An empirical model for amplitude prediction on VIV-galloping instability of rectangular cylinders

  • Niu, Huawei (Wind Engineering Research Center of Hunan University) ;
  • Zhou, Shuai (Wind Engineering Research Center of Hunan University) ;
  • Chen, Zhengqing (Wind Engineering Research Center of Hunan University) ;
  • Hua, Xugang (Wind Engineering Research Center of Hunan University)
  • Received : 2014.10.28
  • Accepted : 2015.05.08
  • Published : 2015.07.25


Aerodynamic forces of vortex-induced vibration and galloping are going to be coupled when their onset velocities are close to each other, which will induce the cross-wind amplitudes of the structures increased continuously with ever-increasing wind velocities. The main purpose of the present work is going to propose an empirical formula to predict the response amplitude of VIV-galloping interaction. Firstly, two typical mathematical models for the coupled oscillations, i.e., Tamura & Shimada model and Parkinson & Corless model are comparatively summarized. Then, the key parameter affecting response amplitude is determined through comparative numerical simulations with Tamura & Shimada model. For rectangular cylinders with the side ratio from 0.5 to 2.5, which are actually prone to develop the VIV and galloping induced interaction responses, an empirical amplitude prediction formula is proposed after regression analysis on comprehensively collected experimental data with the predetermined key parameter.


