An overview of vortex-induced vibration (VIV) of bridge decks

Abstract

A brief overview of vortex-induced vibration (VIV) of circular cylinders is first given as most of VIV studies have been focused on this particular bluff cross-section. A critical literature review of VIV of bridge decks that highlights physical mechanisms central to VIV from a renewed perspective is provided. The discussion focuses on VIV of bridge decks from wind-tunnel experiments, full-scale observations, semi-empirical models and computational fluids dynamics (CFD) perspectives. Finally, a recently developed reduced order model (ROM) based on truncated Volterra series is introduced to model VIV of long-span bridges. This model captures successfully salient features of VIV at “lock-in” and unlike most phenomenological models offers physical significance of the model kernels.

Keywords

vortex-induced vibration (VIV) / Volterra series / bridge

References

[1] Bishop R E D, Hassan A Y. The lift and drag forces on a circular cylinder in a flowing fluid. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1964a, 277(1368): 32–50

[2] Naudascher E, Wang Y. Flow-induced vibrations of prismatic bodies and grids of prisms. Journal of Fluids and Structures, 1993, 7(4): 341–373

[3] Strouhal V. Ueber eine besondere Art der Tonerregung. Annalen der Physik, 1878, 5: 216–251

[4] Rayleigh L. Theory of Sound. 2nd ed. London: Macmillan, 1896

[5] Sarpkaya T. Vortex-induced oscillations. Journal of Applied Mechanics, 1979, 46(2): 241–258

[6] Bearman P W. Vortex shedding from oscillating bluff bodies. Annual Review of Fluid Mechanics, 1984, 16(1): 195–222

[7] Williamson C H K. Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 1996, 28(1): 477–539

[8] Billah K Y R. A study of vortex-induced vibration. Dissertation for the Doctoral Degree, Princeton: Princeton University, 1989

[9] Sarpkaya T. A critical review of the intrinsic nature of VIV. Fluid Mechanics and Its Applications, 2004, 75: 159–161

[10] Williamson C H K, Govardhan R. Vortex-induced vibrations. Annual Review of Fluid Mechanics, 2004, 36(1): 413–455

[11] von Kármán Th, Rubach H. Ueber den mechanismus des flussigkeits-und luftwiderstandes. Physikalische Zeitschrift, 1912, 13: 49–59

[12] Birkhoff G. Formation of vortex streets. Journal of Applied Physics, 1953, 24(1): 98–103

[13] Abernathy F H, Kronauer R E. The formation of vortex streets. Journal of Fluid Mechanics, 1962, 13(01): 1–20

[14] Gerrard J H. The mechanics of the formation region of vortices behind bluff bodies. Journal of Fluid Mechanics, 1966, 25(02): 401–413

[15] Bishop R E D, Hassan A Y. The lift and drag forces on a circular cylinder oscillating in a flowing fluid. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1964, 277(1368): 51–75

[16] Hartlen R T, Currie I G. Lift-oscillator model of vortex-induced vibration. Journal of the Engineering Mechanics Division, 1970, 96(5): 577–591

[17] Skop R A, Griffin O M. A model for the vortex-excited resonant response of bluff cylinders. Journal of Sound and Vibration, 1973, 27(2): 225–233

[18] Landl R. A mathematical model for vortex-excited vibrations of bluff bodies. Journal of Sound and Vibration, 1975, 42(2): 219–234

[19] Iwan W D, Blevins R D. A model for vortex induced oscillation of structures. Journal of Applied Mechanics, 1974, 41(3): 581–586

[20] Dowell E H. Nonlinear oscillator models in bluff body aeroelasticity. Journal of Sound and Vibration, 1981, 75(2): 251–264

[21] Jones G W Jr, Cincotta, J. J., Walker R W.. Aerodynamic Forces on a Stationary and Oscillating Circular Cylinder at High Reynolds Numbers. NASA TR R-300, 1969

[22] Nakamura Y. Vortex excitation of a circular cylinder treated as binary flutter. Rep Res Inst App Mech, 1969, 13: 217–234

[23] Tamura Y, Matsui G. 1979. Wake-oscillator model of vortex-induced oscillation of circular cylinder. In: Proceedings of the Fifth International Conference on Wind Engineering. Fort Collins, Colorado, USA, 1085–1094

[24] Basu R I, Vickery B J. Across-wind vibrations of structures of circular cross-section—Part 2: development of a mathematical model for full-scale application. Journal of Wind Engineering and Industrial Aerodynamics, 1983, 12(1): 75–97

[25] d’Asdia P, Materazzi A L, Radogna E F. Nonlinear model of wind-induced vibrations of slender structures with circular cross-sections. Journal of Wind Engineering and Industrial Aerodynamics, 1993, 48(2-3): 189–203

[26] Nakamura Y, Mizota T. Unsteady lifts and wakes of oscillating rectangular prisms. Journal of the Engineering Mechanics Division, 1975, 101: 855–871

