Abstract
Vortex induced vibrations (VIV) is a widely explored fluid-structure interaction problem with immense applications ranging from heat exchanger tube arrays, power transmission lines to offshore structures. VIV of circular cylinders stands as one of the classical problems in this area, wherein the cylinder undergoes high amplitude vibrations due to the ‘lock-in’ phenomenon. The dynamics of the structure and flow field are well studied in the literature for a varied range of flow and structural parameters. However, real-life situations can be characterized by the presence of ‘noise’, which are fluctuations or uncertainties associated with the incoming flow or geometrical parameters of the system. The dynamical characteristics of the VIV system in the presence of such stochastic fluctuations are a relatively lesser-explored domain of research and not much documentation on this subject is available. In this chapter, we aim to present a comprehensive review of stochastic dynamics of VIV systems, especially we will highlight the presence of novel dynamical states and its implication on the coupled system behaviour that have been reported recently by us. It is known from experimental studies that free-stream noise can increase the response amplitudes of the structure and thus acts as a source of negative aerodynamic damping. Analytical works which model turbulence in experiments as stochastic processes use asymptotic expressions of Lyapunov exponents to determine the stability boundaries of VIV systems. Studies based on mathematical models investigating stochastic dynamics have modelled noise as additive and parametric, in the equations governing the VIV system. The current chapter mainly reviews the literature on stochastic VIV studies based on mathematical models that include wake oscillator models, single degree of freedom and force decomposition models, from a nonlinear dynamics perspective. Brief reviews on previous numerical studies using uncertainty quantification techniques in high fidelity solvers and key experimental results emphasizing the role of free-stream noise are also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anagnostopoulos P, Bearman PW (1992) Response characteristics of a vortex-excited cylinder at low reynolds numbers. J Fluids Struct 6(1):39–50
Arecchi FT, Badii R, Politi A (1985) Generalized multistability and noise-induced jumps in a nonlinear dynamical system. Phys Rev A 32(1):402
Ariaratnam ST (1996) Stochastic stability of viscoelastic systems under bounded noise excitation. In: IUTAM symposium on advances in nonlinear stochastic mechanics. Springer, Berlin, pp 11–18
Aswathy MS, Sarkar S (2018) Manifestation of additional frequencies in vortex induced vibrations in the presence of noise. In: MATEC web of conferences, vol 148. EDP Sciences, p 08003
Aswathy MS, Sarkar S (2019) Effect of stochastic parametric noise on vortex induced vibrations. Int J Mech Sci 153:103–118
Bishop RED, Hassan AY (1964) The lift and drag forces on a circular cylinder oscillating in a flowing fluid. In: Proceedings of the royal society of london a: mathematical, physical and engineering sciences, vol 277. The Royal Society, pp 51–75
Blackburn H, Henderson R (1996) Lock-in behavior in simulated vortex-induced vibration. Exp Therm Fluid Sci 12(2):184–189
Borazjani I, Sotiropoulos F (2009) Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region. J Fluid Mech 621:321–364
Brand HR, Kai S, Wakabayashi S (1985) External noise can suppress the onset of spatial turbulence. Phys Rev Lett 54(6):555–557
Crauel H, Flandoli F (1998) Additive noise destroys a pitchfork bifurcation. J Dyn Differ Equ 10(2):259–274
Crauel H, Gundlach M (1999) Stochastic dynamics. Springer Science & Business Media
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
Feng CC (1968) The measurement of vortex induced effects in flow past stationary and oscillating circular and d-section cylinders. PhD thesis, University of British Columbia
Gabbai RD, Benaroya H (2005) An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J Sound Vib 282(3–5):575–616
Geraci G, de Tullio MD, Iaccarino G (2015) Stochastic analysis of vortex-induced vibrations of two oscillating cylinders in the proximity-wake interference region. In: Annual research briefs, Stanford, CA: Stanford University, Center for Turbulence Research. pp 197–210
Goswami I, Scanlan RH, Jones NP (1993) Vortex-induced vibration of circular cylinders. ii: new model. J Eng Mech 119(11):2288–2302
Griffin OM, RSkop RA, Koopmann GH (1973) The vortex-excited resonant vibrations of circular cylinders. J Sound Vib 31(2):235–IN3
