Acta Mechanica Sinica

, Volume 16, Issue 3, pp 264–272 | Cite as

Bifurcations of a cantilevered pipe conveying steady fluid with a terminal nozzle

  • Xu Jian
  • Huang Yuying


This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.

Key words

nonlinear dynamics bifurcation stability fluid-solid interaction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Holems PJ. Bifurcations to divergence and flutter in flow-induced oscillations: a finuite-dimensional analysis.Journal of Sound and Vibration, 1977, 53: 471–503.Google Scholar
  2. 2.
    Chen Yushu, Langford WF. The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamically buckling problem.Acta Mechanica Sinica, 1988, 20(6): 522–532Google Scholar
  3. 3.
    Ch'ng E, Dowell E H. Flow-Induced Vibrations. New York: ASME, 1979Google Scholar
  4. 4.
    Rousselet J, Herrmann G. Dynamic behavior of continuous cantilevered pipes conveying fluid near critical velocities.ASME Journal of Applied Mechanics, 1981, 48: 945–947CrossRefGoogle Scholar
  5. 5.
    Bajaj AK, Sethna PR, Lundgren TS. Hopf bifurcation phenoma in tubes carrying a fluid.SIAM Journal of Applied Mathematics, 1980, 39: 213–230zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bajaj AK, Sethna PR. Effect of symmetry-breaking perturbations on flow-induced oscillations in tubes.Journal of Fluids and Structures, 1991, 5: 651–679CrossRefGoogle Scholar
  7. 7.
    Semler C, Paidoussis MP. Nonlinear analysis of the parametric resonances of a planar fluid-conveying cantilevered pipe.Journal of Fluids and Structures, 1996, 10: 778–825CrossRefGoogle Scholar
  8. 8.
    Moon FC. Experiments on chaotic motion of a forced nonlinear oscillator: Strange attractors.ASME Journal of Applied Mechanics, 1980, 47: 638–644CrossRefGoogle Scholar
  9. 9.
    Holmes PJ, Moon FC. Strange attractors and chaos in nonlinear mechanics.ASME Journal of Applied Mechanics, 1983, 50: 1021–1032MathSciNetCrossRefGoogle Scholar
  10. 10.
    Tang DM, Dowell EH. Chaotic oscillations of a cantilevered pipe conveying fluid.Journal of Fluids and Structures, 1988, 2: 263–283CrossRefGoogle Scholar
  11. 11.
    Chen Yushu, Xu Jian. Global bifurcations and chaos in a van der Pol-Duffing-Mathieu system with three-well potential oscillator.Acta Mechanica Sinica (English Series), 1995, 11 (4): 357–372CrossRefzbMATHGoogle Scholar
  12. 12.
    Paidoussis MP, Moon FC. Nonlinear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid.Journal of Fluids and Structures, 1988, 2: 567–591CrossRefGoogle Scholar
  13. 13.
    Semler C, Li GX, Paidoussis MP. The nonlinear equations of motion of pipes conveying fluid.Journal of Sound and Vibration, 1994, 169: 577–599zbMATHCrossRefGoogle Scholar
  14. 14.
    Namachchivaya NS, Tien WM. Bifurcation behavior of nonlinear pipes conveying pulsating flow.Journal of Fluids and Structures, 1989, 3: 609–629zbMATHCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2000

Authors and Affiliations

  • Xu Jian
    • 1
  • Huang Yuying
    • 2
  1. 1.Key Laboratory of Solid Mechanics of EMCTongji UniversityShanghaiChina
  2. 2.Department of Engineering MechanicsHuazhong University of Science & TechnologyWuhanChina

Personalised recommendations