Abstract
In this study, the nonlinear dynamics of a pipe subjected to vortex-induced vibrations and unsynchronized support motions are investigated, considering the phase difference of support motions at two ends of pipe. We first use a wake oscillator model based on the van der Pol equation to describe the vortex-induced force, and validate the induced vibration amplitude of structure against the experimental data. Then, a nonlinear theoretical model representing the dynamic responses of the pipe system at different locations is constructed based on the Hamilton principle and Galerkin discretization. The resulting ordinary differential equations are numerically solved providing multi-mode approximations to the cross-flow amplitude and the lift coefficient. It is shown that the cross-flow amplitude of the pipe around the first lock-in region is significantly affected by the support motions, resulting in a greatly suppressed or increased vibration amplitude of the pipe. Moreover, the bandwidth of support excitation frequency between minimum and maximum vibration amplitudes changes with the phase difference, owing to the transition between aperiodic and periodic responses of pipe. In addition, the effect of geometric nonlinearity on the responses of pipe with support motions is also discussed.
Similar content being viewed by others
References
Dai H, Wang L, Qian Q, Ni Q (2013) Vortex-induced vibrations of pipes conveying fluid in the subcritical and supercritical regimes. J Fluids Struct 39:322–334
Païdoussis MP, Price SJ, De Langre E (2010) Fluid-structure interactions: cross-flow-induced instabilities. Cambridge University Press, Cambridge
Williamson C, Govardhan R (2004) Vortex-induced vibrations. Annu Rev Fluid Mech 36:413–455
Blevins RD (1990) Flow-induced vibration. Van Nostrand Reinhold Co, New York
Doan VP, Nishi Y (2015) Modeling of fluid–structure interaction for simulating vortex-induced vibration of flexible riser: finite difference method combined with wake oscillator model. J Mar Sci Technol 20(2):309–321
Wu X, Ge F, Hong Y (2012) A review of recent studies on vortex-induced vibrations of long slender cylinders. J Fluids Struct 28:292–308
Brika D, Laneville A (1993) Vortex-induced vibrations of a long flexible circular cylinder. J Fluid Mech 250:481–481
Khalak A, Williamson C (1996) Dynamics of a hydroelastic cylinder with very low mass and damping. J Fluids Struct 10(5):455–472
Stappenbelt B, Lalji F, Tan G (2007) Low mass ratio vortex-induced motion. In: The 16th Australasian fluid mechanics conference, Gold Coast, pp 1491–1497
Lee J, Bernitsas M (2011) High-damping, high-Reynolds VIV tests for energy harnessing using the VIVACE converter. Ocean Eng 38(16):1697–1712
Facchinetti ML, De Langre E, Biolley F (2004) Coupling of structure and wake oscillators in vortex-induced vibrations. J Fluids Struct 19(2):123–140
Newman DJ, Karniadakis GE (1997) A direct numerical simulation study of flow past a freely vibrating cable. J Fluid Mech 344:95–136
Ogink R, Metrikine A (2010) A wake oscillator with frequency dependent coupling for the modeling of vortex-induced vibration. J Sound Vib 329(26):5452–5473
Pavlovskaia E, Keber M, Postnikov A, Reddington K, Wiercigroch, M (2016) Multi-modes approach to modelling of vortex-induced vibration. Int J Non Linear Mech 80:40–51
Pontaza JP, Chen HC (2007) Three-dimensional numerical simulations of circular cylinders undergoing two degree-of-freedom vortex-induced vibrations. J Offshore Mech Arct Eng 129(3):158–164
Skop R, Balasubramanian S (1997) A new twist on an old model for vortex-excited vibrations. J Fluids Struct 11(4):395–412
Violette R, Langre E de, Szydlowski J (2007) Computation of vortex-induced vibrations of long structures using a wake oscillator model: comparison with DNS and experiments. Comput Struct 85:1134–1141
Wang X, So R, Chan K (2003) A non-linear fluid force model for vortex-induced vibration of an elastic cylinder. J Sound Vib 260(2):287–305
