Coupling of Structure and Wake Oscillators in Vortex-Induced Vibrations

Abstract A class of low-order models for vortex-induced vibrations is analyzed. A classical van der Pol equation models the near wake dynamics describing the fluctuating nature of vortex shedding. This wake oscillator interacts with the equation of motion of a one degree-of-freedom structural oscillator and several types of linear coupling terms modelling the fluid–structure interaction are considered. The model dynamics is investigated analytically and discussed with regard to the choice of the coupling terms and the values of model parameters. Closed-form relations of the model response are derived and compared to experimental results on forced and free vortex-induced vibrations. This allows us to set the values of all model parameters, then leads to the choice of the most appropriate coupling model. A linear inertia force acting on the fluid is thus found to describe most of the features of vortex-induced vibration phenomenology, such as Griffin plots and lock-in domains.

[1]  R. Henderson,et al.  A study of two-dimensional flow past an oscillating cylinder , 1999, Journal of Fluid Mechanics.

[2]  E. D. Langre,et al.  Experiments on vortex-induced traveling waves along a cable , 2022 .

[3]  P. Bearman VORTEX SHEDDING FROM OSCILLATING BLUFF BODIES , 1984 .

[4]  R. King Vortex Excited Oscillations of Yawed Circular Cylinders , 1977 .

[5]  D. Olinger A low-order model for vortex shedding patterns behind vibrating flexible cables , 1998 .

[6]  R. Blevins,et al.  Flow-Induced Vibration , 1977 .

[7]  G. Koopmann,et al.  The vortex-excited resonant vibrations of circular cylinders , 1973 .

[8]  I. G. Currie,et al.  Lift-Oscillator Model of Vortex-Induced Vibration , 1970 .

[9]  Pierre Albarede,et al.  Quasi-periodic cylinder wakes and the Ginzburg–Landau model , 1995, Journal of Fluid Mechanics.

[10]  Fred L. Haan,et al.  VORTEX-EXCITED VIBRATIONS OF UNIFORM PIVOTED CYLINDERS IN UNIFORM AND SHEAR FLOW , 2000 .

[12]  N. C. Perkins,et al.  TWO-DIMENSIONAL VORTEX-INDUCED VIBRATION OF CABLE SUSPENSIONS , 2002 .

[13]  R. Landl,et al.  A mathematical model for vortex-excited vibrations of bluff bodies , 1975 .

[14]  R. A. Skop,et al.  An inverse-direct method for predicting the vortex-induced vibrations of cylinders in uniform and nonuniform flows , 2001 .

[15]  Bernd R. Noack,et al.  On cell formation in vortex streets , 1991 .

[16]  C. Williamson,et al.  Modes of vortex formation and frequency response of a freely vibrating cylinder , 2000, Journal of Fluid Mechanics.

[17]  G. V. Parkinson,et al.  Phenomena and modelling of flow-induced vibrations of bluff bodies , 1989 .

[18]  P. Plaschko GLOBAL CHAOS IN FLOW-INDUCED OSCILLATIONS OF CYLINDERS , 2000 .

[19]  Xiao-Yun Lu,et al.  Calculation of the Timing of Vortex Formation from AN Oscillating Cylinder , 1996 .

[20]  D. Rockwell,et al.  FORCES AND WAKE MODES OF AN OSCILLATING CYLINDER , 2001 .

[21]  E. de Langre,et al.  Vortex shedding modeling using diffusive van der Pol oscillators , 2002 .

[22]  R. Bishop,et al.  The lift and drag forces on a circular cylinder oscillating in a flowing fluid , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  George Em Karniadakis,et al.  Vortex dislocations and force distribution of long flexible cylinders subjected to sheared flows , 2001 .

[24]  L. Redekopp,et al.  A model for pattern selection in wake flows , 1992 .

[25]  A. Nayfeh Introduction To Perturbation Techniques , 1981 .

[26]  Stephane Etienne,et al.  VIV of two cylinders in tandem arrangement: analytical and numerical modeling. , 2002 .

[27]  G. Pedrizzetti,et al.  Vortex Dynamics , 2011 .

[28]  Anthony Leonard,et al.  Flow-induced vibration of a circular cylinder at limiting structural parameters , 2001 .

[29]  Søren Nielsen,et al.  Energy Balanced Double Oscillator Model for Vortex-Induced Vibrations , 1999 .

[30]  Charles H. K. Williamson,et al.  Phase dynamics of Kármán vortices in cylinder wakes , 1996 .

[31]  R. Skop,et al.  A new twist on an old model for vortex-excited vibrations , 1997 .

[32]  Peter Stansby,et al.  The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows , 1976, Journal of Fluid Mechanics.

[33]  Anthony Leonard,et al.  ASPECTS OF FLOW-INDUCED VIBRATION , 2001 .

[34]  O. M. Griffin,et al.  Vortex-Excited Cross-Flow Vibrations of a Single Cylindrical Tube , 1980 .

[35]  C. M. Larsen,et al.  Added Mass and Oscillation Frequency for a Circular Cylinder Subjected to Vortex-Induced Vibrations and External Disturbance , 2000 .

[36]  R. A. Skop,et al.  A NONLINEAR OSCILLATOR MODEL FOR VORTEX SHEDDING FROM CYLINDERS AND CONES IN UNIFORM AND SHEAR FLOWS , 1996 .

[37]  M. K. Au-Yang Vortex-Induced Vibration , 2001 .

[38]  C. Williamson,et al.  MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW MASS-DAMPING , 1999 .