Abstract
In this paper, we propose a model for the transverse oscillation of a square-section cylinder under flow. The fluctuating transverse force due to vortex shedding is represented using a coupled nonlinear wake oscillator, while the unsteady force for galloping caused by the varying incidence angle effects is modelled using the quasi-steady approach. First, we analytically investigate the lift behavior and phase angle variation of the square cylinder under forced vibrations. Comparison with experimental data is used to determine the form of the coupling terms and its values. The present model shows advantages in predicting the phase angle, and it successfully captures the change in sign of the phase. Second, the proposed model is directly applied in predicting free oscillation cases without any tuning. The dynamical behaviors predicted by this model are compared with published experiments under different Scruton numbers, and reasonable agreement can be found. The results indicate that the model can not only be applied in simulating the “pure galloping” and “pure VIV,” but also is able to capture the interactions of VIV and galloping, including combined and separate VIV-galloping motions.
Similar content being viewed by others
References
Blevins, R.D.: Flow-Induced Vibration. Krieger Publishing Company, Florida (1977)
Parkinson, G.V.: Phenomena and modelling of flow-induced vibrations of bluff bodies. Prog. Aerosp. Sci. 26(2), 169–224 (1989)
Bearman, P.W.: Vortex shedding from oscillating bluff bodies. Ann. Rev. Fluid Mech. 16(1), 195–222 (1984)
Williamson, C.H.K., Govardhan, R.: Vortex-induced vibrations. Ann. Rev. Fluid Mech. 36(1), 413–455 (2004)
Sarpkaya, T.: A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19(4), 389–447 (2004)
Lucor, D., Foo, J., Karniadakis, G.E.: Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping. J. Fluids Struct. 20(4), 483–503 (2005)
Hartlen, R.T., Currie, I.G.: Lift-oscillator model of vortex-induced vibration. J. Eng. Mech. Div. EM5, 577–591 (1970)
Skop, R.A., Balasubramanian, S.: A new twist on an old model for vortex-excited vibrations. J. Fluids Struct. 11(4), 395–412 (1997)
Abdelkefi, A., Hajj, M.R., Nayfeh, A.H.: Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders. Nonlinear Dyn. 70(2), 1377–1388 (2012)
Facchinetti, M.L., de Langre, E., Biolley, F.: Coupling of structure and wake oscillators in vortex-induced vibrations. J. Fluids Struct. 19(2), 123–140 (2004)
Facchinetti, M.L., de Langre, E., Biolley, F.: Vortex-induced travelling waves along a cable. Eur. J. Mech. B/Fluids 23(1), 199–208 (2004)
Violette, R., de Langre, E., Szydlowski, J.: Computation of vortex-induced vibrations of long structures using a wake oscillator model: comparison with dns and experiments. Comput. Struct. 85(11–14), 1134–1141 (2007)
Grouthier, C., Michelin, S., Bourguet, R., Modarres-Sadeghi, Y., de Langre, E.: On the efficiency of energy harvesting using vortex-induced vibrations of cables. J. Fluids Struct. 49, 427–440 (2014)
Zanganeh, H., Srinil, N.: Three-dimensional VIV prediction model for a long flexible cylinder with axial dynamics and mean drag magnifications. J. Fluids Struct. 66, 127–146 (2016)
Gabbai, R.D., Benaroya, H.: An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J. Sound Vib. 282(3–5), 575–616 (2005)
Tamura, Y., Matsui, G.: Wake-oscillator model of vortex-induced oscillation of circular cylinder. In: Proceedings of the 5th international conference on wind engineering, pp. 1085–1094, Bowness-on-Windermere, (1980)
Benaroya, H., Gabbai, R.D.: Modelling vortex-induced fluid-structure interaction. Philos. Trans. A Math. Phys. Eng. Sci. 366(1868), 1231–74 (2008)
Meliga, P., Chomaz, J.-M.: An asymptotic expansion for the vortex-induced vibrations of a circular cylinder. J. Fluid Mech. 671, 137–167 (2011)
