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2002, 8

Ayman A. Al-Maaitah, Kamal Kardsheh

Flow-induced vibration of a Y-shaped tube conveying fluid

language: English

received 24.05.2002, published 09.07.2002

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This work investigates out of plane vibration of a Y-shaped tube conveying fluid with clamed ends conditions. The mathematical model is based on the equation of motion of each tube coupled with matched boundary conditions at the junction of the three segments. The resulting equations are then resolved using Galerkin approach. The resulting eigen-values, eigen-function and shape modes are found numerically. A stability analysis of the solution is then performed. The effect of geometrical and flow parameters on the vibration of the Y-shaped tube conveying fluid is investigated. Results show that for small length of branching side compared to the supplying tube and for zero branching angle then the first three non-dimensional frequency is close to those of straight single tube with clamped-clamped conditions. Moreover, neutral stability regions were observed in firs, second, and third modes for large range of dimensionless flow velocity. Results further demonstrate that an increase in dimensionless flow velocity results in decreasing of the non-dimensional frequency for the first three modes. Effect of branching angle and geometrical configuration of the mode shape and frequency is also investigated.

12 pages, 11 figures

Сitation: Ayman A. Al-Maaitah, Kamal Kardsheh. Flow-induced vibration of a Y-shaped tube conveying fluid. Electronic Journal “Technical Acoustics”,, 2006, 8.


[1] H. Ashley, G. Haviland. Bending vibration of a pipeline containing fluid. Journal of Applied Mechanics, (1950), pp. 229-232.
[2] G. W. Housner. Bending vibration of a pipeline containing fluid. Journal of Applied Mechanics, (1952), pp. 205-208.
[3] T. Benjamin. Dynamics of systems of articulated pipes conveying fluids; Part I theory, Part II Experiment. Proceedings of Royal Society (London), (1961), pp. 457-499.
[4] R. W. Gregory, M. Paidoussis. Unstable oscillation of tubular cantilever conveying fluid. Proceedings of Royal Society (London), (1966), pp. 512-542.
[5] M. Paidoussis, C. Sundrajan. Parametric and combination resonance of a pipe conveying pulsating fluid. Transaction of the ASME, (1975), pp. 780-784.
[6] T. Lundgren, P. Sethna, A. K. Bajaj. Stability boundaries for flow-induced motions of tubes with inclined terminal nozzle. Journal of Sound and Vibration, vol. 64, No. 4, (1979), pp. 553-571.
[7] M. Paidoussis. Review of flow-induced vibrations in reactors and reactors components. Journal of Nuclear Engineering and Design, vol. 74, No. 1, (1982), pp. 31-60.
[8] M. Hannoyer, M. Paidoussis. Dynamics of slender non-uniform beams subjected to flow. Journal of Applied Mechanics, vol. 46, (1979), pp. 45-51.
[9] M. A. Silva. Influence of eccentric values on the vibration of fluid conveying pipes. Journal of Nuclear Engineering and Design, vol. 64, No. 1, (1981), pp. 129-134.
[10] D. J. Gorman. Exact analytical solutions for the free vibration of steam generator U-tubes. Transaction of the ASME, vol. 110, November 1988.
[11] N. Sri Namchivaya. Non-linear dynamics of supported pipes conveying pulsating fluid, I sub-harmonic resonance. Journal of Sound and Vibration, vol. 144, No. 1, (1988), pp.185-196.
[12] X. Q. Dang. Efficient numerical analysis for dynamic stability of pipes conveying fluids. Journal of Pressure Vessel Technology, vol. 111, No. 2, (1989), pp. 143-148.
[13] R. Aithai and G. Steven Gipson. Instability of internally damped curved pipes. Journal of Engineering Mechanics, vol. 116, No. 1, (1990), pp. 123-131.
[14] M. N. Zeigler. Numerical Methods for Engineering Application. McGraw Hill, London, (1989).
[15] J. R. Dongarra. Linpack Users Guide. SIAM publishing, Philadelphia, (1979).


Ayman A. Al-Maaitah , PhD, Associated Professor at Mutah University, Mutah, Jordan
Address : PO Box 928100, Postal Code 11190, Abdali,
Amman, Jordan.
E-mail: aymanmaaitah(at)

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Kamal Kardsheh was a post graduate student at Jordan University of Science and Technology (Irbid) when he studied the problem discussed in the article. Presently Kamal Kardsheh works in the Kuwait.