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

Ravi Kumar R. Tumkur, Elad Domany, Oleg V. Gendelman, Arif Masud, Lawrence A. Bergman, Alexander F. Vakakis

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1916-1930
Number of pages15
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number7
StatePublished - Jul 2013


  • Nonlinear energy sink
  • Reduced-order model
  • Targeted energy transfer
  • Vortex-induced vibration

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


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