Analysis of Nonlinear Dynamic Stability of Liquid-Conveying Pipes

ZHANG Li-xiang; HUANG Wen-hu

Volume 23 Issue 9

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(9): 951-960

ZHANG Li-xiang, HUANG Wen-hu. Analysis of Nonlinear Dynamic Stability of Liquid-Conveying Pipes[J]. Applied Mathematics and Mechanics, 2002, 23(9): 951-960.

Citation:

ZHANG Li-xiang, HUANG Wen-hu. Analysis of Nonlinear Dynamic Stability of Liquid-Conveying Pipes[J]. Applied Mathematics and Mechanics, 2002, 23(9): 951-960.

Citation:

ZHANG Li-xiang, HUANG Wen-hu. Analysis of Nonlinear Dynamic Stability of Liquid-Conveying Pipes[J]. Applied Mathematics and Mechanics, 2002, 23(9): 951-960.

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Analysis of Nonlinear Dynamic Stability of Liquid-Conveying Pipes

ZHANG Li-xiang¹,
HUANG Wen-hu²

1.
Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650051, P. R. China;
2.
School of Aeronautics, Harbin Institute of Technology, Harbin 150001, P. R. China

Received Date: 2000-11-22
Rev Recd Date: 2002-05-28
Publish Date: 2002-09-15

Abstract

Abstract

Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effect of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by 4 nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.
- piping flow,
- fluid structure interaction,
- nonlinear vibration,
- bifurcation

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References(20)

References

[1]	Holmes P J.Pipes supported at both ends cannot flutter[J].Journal of Applied Mechanics,1978,45(3):619-622.
[2]	Holmes P J.Bifurcation to divergence and flutter in flow-induced oscillations:a finite dimensional analysis[J].Journal of Sound and Vibration,1977,53(4):471-503.
[3]	Bajaj A K,Sethna P R.Hopf bifurcation phenomena in tubes carrying a fluid[J].SIAM J Appl Math,1980,39(2):213-230.
[4]	Thurman A L,Mote C D Jr.Free,periodic,nonlinear oscillation of an axially moving trip[J].Journal of Applied Mechanics,1969,36(1):83-91.
[5]	Paidoussis M P,Issid N T.Dynamics stability of pipes conveying fluid[J].Journal of Sound and Vibration,1974,33(2):267-294.
[6]	Paidoussis M P.Flutter of conservative systems of pipes conveying incompressible fluid[J].Journal of Mechanical Engineering Science,1975,17(1):19-25.
[7]	Paidoussis M P.Fluid-induced instabilities of cylindrical structures[J].Applied Mechanics Reviews,1987,40(1):163-175.
[8]	Lundgren T S,Sethna P R,Bajaj A K.Stability boundaries for flow induced motion of tubes with an inclined terminal nozzle[J].Journal of Sound and Vibration,1979,64(4):553-571.
[9]	Bajaj A K,Sethna P R.Flow induced Bifurcation to three-dimensional oscillatory motion in continuous tubes[J].SIAM J Appl Math,1984,43(2):270-286.
[10]	Bajaj A K,Sethna P R.Effect of symmetry-breaking perturbation on flow-induced oscillations in tubes[J].Journal of Fluids and Structures,1991,5(4):651-679.
[11]	Rousslete J,Herrmann G.Flutter of articulated pipes at finite amplitude[J].Journal of Applied Mechanics,1977,44(1):154-158.
[12]	Li G X,Paidoussis P M.Stability,double degeneracy and chaos in cantilevered pipes conveying fluid[J].Journal of Non-Linear Mechanics,1994,29(1):83-107.
[13]	Paidoussis M P,Moon F C.Nonlinear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid[J].Journal of Fluids and Structures,1988,2(4):567-591.
[14]	Paidoussis M P,Li G X,Moon F C.Chaotic oscillations of the autonomous system of constrained pipe conveying fluid[J].Journal of Sound and Vibration,1989,135(1):1-19.
[15]	Heinsbroek A G T J,Tijsseling A S.The influence of support rigidity on waterhammer pressures and pipe stresses[A].In:D S Miller Ed.BHRG Proceedings of International Conference on Water Pipeline Systems[C].London:Mechanical Engineering Publication Ltd,1994,17-29.
[16]	Paidoussis P M,Cusumano J P,Copeland G S.Low-dimensional chaos in a flexible tube conveying fluid[J].Journal of Applied Mechanics,1992,59(1):196-205.
[17]	ZHANG Li-xiang,Tijsseling A S,Vardy A E.FSI analysis of liquid-filled pipes[J].Journal of Sound and Vibration,1999,224(1):69-99.
[18]	张立翔,黄文虎.输流管道非线性流固耦合振动的数学建模[J].水动力学研究与进展,2000,15(1):116-128.
[19]	Gorman D G,Reese J M,Zhang Y L.Vibration of a flexible pipe conveying viscous pulsating fluid flow[J].Journal of Sound and Vibration[J].2000,230(2):379-392.
[20]	Lee U,Pak C H,Hong S C.The dynamic of a piping system with internal unsteady flow[J].Journal of Sound and Vibration,1995,182(2):297-311.

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