Griffin OM, Koopmann GH (1977) The vortex-excited lift and reaction forces on resonantly vibrating cylinders. J Sound Vib 54(3):435–448
Hartlen RT, Currie IG (1970) Lift-oscillator model of vortex-induced vibration. J Eng Mech Div 96(5):577–591
Horsthemke W, Lefever R (1984) Noise-induced transitions: theory and application in physics, chemistry, and biology, vol 15. Springer, Berlin
Iwan WD, Blevins RD (1974) A model for vortex induced oscillation of structures. J Appl Mech 41(3):581–586
Khalak A, Williamson CHK (1996) Dynamics of a hydroelastic cylinder with very low mass and damping. J Fluids Struct 10(5):455–472
Khalak A, Williamson CHK (1999) Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. J Fluids Struct 13(7–8):813–851
Krenk S, Nielsen SRK (1999) Energy balanced double oscillator model for vortex-induced vibrations. J Eng Mech 125(3):263–271
Leontini JS, Thompson MC, Hourigan K (2006) The beginning of branching behaviour of vortex-induced vibration during two-dimensional flow. J Fluids Struct 22(6–7):857–864
Ng L, Rand RH, Wei T, Keith WL (2001) An examination of wake oscillator models for vortex-induced vibrations. Technical report, Naval Undersea Warfare Center Newport Div ri
Nielsen SRK, Krenk S (1997) Stochastic response of energy balanced model for vortex-induced vibration. Aalborg University, Denmark, Technical report, Dept. of Building Technology and Structural Engineering
Poirel DCM, Price SJ (2001) Structurally nonlinear fluttering airfoil in turbulent flow. AIAA J 39(10):1960–1968
Poirel DCM, Price SJ (2007) Bifurcation characteristics of a two-dimensional structurally non-linear airfoil in turbulent flow. Nonlinear Dyn 48(4):423–435
Prasanth TK, Mittal S (2008) Vortex-induced vibrations of a circular cylinder at low reynolds numbers. J Fluid Mech 594:463–491
Sarpkaya T (2003) A critical review of the intrinsic nature of viv. In: IUTAM symposium on integrated modeling of fully coupled fluid structure interactions using analysis, computations and experiments. Springer, Berlin, pp 159–161
Sarpkaya T (1978) Fluid forces on oscillating cylinders. Nasa Sti/Recon Tech Rep A 78:275–290
Skop RA, Griffin OM (1973) A model for the vortex-excited resonant response of bluff cylinders. J Sound Vib 27(2):225–233
So RM, Wang XQ, Xie W-C, Zhu J (2008) Free-stream turbulence effects on vortex-induced vibration and flow-induced force of an elastic cylinder. J Fluids Struct 24(4):481–495
Sri Namachchivaya N, Vedula L (2000) Stabilization of linear systems by noise: application to flow induced oscillations. Dyn Stab Syst 15(2):185–208
Srinil N, Zanganeh H (2012) Modelling of coupled cross-flow/in-line vortex-induced vibrations using double duffing and van der pol oscillators. Ocean Eng 53:83–97
Venkatramani J, Nair V, Sujith RI, Gupta S, Sarkar S (2016) Precursors to flutter instability by an intermittency route: a model free approach. J Fluids Struct 61:376–391
Vickery BJ, Basu RI (1983) Across-wind vibrations of structures of circular cross-section. part i. development of a mathematical model for two-dimensional conditions. J Wind Eng Ind Aerodyn 12(1):49–73
Wang XQ, So RMC, Chan KT (2003) A non-linear fluid force model for vortex-induced vibration of an elastic cylinder. J Sound Vib 260(2):287–305
Xu Y, Gu R, Zhang H, Xu W, Duan J (2011) Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise. Phys Rev E 83(5):056215
Zakharova A, Vadivasova T, Anishchenko V, Koseska A, Kurths J (2010) Stochastic bifurcations and coherence like resonance in a self-sustained bistable noisy oscillator. Phys Rev E 81(1):011106
Zhao D, Zhang Q, Tan Y (2009) Random flutter of a 2-dof nonlinear airfoil in pitch and plunge with freeplay in pitch. Nonlinear Dyn 58(4):643–654
Zhou CY, So RMC, Lam K (1999) Vortex-induced vibrations of an elastic circular cylinder. J Fluids Struct 13(2):165–189
Zhu J, Wang XQ, Xie WC, So RMC (2008) Flow-induced instability under bounded noise excitation in cross-flow. J Sound Vib 312(3):476–495
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Aswathy, M.S., Sarkar, S. (2020). Nonlinear Dynamics of Circular Cylinders Undergoing Vortex Induced Vibrations in Presence of Stochastic Noise. In: Mukhopadhyay, A., Sen, S., Basu, D., Mondal, S. (eds) Dynamics and Control of Energy Systems. Energy, Environment, and Sustainability. Springer, Singapore. https://doi.org/10.1007/978-981-15-0536-2_9
Download citation
DOI: https://doi.org/10.1007/978-981-15-0536-2_9
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0535-5
Online ISBN: 978-981-15-0536-2
eBook Packages: EnergyEnergy (R0)