamped-pinned cylindrical shells conveying fluid. Journal of Fluids and Structures 15, 1153–1166.CrossRefGoogle Scholar
  21. Mote, C.D. Jr. 2002 Private communication (15 Mar 2002).Google Scholar
  22. Nguyen, V.B., Païdoussis, M.P. & Misra, A.K. 1994 A CFD model for the study of the stability of cantilevered coaxial cylindrical shells conveying viscous fluid. Journal of Sound and Vibration 176, 105–125.zbMATHCrossRefGoogle Scholar
  23. Païdoussis, M.P. 1998 Fluid-Structure Interations: Slender Structures and Axial Flow. Volume 1. London: Academic Press.Google Scholar
  24. Païdoussis, M.P. 1999 Aspirating pipes do not flutter at infinitesimally small flow. Journal of Fluids and Structures 13, 419–425.CrossRefGoogle Scholar
  25. Païdoussis, M.P. 2003 Fluid-Structure Interations: Slender Structures and Axial Flow. Volume 2. Oxford: Elsevier.Google Scholar
  26. Païdoussis, M.P. & Denise, J.-P. 1972 Flutter of thin cylindrical shells conveying fluid. Journal of Sound and Vibration 20, 9–26.zbMATHCrossRefGoogle Scholar
  27. Païdoussis, M.P. & Issid, N.T. 1974 Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration 33, 267–294.CrossRefGoogle Scholar
  28. Païdoussis, M.P. & Luu, T.P. 1985 Dynamics of a pipe aspirating fluid, such as might be used in ocean mining. ASME Journal of Energy Resources Technology 107, 250–255.CrossRefGoogle Scholar
  29. Païdoussis, M.P. & Semler, C. 1993 Nonlinear dynamics of a fluid-conveying cantilevered pipe with an intermediate support. Journal of Fluids and Structures 7, 269–298.CrossRefGoogle Scholar
  30. Pramila, A. 1986 Sheet flutter and the interaction between sheet and air. TAPPI Journal 69, 70–74.Google Scholar
  31. Pramila, A. 1987 Natural frequencies of a submerged axially moving band. Journal of Sound and Vibration 113, 198–203.CrossRefGoogle Scholar
  32. Shayo, L.K. & Ellen, C.H. 1974 The stability of finite length circular cross-section pipes conveying inviscid fluid. Journal of Sound and Vibration 37, 535–545.zbMATHCrossRefGoogle Scholar
  33. Spurr, A. & Hobson, D.E. 1984 Forces on the vibrating centrebody of an annular diffuser. Proceedings Symposium on Flow-Induced Vibrations, Vol. 4 (eds M.P. Païdoussis & M.K. Au-Yang), pp. 41–52. New York: ASME.Google Scholar
  34. Taleb, I.A. & Misra, A.K. 1981 Dynamics of axially moving beam submerged in a fluid. AIAA Journal of Hydronautics 15, 62–66.CrossRefGoogle Scholar
  35. Triantafyllou, M.S. 1998 Private communication (3 Nov 1998).Google Scholar
  36. Weaver, D.S. & Unny, T.E. 1973 On the dynamic stability of fluid-conveying pipes. Journal of Applied Mechanics 40, 48–52.zbMATHCrossRefGoogle Scholar
  37. Wong, S.T.-M. 2000 Dynamics of fluid-conveying shells with symmetric and asymmetric end-supports. M.Eng. Thesis, Department of Mechanical Engineering, McGill University, Montreal, Québec, Canada.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Michael P. PaïDoussis
    • 1
  1. 1.Thomas Workman Emeritus ChairDepartment of Mechanical Engineering, McGill UniversityMontrealCanada

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