Random vortex induced vibration response of suspended flexible cable to fluctuating wind

doi:10.1007/s10483-023-3058-8

Abstract

Abstract: A popular dynamical model for the vortex induced vibration (VIV) of a suspended flexible cable consists of two coupled equations. The first equation is a partial differential equation governing the cable vibration. The second equation is a wake oscillator that models the lift coefficient acting on the cable. The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity, which makes the VIV model be a deterministic one. In the real world, however, the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration. In the present paper, the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind. Using the normal mode approach, the random VIV system is transformed into an infinite-dimensional modal vibration system. Depending on whether a modal frequency is close to the aeolian frequency or not, the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration. By applying the stochastic averaging method of quasi Hamiltonian systems, the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted. Then, the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations. Some numerical simulation results confirm the obtained analytical results. It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration. Thus, the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

Key words: vortex induced vibration (VIV), wake oscillator, random response, suspended flexible cable, fluctuating wind

2010 MSC Number:

Genjin MU, Weiqiu ZHU, Maolin DENG. Random vortex induced vibration response of suspended flexible cable to fluctuating wind. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2207-2226.

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References

[1] FACCHINETTI, M. L., DE LANGRE, E., and BIOLLEY, F. Coupling of structure and wakeoscillators in vortex-induced vibrations. Journal of Fluids and Structures, 19, 123–140(2004)
[2] DOAN, V. P. and NISHI, Y. Modeling of fluid-structure interaction for simulating vortex-induced vibration of flexible riser: finite difference method combined with wake oscillator model. Journal of Marine Science and Technology, 20, 309–321(2015)
[3] GU, J. J., AN, C., and LEVI, C. Prediction of vortex-induced vibration of long flexible cylinders modeled by a coupled nonlinear oscillator: integral transform solution. Journal of Hydrodynamics, 24, 888–898(2012)
[4] VIOLETTE, R., DE LANGRE, E., and SZYDLOWSKI, J. Computation of vortex-induced vibrations of long structures using a wake oscillator model: comparison with DNS and experiments. Computers and Structures, 85, 1134–1141(2007)
[5] FENG, Y. L., CHEN, D. Y., LI, S. W., XIAO, Q., and LI, W. Vortex-induced vibrations of flexible cylinders predicted by wake oscillator model with random components of mean drag coefficient and lift coefficient. Ocean Engineering, 251, 110960(2022)
[6] HARTLEN, R. T. and CURRIE, I. G. Lift-oscillator model of vortex-induced vibration. Journal of Engineering Mechanics Division, 96, 577–591(1970)
[7] GABBAI, R. D. and BENAROYA, H. An overview of modeling and experiments of vortex-induced vibration of circular cylinders. Journal of Sound and Vibration, 282, 575–616(2005)
[8] KIM, W. J. and PERKINS, N. C. Two-dimensional vortex-induced vibration of cable suspensions. Journal of Fluids and Structures, 16, 229–245(2002)
[9] XU, W. H., ZENG, X. H., and WU, Y. X. High aspect ratio (L/D) riser VIV prediction using wake oscillator model. Ocean Engineering, 35, 1769–1774(2008)
[10] SRINIL, N., WIERCIGROCH, M., and O’BRIEN, P. Reduced-order modelling of vortex-induced vibration of catenary riser. Ocean Engineering, 36, 1404–1414(2009)
[11] OLINGER, D. J. A low-order model for vortex shedding patterns behind vibrating flexible cables. Physics of Fluids, 10, 1953–1961(1998)
[12] BALASUBRAMANIAN, S. and SKOP, R. A. A nonlinear oscillator model for vortex shedding from cylinders and cones in uniform and shear flows. Journal of Fluids and Structures, 10, 197–214(1996)
[13] FORTALEZA, E., CREFF, Y., and LÉVINE, J. Active control of vertical risers undergoing vortex-induced vibrations. ASME 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal (2008)
[14] SKOP, R. A. and GRIFFIN, O. M. On a theory for the vortex-excited oscillations of flexible cylindrical structures. Journal of Sound and Vibration, 41, 263–274(1975)
[15] SKOP, R. A. and BALASUBRAMANIAN, S. A new twist on an old model for vortex-excited vibrations. Journal of Fluids and Structures, 11, 395–412(1997)
[16] WANG, D., CHEN, Y. S., WIERCIGROCH, M., and CAO, Q. J. Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices. Applied Mathematics and Mechanics (English Edition), 37(9), 1251–1274(2016) https://doi.org/10.1007/s10483-016-2128-6
[17] NAUDASCHER, E. and ROCKWELL, D. Flow-Induced Vibrations: An Engineering Guide, Dover Publications, Inc., New York (2005)
[18] SIMIU, E. and SCANLAN, R. H. Wind Effects on Structures: An Introduction to Wind Engineering, John Wiley & Sons, New York (1978)
[19] DENG, M. L., MU, G. J., and ZHU, W. Q. Random response of wake-oscillator excited by fluctuating wind. Journal of Applied Mechanics, 88, 101002(2021)
[20] XU, Z. and CHUNG, Y. K. Averaging method using generalized harmonic functions for strongly non-linear oscillators. Journal of Sound and Vibration, 174, 563–576(1994)
[21] ZHU, W. Q. Nonlinear stochastic dynamics and control in Hamiltonian formulation. ASME Applied Mechanics Reviews, 59, 230–248(2006)
[22] ZHU, W. Q., HUANG, Z. L., and SUZUKI, Y. Response and stability of strongly non-linear oscillators under wide-band random excitation. International Journal of Non-Linear Mechanics, 36, 1235–1250(2001)
[23] DENG, M. L. and ZHU, W. Q. Stochastic averaging of MDOF quasi integrable Hamiltonian systems under wide-band random excitation. Journal of Sound and Vibration, 305, 783–794(2007)
[24] IRVINE, H. M. Cable Structures, MIT Press, Cambridge, Massachusetts (1981)
[25] SIMIU, E. and SCANLAN, R. H. Wind Effects on Structures: Fundamental and Application to Design, 3rd ed., John Wiley & Sons, Inc., New Jersey (1996)
[26] SHIOTANI, M. and IWATANI, Y. Correlations of wind velocities in relation to the gust loadings. Proceedings of the Third International Conference on Wind Effects on Buildings and Structures, Saikon Publishing Co., Ltd., Tokyo (1971)
[27] CAI, G. Q. and ZHU, W. Q. Elements of Stochastic Dynamics, World Scientific, New Jersey (2016)
[28] KHASMINSKII, R. Z. On the averaging principle for Itô stochastic differential equations (in Russian). Kibernetika, 3, 260–279(1968)