Dynamical stability of cantilevered pipe conveying fluid in the presence of linear dynamic vibration absorber
Document Type : Research Paper
Authors
1 Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
2 Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China
Abstract
When the velocity of fluid flow in a cantilevered pipe is successively increased, the system may become unstable and flutter instability would occur at a critical flow velocity. This paper is concerned with exploring the dynamical stability of a cantilevered fluid-conveying pipe with an additional linear dynamic vibration absorber (DVA) attachment. It is endeavoured to show that the stability of the pipe may be considerably enhanced due to the presence of DVA. The quasi-analytical results show that the energy transferred from the flowing fluid to the pipe may be partially transferred to the additional mass. In most cases, thus, the critical flow velocity at which the pipe becomes unstable would become larger, meanwhile the flutter instability of the DVA is not easy to achieve. In such a fluid-structure interaction system, it is also found that flutter instability may first occur in the mode of the DVA. The effects of damping coefficient, weight, location and spring stiffness of the DVA on the critical flow velocities and nonlinear oscillations of the system have also been analyzed.
Keywords
- Pipe conveying fluid
- Linear dynamic vibration absorber
- Stability
- Critical flow velocity
- Nonlinear oscillation
Main Subjects
[1] M. P. Paidoussis, G. X. Li, Pipes conveying fluid: a model dynamical problem, Journal of Fluids and Structures, Vol. 7, No. 2, pp. 137-204, 1993.
[2] M. P. Paidoussis, The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics, Journal of Sound and Vibration, Vol. 310, No. 3, pp. 462-492, Feb 10, 2008.
[3] Y. Yang, J. Wang, Y. Yu, Wave propagation in fluid-filled single-walled carbon nanotube based on the nonlocal strain gradient theory, Acta Mechanica Solida Sinica, Vol. 31, No. 4, pp. 484-492, 2018.
[4] M. Hosseini, H. H. Gorgani, M. Shishesaz, A. Hadi, Size-dependent stress analysis of single-wall carbon nanotube based on strain gradient theory, International Journal of Applied Mechanics, Vol. 9, No. 06, pp. 1750087, 2017.
[5] V. Feodos’Ev, Vibrations and stability of a pipe when liquid flows through it, Inzhenernyi Sbornik, Vol. 10, pp. 169-170, 1951.
[6] G. Housener, Bending vibration of a pipeline containing flowing fluid, Journal of Applied Mechancis, Vol. 19, pp. 205, 1952.
[7] F. I. Niordson, 1953, Vibrations of a cylindrical tube containing flowing fluid, Kungliga Tekniska Hogskolans Handlinar (Stockholm),
[8] R. D. Blevins, 1977, Flow-induced vibration, Van Nostrand Reinhold Co., New York
[9] F.-J. Bourrières, 1939, Sur un phénomène d'oscillation auto-entretenue en mécanique des fluides réels, E. Blondel La Rougery,
[10] T. B. Benjamin, Dynamics of a system of articulated pipes conveying fluid. I. Theory, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 261, No. 1307, pp. 457-486, 1961.
[11] T. B. Benjamin, Dynamics of a system of articulated pipes conveying fluid. II. Experiments, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 261, No. 1307, pp. 487-499, 1961.
[12] M. P. Paidoussis, Oscillations of liquid-filled flexible tubes, Thesis, University of Cambridge, 1963.
[13] R. W. Gregory, M. P. Paidoussis, Unstable oscillation of tubular cantilevers conveying fluid I. Theory, Proc. R. Soc. Lond. A, Vol. 293, No. 1435, pp. 512-527, 1966.
[14] R. W. Gregory, M. P. Paidoussis, Unstable oscillation of tubular cantilevers conveying fluid II. Experiments, Proc. R. Soc. Lond. A, Vol. 293, No. 1435, pp. 528-542, 1966.
[15] J. Hill, C. Swanson, Effects of lumped masses on the stability of fluid conveying tubes, Journal of Applied Mechanics, Vol. 37, No. 2, pp. 494-497, 1970.
[16] S. Chen, J. Jendrzejczyk, General characteristics, transition, and control of instability of tubes conveying fluid, The Journal of the Acoustical Society of America, Vol. 77, No. 3, pp. 887-895, 1985.
[17] J. A. Jendrzejczyk, S. S. Chen, Experiments on tubes conveying fluid, Thin-Walled Structures, Vol. 3, No. 2, pp. 109-134, 1985.
[18] Y. Sugiyama, H. Kawagoe, T. Kishi, S. Nishiyama, Studies on the Stability of Pipes Conveying Fluid: The Combined Effect of a Spring Support and a Lumped Mass, JSME international journal. Ser. 1, Solid mechanics, strength of materials, Vol. 31, No. 1, pp. 20-26, 1988.
[19] M. A. G. Silva, Influence of eccentric valves on the vibration of fluid conveying pipes, Nuclear Engineering and Design, Vol. 64, No. 1, pp. 129-134, 1981.