Parkinson, G.V., Smith, J.D.: The square prism as an aeroelastic non-linear oscillator. Q. J. Mech. Appl. Math. 17(2), 225–239 (1964)
Joly, A., Etienne, S., Pelletier, D.: Galloping of square cylinders in cross-flow at low reynolds numbers. J. Fluids Struct. 28, 232–243 (2012)
Norberg, C.: Flow around rectangular cylinders: pressure forces and wake frequencies. J. Wind Eng. Ind. Aerodyn. 49(1), 187–196 (1993)
Wawzonek, M. A.: Aeroelastic behavior of square section prisms in uniform flow. PhD thesis, University of British Columbia (1979)
Abdelkefi, A., Hajj, M.R., Nayfeh, A.H.: Power harvesting from transverse galloping of square cylinder. Nonlinear Dyn. 70(2), 1355–1363 (2012)
Andrianne, T., Aryoputro, R.P., Laurent, P., Colson, G., Amandolèse, X., Hémon, P.: Energy harvesting from different aeroelastic instabilities of a square cylinder. J. Wind Eng. Ind. Aerodyn. 172, 164–169 (2018)
Bouclin, D. N.: Hydroelastic oscillations of square cylinders. PhD thesis, University of British Columbia (1979)
Corless, R.M., Parkinson, G.V.: A model of the combined effects of vortex-induced oscillation and galloping. J. Fluids Struct. 2(3), 203–220 (1988)
Tamura, Y., Shimada, K.: A mathematical model for the transverse oscillations of square cylinders. In: Proceedings of the 1st international conference on flow induced vibrations, pp. 267–276, Bowness-on-Windermere (1987)
Mannini, C., Massai, T., Marra, A.M., Bartoli, G.: Modelling the interaction of VIV and galloping for rectangular cylinders. In: The 14th international conference on wind engineering, pp. 1–20, Porto Alegre (2015)
Liu, Y.Z., Ma, C.M., Li, Q.S., Yan, B.W., Liao, H.L.: A new modeling approach for transversely oscillating square-section cylinders. J. Fluids Struct. 81, 492–513 (2018)
Nayfeh, A.H.: Introduction to Perturbation Techniques. John Wiley & Sons, New Jersey (2011)
de Langre, E.: Frequency lock-in is caused by coupled-mode flutter. J. Fluids Struct. 22(6–7), 783–791 (2006)
Li, X., Lyu, Z., Kou, J., Zhang, W.: Mode competition in galloping of a square cylinder at low reynolds number. J. Fluid Mech. 867, 516–555 (2019)
Bishop, R.E.D., Hassan, A.Y.: The lift and drag forces on a circular cylinder in a flowing fluid. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 277(1368), 32–50 (1964)
Luo, S.C., Bearman, P.W.: Predictions of fluctuating lift on a transversely oscillating square-section cylinder. J. Fluids Struct. 4(2), 219–228 (1990)
Carassale, A., Freda, L., Banfi, L.: Motion excited forces acting on a square prism: a qualitative analysis. In: The 14th international conference on wind engineering, Porto Alegre (2015)
Freda, A., Carassale, L., Piccardo, G.: Aeroelastic crosswind response of sharp-edge square sections: experiments versus theory. In: The 14th international conference on wind engineering, 01 (2015)
Carassale, L., Freda, A., Marrè-Brunenghi, M.: Experimental investigation on the aerodynamic behavior of square cylinders with rounded corners. J. Fluids Struct. 44, 195–204 (2014)
Bearman, P.W., Gartshore, I.S., Maull, D.J., Parkinson, G.V.: Experiments on flow-induced vibration of a square-section cylinder. J. Fluids Struct. 1(1), 19–34 (1987)
Cheng, L., Zhou, Y., Zhang, M.M.: Perturbed interaction between vortex shedding and induced vibration. J. Fluids Struct. 17(7), 887–901 (2003)
Amandolèse, X., Hémon, P.: Vortex-induced vibration of a square cylinder in wind tunnel. Comptes Rendus Méc. 338(1), 12–17 (2010)
Nakamura, Y., Mizota, T.: Unsteady lifts and wakes of oscillating rectangular prisms. J. Eng. Mech. Div. 101, 855–871 (1975)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Han, P., Hémon, P., Pan, G. et al. Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow. Nonlinear Dyn 103, 3113–3125 (2021). https://doi.org/10.1007/s11071-020-06078-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-020-06078-4