[27] Fail R, Lawford J A,Eyre R C W. Low Speed Experiments on the Wake Characteristics of Flat Plates Normal to an Air Stream. British ARC R&M 3120, 1959

[28] Wootton L R. The oscillations of large circular stacks in wind. Proceedings- Institution of Civil Engineers, 1969, 43(4): 573–598

[29] Komatsu S, Kobayashi H. Vortex-induced oscillation of bluff cylinders. Journal of Wind Engineering and Industrial Aerodynamics, 1980, 6(3-4): 335–362

[30] Shiraishi N, Matsumoto M. On classification of vortex-induced oscillation and its application for bridge structures. Journal of Wind Engineering and Industrial Aerodynamics, 1983, 14(1-3): 419–430

[31] Van der Pol B, Van Der Mark J. Frequency demultiplication. Nature, 1927, 120(3019): 363–364

[32] Zhang W, Wei Z, Yang Y, Ge Y. Comparison and analysis of Vortex induced vibration for twin-box bridge sections based on experiments in different Reynolds numbers. Journal of Tongji University(Natural Sicience), 2008, 36(1): 6–11

[33] Nakamura Y, Nakashima M. Vortex excitation of prisms with elongated rectangular, H and h cross-sections. Journal of Fluid Mechanics, 1986, 163: 149–169

[34] Koopman G H. The vortex wakes of vibrating cylinders at low Reynolds numbers. Journal of Fluid Mechanics, 1967, 28(03): 501–512

[35] Matsumoto M, Shiraishi N, Shirato H, Stoyanoff S, Yagi T. Mechanism of, and turbulence effect on vortex-induced oscillations for bridge box girders. Journal of Wind Engineering and Industrial Aerodynamics, 1993, 49(1-3): 467–476

[36] Sarpkaya T, Schoaff R L. A Discrete Vortex Analysis of Flow about Stationary and Transversely Oscillating Circular Cylinders. Tech. Rep. NPS-69sl79011, Naval Postgrad Sch, Monterey, Calif, 1979

[37] Scanlan R H. Amplitude and turbulence effects on bridge flutter derivatives. Journal of Structural Engineering, 1997, 123(2): 232–236

[38] Haan F L Jr, Kareem A. Anatomy of turbulence effects on the aerodynamics of an oscillating prism. Journal of Engineering Mechanics, 2009, 135(9): 987–999

[39] Kareem A, Wu T. Wind induced effects on bluff bodies in turbulent flows: nonstationary, non-gaussian and nonlinear features. In: Porceedings of the 7th International Colloquium on Bluff-Body Aerodynamics and its Application (BBAAVII). September 2012, Shanghai, China, 2012

[40] Larose G L, Larsen S V, Larsen A, Hui M, Jensen A G. Sectional model experiments at high Reynolds number for the deck of a 1018 m span cable-stayed bridge. In: Proceedings of 11th International Conference on Wind Engineering. Lubbock, 2003, 373–380

[41] Larsen S V, Smitt L W, Gjelstrup H,Larsen A. Investigation of vortex-induced motion at high Reynolds numbers using large scale section model. 2004

[42] Sarpkaya T. Fluid forces on oscillating cylinders. Journal of the Waterway Port Coastal and Ocean Division, 1978, 104(3): 275–290

[43] Griffin O M, Koopmann G H. The vortex-excited lift and reaction forces on resonantly vibrating cylinders. Journal of Sound and Vibration, 1977, 54(3): 435–448

[44] Diana G, Resta F, Belloli M, Rocchi D. On the vortex shedding forcing on suspension bridge deck. Journal of Wind Engineering and Industrial Aerodynamics, 2006, 94(5): 341–363

[45] Schewe G, Larsen A. Reynolds number effects in the flow around a bluff bridge deck cross section. Journal of Wind Engineering and Industrial Aerodynamics, 1998, 74-76: 829–838

[46] Smith I J. Wind induced dynamic response of the Wye bridge. Engineering Structures, 1980, 2(4): 202–208

[47] Kumarasena T, Scanlan R H, Morris G R. Deer Isle Bridge: field and computed vibrations. Journal of Structural Engineering, 1989, 115(9): 2313–2327

[48] Kumarasena T, Scanlan R H, Ehsan F. Wind-induced motions of Deer Isle Bridge. Journal of Structural Engineering, 1991, 117(11): 3356–3374

[49] Owen J S, Vann A M, Davies J P, Blakeborough A. The prototype testing of Kessock Bridge: response to vortex shedding. Journal of Wind Engineering and Industrial Aerodynamics, 1996, 60: 91–108

[50] Ronaldo C B, Michèle S P. Reduction of vortex-induced oscillations of Rio-Niterói bridge by dynamic control devices. Journal of Wind Engineering and Industrial Aerodynamics, 2000, 84(3): 273–288