[20] M. P. Paidoussis, C. Semler, Non-linear dynamics of a fluid-conveying cantilevered pipe with a small mass attached at the free end, International Journal of Non-Linear Mechanics, Vol. 33, No. 1, pp. 15-32, 1998.
[21] Y. Modarres-Sadeghi, C. Semler, M. Wadham-Gagnon, M. P. Païdoussis, Dynamics of cantilevered pipes conveying fluid. Part 3: Three-dimensional dynamics in the presence of an end-mass, Journal of Fluids and Structures, Vol. 23, No. 4, pp. 589-603, 2007.
[22] S. Rinaldi, M. P. Paidoussis, Dynamics of a cantilevered pipe discharging fluid, fitted with a stabilizing end-piece, Journal of Fluids and Structures, Vol. 26, No. 3, pp. 517-525, 2010.
[23] M. H. Ghayesh, M. P. Paidoussis, Y. Modarres-Sadeghi, Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass, Journal of Sound and Vibration, Vol. 330, No. 12, pp. 2869-2899, 2011.
[24] L. Wang, H. L. Dai, Vibration and enhanced stability properties of fluid-conveying pipes with two symmetric elbows fitted at downstream end, Archive of Applied Mechanics, Vol. 82, No. 2, pp. 155-161, 2012/02/01, 2012.
[25] T. Z. Yang, X. D. Yang, Y. H. Li, B. Fang, Passive and adaptive vibration suppression of pipes conveying fluid with variable velocity, Journal of Vibration and Control, Vol. 20, No. 9, pp. 1293-1300, 2014.
[26] R. D. Firouz-Abadi, A. R. Askarian, M. Kheiri, Bending–torsional flutter of a cantilevered pipe conveying fluid with an inclined terminal nozzle, Journal of Sound and Vibration, Vol. 332, No. 12, pp. 3002-3014, 2013/06/10/, 2013.
[27] G. S. Copeland, F. C. Moon, Chaotic flow-induced vibration of a flexible tube with end mass, Journal of Fluids and Structures, Vol. 6, No. 6, pp. 705-718, 1992/11/01/, 1992.
[28] A. E. Mamaghani, S. Khadem, S. Bab, Vibration control of a pipe conveying fluid under external periodic excitation using a nonlinear energy sink, Nonlinear Dynamics, Vol. 86, No. 3, pp. 1761-1795, 2016.
[29] G. B. Song, P. Zhang, L. Li, M. Singla, D. Patil, H. N. Li, Y. L. Mo, Vibration control of a pipeline structure using pounding tuned mass damper, Journal of Engineering Mechanics, Vol. 142, No. 6, pp. 04016031, 2016.
[30] S. Rechenberger, D. Mair, Vibration Control of Piping Systems and Structures Using Tuned Mass Dampers, ASME 2017 Pressure Vessels and Piping Conference, Hawaii, USA, Vol. PVP2017-65448, pp. V03BT03A035, 2017.
[31] K. Zhou, F. R. Xiong, N. B. Jiang, H. L. Dai, H. Yan, L. Wang, Q. Ni, Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink, Nonlinear Dynamics, pp. 1-22, 2018.
[32] C. Semler, Nonlinear dynamics and chaos of a pipe conveying fluid, McGill University, 1992.
[33] Y. W. Zhang, B. Yuan, B. Fang, L. Q. Chen, Reducing thermal shock-induced vibration of an axially moving beam via a nonlinear energy sink, Nonlinear Dynamics, Vol. 87, No. 2, pp. 1159-1167, 2017.
[34] L. Wang, Z. Y. Liu, A. Abdelkefi, Y. K. Wang, H. L. Dai, Nonlinear dynamics of cantilevered pipes conveying fluid: Towards a further understanding of the effect of loose constraints, International Journal of Non-Linear Mechanics, Vol. 95, pp. 19-29, 2017.
[35] Z. Y. Liu, L. Wang, X. P. Sun, Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid, Acta Mechanica Solida Sinica, Vol. 31, No. 1, pp. 32-50, February 01, 2018.
[36] Z. Y. Liu, L. Wang, H. L. Dai, P. Wu, T. L. Jiang, Nonplanar vortex-induced vibrations of cantilevered pipes conveying fluid subjected to loose constraints, Ocean Engineering, Vol. 178, pp. 1-19, 2019.
[37] M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Vol. 3, No. 2, pp. 47-56, 2011.
[38] M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.
[39] M. P. Paidoussis, N. T. Issid, Dynamic stability of pipes conveying fluid, Journal of sound and vibration, Vol. 33, No. 3, pp. 267-294, 1974.
)
Volume 50, Issue 1
June 2019Pages 182-190
- Receive Date: 23 February 2019
- Revise Date: 26 March 2019
- Accept Date: 26 March 2019