Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber

Abstract The nonlinear interaction of a laminar flow and a sprung rigid circular cylinder results in vortex-induced vibration (VIV) of the cylinder. Passive suppression of the VIV by attaching an internal nonlinear vibration absorber that acts, in essence, as a nonlinear energy sink (NES) to the cylinder has been observed in finite-element computations involving thousands of degrees of freedom (DOF). A single-DOF self-excited oscillator is developed to approximate the limit-cycle oscillation (LCO) of the cylinder undergoing VIV. This self-excited oscillator models the interaction of the flow and the cylinder. Then, a two-DOF reduced-order model for the system with the internal NES is constructed by coupling the single-DOF NES to the single-DOF self-excited oscillator. Hence, the complicated high-dimensional system of flow-cylinder-NES involving thousands of DOF is reduced to a two-DOF model. The two targeted energy transfer mechanisms responsible for passive VIV suppression that are observed in the finite-element computations are fully reproduced using the two-DOF reduced-order model. This reduction of the dynamics to an easily tractable low-dimensional reduced-order model facilitates the approximate analysis of the underlying dynamics. Moreover, the underlying assumptions of the order reduction, and the parameter ranges of validity of the reduced-order model are formulated and systematically studied.

[1]  Alexander F. Vakakis,et al.  Computational study of vortex-induced vibration of a sprung rigid circular cylinder with a strongly nonlinear internal attachment , 2013 .

[2]  Arif Masud,et al.  A multiscale stabilized ALE formulation for incompressible flows with moving boundaries , 2010 .

[3]  Peter W. Bearman,et al.  Suppression of wake-induced vibration of tandem cylinders with free-to-rotate control plates , 2010 .

[4]  Oleg Gendelman,et al.  Bifurcations of self-excitation regimes in a Van der Pol oscillator with a nonlinear energy sink , 2010 .

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

[6]  Arif Masud,et al.  Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows , 2006 .

[7]  Arif Masud,et al.  A variational multiscale stabilized formulation for the incompressible Navier–Stokes equations , 2009 .

[8]  Carl M. Larsen,et al.  Direct Numerical Simulation and Experimental Investigation on Suppression of Vortex Induced Vibrations of Circular Cylinders by Radial Water Jets , 2003 .

[9]  O. M. Griffin,et al.  A model for the vortex-excited resonant response of bluff cylinders , 1973 .

[10]  Peter W. Bearman,et al.  Passive control of VIV with drag reduction , 2001 .

[11]  Kamaldev Raghavan,et al.  Reduction/Suppression of VIV of Circular Cylinders Through Roughness Distribution at 8×103 < Re < 1.5×105 , 2008 .

[12]  Oleg Gendelman,et al.  Targeted energy transfer in systems with external and self-excitation , 2011 .

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

[14]  Shijun Liao,et al.  Commun Nonlinear Sci Numer Simulat , 2013 .

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

[16]  G. Kerschen,et al.  Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems , 2008 .

[17]  C. Williamson,et al.  Vortex-Induced Vibrations , 2004, Wind Effects on Structures.

[18]  Alexander F. Vakakis,et al.  Asymptotic Analysis of Passive Nonlinear Suppression of Aeroelastic Instabilities of a Rigid Wing in Subsonic Flow , 2010, SIAM J. Appl. Math..

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

[20]  G. Triantafyllou,et al.  Elimination of vortex streets in bluff-body flows. , 2008, Physical review letters.

[21]  Haym Benaroya,et al.  An overview of modeling and experiments of vortex-induced vibration of circular cylinders , 2005 .

[22]  E. de Langre,et al.  Coupling of Structure and Wake Oscillators in Vortex-Induced Vibrations , 2004 .

[23]  Christopher W. Olenek.  Study of reduced order models for vortex-induced vibration and comparison with CFD results , 2011 .