Supported by : Natural Science Foundation of China


  1. Allison E, A.M. and Corless, R.M. (1995), "Prediction of closed-loop hysteresis with a flow-induced vibration model", Proceedings of the 15th Canadian Congress of Applied Mechanics, Victoria, Canada, May.
  2. Bearman, P.W. (1984), "Vortex shedding from oscillating bluff bodies", Annu. Rev. Fluid Mech., 16(1), 195-222.
  3. Bearman, P.W., Gartshore, I.S., Maull, D.J. and Parkinson, G.V. (1987), "Experiments on flow-induced vibration of a square section cylinder", J. Fluids Struct., 1(1), 19-34.
  4. Borri, C., Zhou, S. and Chen, Z. (2012), "Coupling investigation on vortex-induced vibration and galloping of rectangular cylinders", Proceedings of the Seventh International Colloquium on Bluff Body Aerodynamics and Applications, Shanghai, China, September.
  5. Corless, R.M. and Parkinson, G.V. (1988), "A model of the combined effects of vortex-induced oscillation and galloping", J. Fluids Struct., 2(3), 203-220.
  6. Den Hartog, J.P. (1932), "Transmission-line vibration due to sleet", AIEE, 51, 1074-1086.
  7. EN 1991-1-4 (2010), Eurocode 1-Actions on Structures, Parts 1-4: General Actions-Wind Actions.
  8. Facchinetti, M.L., Langrea, and Biolley, F. (2004), "Coupling of structure and wake oscillators in vortex-induced vibrations", J. Fluids Struct., 19(2) ,123-140
  9. Garrett, J.L. (2003), Flow-induced vibration of elastically supported rectangular cylinders, Ph.D. Dissertation, Iowa State University, Ames.
  10. Govardhan, R.N. and Williamson, C.H.K. (2006), "Defining the 'modified griffin plot' in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping", J. Fluid Mech., 561,147-180.
  11. Gjelstrup, H. and Georgakis, C.T. (2011), "A quasi-steady 3 degree-of-freedom model for the determination of the onset of bluff body galloping instability", J. Fluids Struct., 27(7), 1021-1034
  12. Hansen, S.O. (2013), "Wind loading design codes", Fifty Years of Wind Engineering-Prestige Lectures from the Sixth European and African Conference on Wind Engineering, Cambridge, UK, July.
  13. Hortmanns, M. and Ruscheweyh, H. (1997), "Development of a method for calculating galloping amplitudes considering nonlinear aerodynamic coefficients measured with the forced oscillation method", J. Wind Eng. Ind. Aerod., 69-71, 251-261.
  14. Hemon, P. (1999), "An improvement of time delayed quasi-steady model for the oscillations of circular cylinders in cross-flow", J. Fluids Struct., 13(3), 291-307.
  15. Joly, A., Etienne, S. and Pelletier, D. (2012), "Galloping of square cylinders in cross-flow at low Reynolds numbers", J. Fluids Struct., 28, 232-243.
  16. Luo, S.C., Chew, Y.T. and Ng, Y.T. (2003), "Hysteresis phenomenon in the galloping oscillation of a square cylinder", J. Fluids Struct., 18(1), 103-118.
  17. Macdonald, H.G. and Larose, G.L. (2006), "A unified approach to aerodynamic damping and drag/lift instabilities, and its application to dry inclined cable galloping", J. Fluids Struct., 22(2), 229-252.
  18. Mannini, C., Marra, A.M., Massai, T. and Bartoli, G. (2013), "VIV and galloping interaction for a 3:2 rectangular cylinder", Proceedings of the 6th European and African Conference on Wind Engineering, Cambridge, UK, July.
  19. Mannini C., Marra A.M. and Bartoli G. (2014), "VIV-galloping instability of rectangular cylinders: Review and new experiments", J. Wind Eng. Ind. Aerod., 132, 109-124.
  20. Marra, A.M., Mannini, C .and Bartoli, G. (2011), "Van der Pol-type equation for modeling vortex-induced oscillations of bridge decks", J. Wind Eng. Ind. Aerod., 99(6-7), 776-785.
  21. Matsumoto, M. (1999), "Vortex shedding of bluff bodies: a review", J. Fluids Struct., 13(7-8), 791-811.
  22. Names, A., Zhao, J., Lo Jacono, D. and Sheridan, J. (2012), "The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack", J. Fluid Mech., 710, 102-130.
  23. Parkinson, G.V. and Bouclin, D. (1977), "Hydroelastic oscillation of square cylinders", International Research Seminar on Safety of Structures under Dynamic Loading, Trondheim, Norway, June.
  24. Parkinson, G.V. and Brooks, N.P.H. (1961), "On the aeroelastic instability of bluff cylinders", J. Appl. Mech.-T ASME, 28(2), 252-258.
  25. Parkinson, G.V. and Smith, J.D. (1964), "The square cylinder as an aeroelastic non-linear oscillator", Quart. J. Mech. Appl. Math., 17(2), 225-239.
  26. Parkinson, G.V. (1965), "Aeroelastic galloping in one degree of freem", Wind Effects on Buildings and Structures: Proceedings of the Conference Held at the National Physical Laboratory, Teddington, UK, June.
  27. Parkinson, G.V. and Wawzonak, M.A. (1981), "Some consideration of combined effects of galloping and vortex resonance", J. Wind Eng. Ind. Aerod., 8(1-2), 135-143.
  28. Skop, R.A. and Griffin, O.M. (1973), "A model for the vortex-excited resonant response of bluff cylinders", J. Sound Vib., 27(2), 225-233.
  29. Sarpkaya, T. (1979), "Vortex-induced oscillations: a selective review", J. Appl. Mech.-T ASME, 46(2), 241-258.
  30. Sarpkaya, T. (2004), "A critical review of the intrinsic nature of vortex-induced vibrations", J. Fluids Struct., 19(4), 389-447.
  31. Tamura, Y. and Matsui, G. (1979), "Wake-oscillator model of vortex-induced oscillation of circular cylinder", Proceedingsof the 5th international conference on wind engineering, Fort Collins, USA, July.
  32. Tamura, Y. (1983), "Mathematical model for vortex-induced oscillations of continuous systems with circular cross section", J. Wind Eng. Ind. Aerod., 14, 431-442.
  33. Tamura, Y. and Shimada, K. (1987), "A mathematical model for the transverse oscillations of square cylinders", Proceedings of the 1st International Conference on Flow Induced Vibrations, Bowness on Windermere, UK, May.
  34. Vio, G.A., Dimitriadis, G. and Cooper, J.E. (2007), "Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem", J. Fluids Struct., 23(7), 983-1011.
  35. Williamson, C. and Govardhan, R. (2008), "A brief review of recent results in vortex-induced vibrations", J. Wind Eng. Ind. Aerod., 96(6-7), 713-735.

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