Chen W, Li M, Guo S, Gan K (2014) Dynamic analysis of coupling between floating top-end heave and riser’s vortex-induced vibration by using finite element simulations. Appl Ocean Res 48:1–9
Dai HL, Wang L, Qian Q, Gan J (2012) Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method. Appl Math Comput 219(5):2453–2464
Dai HL, Wang L, Qian Q, Ni Q (2014) Vortex-induced vibrations of pipes conveying pulsating fluid. Ocean Eng 77:12–22
Gu J, Wang Y, Zhang Y, Duan M, Levi C (2013) Analytical solution of mean top tension of long flexible riser in modeling vortex-induced vibrations. Appl Ocean Res 41:1–8
Han X, Lin W, Zhang X, Tang Y, Zhao C (2016) Two degree of freedom flow-induced vibration of cylindrical structures in marine environments: frequency ratio effects. J Mar Sci Technol 21:479–492
He F, Dai H, Huang Z, Wang L (2017) Nonlinear dynamics of a fluid-conveying pipe under the combined action of cross-flow and top-end excitations. Appl Ocean Res 62:199–209
Wang Z, Yang H (2016) Parametric instability of a submerged floating pipeline between two floating structures under combined vortex excitations. Appl Ocean Res 59:265–273
Zhu H, Lin P, Yao J (2016) An experimental investigation of vortex-induced vibration of a curved flexible pipe in shear flows. Ocean Eng 121:62–75
Zhu H, Zhao H, Yao J, Tang Y (2016) Numerical study on vortex-induced vibration responses of a circular cylinder attached by a free-to-rotate dartlike overlay. Ocean Eng 112:195–210
Yang B, Gao F, Jeng D-S, Wu Y (2009) Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow. Acta Mech Sin 25(1):51–63
Lei C, Cheng L, Armfield S, Kavanagh K (2000) Vortex shedding suppression for flow over a circular cylinder near a plane boundary. Ocean Eng 27(10):1109–1127
Zhao M, Cheng L (2011) Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary. J Fluids Struct 27(7):1097–1110
Zheng H, Price RE, Modarres-Sadeghi Y, Triantafyllou MS (2014) On fatigue damage of long flexible cylinders due to the higher harmonic force components and chaotic vortex-induced vibrations. Ocean Eng 88:318–329
Jin Y, Dong P (2016) A novel Wake Oscillator Model for simulation of cross-flow vortex induced vibrations of a circular cylinder close to a plane boundary. Ocean Eng 117:57–62
Lemoël M, Brown P, Jean P, Shepheard B (2008) Design of the World’s 1st Gravity Actuated Pipe (GAP) for Murphy’s Kikeh Deepwater Development, East Malaysia, ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers, pp 519–529
Leklong J, Chucheepsakul S, Kaewunruen S (2008) Dynamic responses of marine risers/pipes transporting fluid subject to top end excitations. In: Proceedings of the eighth ISOPE Pacific/Asia offshore mechanics symposium, Bangkok, Thailand, November 10–14, 2008
Timoshenko S, Young D (1955) Vibration problems in engineering. Van Nostrand, Princeton
Clough RW, Penzien J (1993) Dynamics of structures. McGraw-Hill, New York
Li M (2015) Analytical study on the dynamic response of a beam with axial force subjected to generalized support excitations. J Sound Vib 338:199–216
Chaplin JR, Bearman PW, Cheng Y et al (2005) Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser. J Fluids Struct 21(1):25–40
Larsen CM, Halse KH (1997) Comparison of models for vortex induced vibrations of slender marine structures. Mar Struct 10(10):413–441
Farshidianfar A, Zanganeh H (2010) A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio. J Fluids Struct 26(3):430–441
Acknowledgements
The authors gratefully acknowledge the supports provided by the National Natural Science Foundation of China (Nos. 11602090, 51609211 and 11622216), Natural Science Foundation of Hubei Province (2017CFB429) and Fundamental Research Funds for the Central Universities, HUST (2017KFYXJJ135).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
He, F., Dai, H. & Wang, L. Vortex-induced vibrations of a pipe subjected to unsynchronized support motions. J Mar Sci Technol 23, 978–990 (2018). https://doi.org/10.1007/s00773-017-0526-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00773-017-0526-y