Vortex-induced vibrations of a pipe subjected to unsynchronized support motions

  • Fang He
  • Huliang Dai
  • Lin Wang
Original article


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.


Vortex-induced vibration Unsynchronized support motions Multi-mode Lock-in Nonlinear dynamics 



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).


  1. 1.
    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 39:322–334CrossRefGoogle Scholar
  2. 2.
    Païdoussis MP, Price SJ, De Langre E (2010) Fluid-structure interactions: cross-flow-induced instabilities. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  3. 3.
    Williamson C, Govardhan R (2004) Vortex-induced vibrations. Annu Rev Fluid Mech 36:413–455MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Blevins RD (1990) Flow-induced vibration. Van Nostrand Reinhold Co, New YorkMATHGoogle Scholar
  5. 5.
    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):309–321CrossRefGoogle Scholar
  6. 6.
    Wu X, Ge F, Hong Y (2012) A review of recent studies on vortex-induced vibrations of long slender cylinders. J Fluids Struct 28:292–308CrossRefGoogle Scholar
  7. 7.
    Brika D, Laneville A (1993) Vortex-induced vibrations of a long flexible circular cylinder. J Fluid Mech 250:481–481CrossRefGoogle Scholar
  8. 8.
    Khalak A, Williamson C (1996) Dynamics of a hydroelastic cylinder with very low mass and damping. J Fluids Struct 10(5):455–472CrossRefGoogle Scholar
  9. 9.
    Stappenbelt B, Lalji F, Tan G (2007) Low mass ratio vortex-induced motion. In: The 16th Australasian fluid mechanics conference, Gold Coast, pp 1491–1497Google Scholar
  10. 10.
    Lee J, Bernitsas M (2011) High-damping, high-Reynolds VIV tests for energy harnessing using the VIVACE converter. Ocean Eng 38(16):1697–1712CrossRefGoogle Scholar
  11. 11.
    Facchinetti ML, De Langre E, Biolley F (2004) Coupling of structure and wake oscillators in vortex-induced vibrations. J Fluids Struct 19(2):123–140CrossRefGoogle Scholar
  12. 12.
    Newman DJ, Karniadakis GE (1997) A direct numerical simulation study of flow past a freely vibrating cable. J Fluid Mech 344:95–136CrossRefMATHGoogle Scholar
  13. 13.
    Ogink R, Metrikine A (2010) A wake oscillator with frequency dependent coupling for the modeling of vortex-induced vibration. J Sound Vib 329(26):5452–5473CrossRefGoogle Scholar
  14. 14.
    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 80:40–51CrossRefGoogle Scholar
  15. 15.
    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):158–164CrossRefGoogle Scholar
  16. 16.
    Skop R, Balasubramanian S (1997) A new twist on an old model for vortex-excited vibrations. J Fluids Struct 11(4):395–412CrossRefGoogle Scholar
  17. 17.
    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 85:1134–1141CrossRefGoogle Scholar
  18. 18.
    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):287–305CrossRefGoogle Scholar
  19. 19.
    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 48:1–9CrossRefGoogle Scholar
  20. 20.
    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):2453–2464MathSciNetMATHGoogle Scholar
  21. 21.
    Dai HL, Wang L, Qian Q, Ni Q (2014) Vortex-induced vibrations of pipes conveying pulsating fluid. Ocean Eng 77:12–22CrossRefGoogle Scholar
  22. 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 41:1–8CrossRefGoogle Scholar
  23. 23.
    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 21:479–492CrossRefGoogle Scholar
  24. 24.
    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 62:199–209CrossRefGoogle Scholar
  25. 25.
    Wang Z, Yang H (2016) Parametric instability of a submerged floating pipeline between two floating structures under combined vortex excitations. Appl Ocean Res 59:265–273CrossRefGoogle Scholar
  26. 26.
    Zhu H, Lin P, Yao J (2016) An experimental investigation of vortex-induced vibration of a curved flexible pipe in shear flows. Ocean Eng 121:62–75CrossRefGoogle Scholar
  27. 27.
    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 112:195–210CrossRefGoogle Scholar
  28. 28.
    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):51–63CrossRefGoogle Scholar
  29. 29.
    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):1109–1127CrossRefGoogle Scholar
  30. 30.
    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):1097–1110CrossRefGoogle Scholar
  31. 31.
    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 88:318–329CrossRefGoogle Scholar
  32. 32.
    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 117:57–62CrossRefGoogle Scholar
  33. 33.
    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 519–529Google Scholar
  34. 34.
    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, 2008Google Scholar
  35. 35.
    Timoshenko S, Young D (1955) Vibration problems in engineering. Van Nostrand, PrincetonGoogle Scholar
  36. 36.
    Clough RW, Penzien J (1993) Dynamics of structures. McGraw-Hill, New YorkMATHGoogle Scholar
  37. 37.
    Li M (2015) Analytical study on the dynamic response of a beam with axial force subjected to generalized support excitations. J Sound Vib 338:199–216CrossRefGoogle Scholar
  38. 38.
    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):25–40CrossRefGoogle Scholar
  39. 39.
    Larsen CM, Halse KH (1997) Comparison of models for vortex induced vibrations of slender marine structures. Mar Struct 10(10):413–441CrossRefGoogle Scholar
  40. 40.
    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):430–441CrossRefGoogle Scholar

Copyright information

© JASNAOE 2018

Authors and Affiliations

  1. 1.Ocean CollegeZhejiang UniversityHangzhouChina
  2. 2.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina

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