[51] Larsen A, Esdahl S, Andersen J E, Vejrum T. Storebæl suspension bridge-vortex shedding excitation and mitigation by guide vanes. Journal of Wind Engineering and Industrial Aerodynamics, 2000, 88(2-3): 283–296

[52] Frandsen J B. Simultaneous pressures and accelerations measured full-scale on the Great Belt East suspension bridge. Journal of Wind Engineering and Industrial Aerodynamics, 2001, 89(1): 95–129

[53] Fujino Y, Yoshida Y. Wind-induced vibration and control of Trans-Tokyo Bay Crossing Bridge. Journal of Structural Engineering, 2002, 128(8): 1012–1025

[54] Li H, Laima S, Ou J, Zhao X, Zhou W, Yu Y, Li N, Liu Z. Investigation of vortex-induced vibration of a suspension bridge with two separated steel box girders based on field measurements. Engineering Structures, 2011, 33(6): 1894–1907

[55] Wilkinson R H. Fluctuating pressures on an oscillating square prism. Part II. Spanwise correlation and loading. Aero Quarterly, 1981, 32(2): 111–125

[56] Scanlan R H. State-of-the-art Methods for Calculating Flutter, Vortex-induced, and Buffeting Response of Bridge Structures. Federal Highway Administration Report No. FHWA/RD-80/50. 1981

[57] Zdravkovich M. Scruton number: A proposal. Journal of Wind Engineering and Industrial Aerodynamics, 1982, 10(3): 263–265

[58] Griffin O M, Ramberg S E. Some recent studies of vortex shedding with application to marine tubulars and risers. Journal of Energy Resources Technology, 1982, 104(1): 2–13

[59] Ehsan F, Scanlan R H. Vortex-induced vibrations of flexible bridges. Journal of Engineering Mechanics, 1990, 116(6): 1392–1411

[60] Goswami I, Scanlan R H, Jones N P. Vortex-induced vibration of circular cylinders-Part2: new model. Journal of Engineering Mechanics, 1993, 119(11): 2288–2302

[61] Larsen A. A generalized model for assessment of vortex-induced vibrations of flexible structures. Journal of Wind Engineering and Industrial Aerodynamics, 1995, 57(2-3): 281–294

[62] Fujiwara A, Kataoka H,Ito M.Numerical simulation of flow field around an oscillating bridge using finite difference method. Journal of Wind Engineering and Industrial Aerodynamics, 1993, 46-47: 567-575

[63] Nomura T. Finite element analysis of vortex-induced vibrations of bluff cylinders. Journal of Wind Engineering and Industrial Aerodynamics, 1993, 46-47: 587–594

[64] Lee S, Lee J S, Kim J D. Prediction of vortex-induced wind loading on long-span bridges. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 67-68: 267–278

[65] Sarwar M W, Ishihara T. Numerical study on suppression of vortex-induced vibrations of box girder bridge section by aerodynamic countermeasures. Journal of Wind Engineering and Industrial Aerodynamics, 2010, 98(12): 701–711

[66] Sarpkaya T, Schoaff R L. Inviscid model of two-dimensional vortex shedding by a circular cylinder. AIAA Journal, 1979, 17(11): 1193–1200

[67] Larsen A, Walther J H. Aeroelastic analysis of bridge girder sections based on discrete vortex simulations. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 67-68: 253–265

[68] Walther J H, Larsen A. Two dimensional discrete vortex method for application to bluff body aerodynamics. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 67-68: 183–193

[69] Larsen A, Walther J H. Discrete vortex simulation of flow around five generic bridge deck sections. Journal of Wind Engineering and Industrial Aerodynamics, 1998, 77-78: 591–602

[70] Frandsen J B. Computational fluid-structure interaction applied to long-span bridge design. Dissertation for the Doctoral Degree. Cambridge: University of Cambridge, 1999

[71] Morgenthal G. Comparison of numeridal methods for bridge-deck aerodynamics. Master Thesis<DissertationTip/>, Cambridge: University of Cambridge, 2000

[72] Raveh D E. Reduced-order models for nonlinear unsteady aerodynamics. AIAA Journal, 2001, 39(8): 1417–1429

[73] Lucia D J, Beran P S, Silva W A. Reduced-order modeling: new approaches for computational physics. Progress in Aerospace Sciences, 2004, 40(1-2): 51–117

[74] Wu T, Kareem A. Volterra series based nonlinear oscillator for vortex-induced vibration modeling. In: Proceedings of 2012 Joint Conference of the Engineering Mechanics Institute and the 11th ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability. June, University of Notre Dame, IN, USA, 2012

[75] Rugh W J. Nonlinear System Theory, Baltimore: the John Hopkins University Press, 1981

[76] Wu T, Kareem A. Nonlinear aerodynamic and aeroelastic analysis framework for cable-supported bridges. In: Proceedings of the 3rd American Association for Wind Engineering Workshop. August, Hyannis, Massachusetts, USA, 2012

Acknowledgement

This work was supported by the NSF Grant No. CMMI 09-28282.

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg