We study cross-flow vortex-induced vibration (VIV) of a linearly sprung circular cylinder equipped with a dissipative oscillator with cubic stiffness nonlinearity, restrained to move in the direction of travel of the cylinder. The dissipative, essentially nonlinear coupling between the cylinder and the oscillator allows for targeted energy transfer (TET) from the former to the latter, whereby the oscillator acts as a nonlinear energy sink (NES) capable of passively suppressing cylinder oscillations. For fixed values of the Reynolds number (Re = 48, slightly above the fixed-cylinder Hopf bifurcation), cylinder-to-fluid density ratio, and dimensionless cylinder spring constant, spectral-element simulations of the Navier–Stokes equations coupled to the rigid-body motion show that different combinations of NES parameters lead to different long-time attractors of the dynamics. We identify four such attractors which do not coexist at any given point in the parameter space, three of which lead to at least partial VIV suppression. We construct a reduced-order model (ROM) of the fluid–structure interaction (FSI) based on a wake oscillator to analytically study those four mechanisms seen in the high-fidelity simulations and determine their respective regions of existence in the parameter space. Asymptotic analysis of the ROM relies on complexification-averaging (CX-A) and slow–fast partition of the transient dynamics and predicts the existence of complete and partial VIV-suppression mechanisms, relaxation cycles, and Hopf and Shilnikov bifurcations. These outcomes are confirmed by numerical integration of the ROM and comparisons with spectral-element simulations of the full system.
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August 2017
Research-Article
Passive Suppression Mechanisms in Laminar Vortex-Induced Vibration of a Sprung Cylinder With a Strongly Nonlinear, Dissipative Oscillator
Antoine Blanchard,
Antoine Blanchard
Department of Aerospace Engineering,
University of Illinois,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
University of Illinois,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
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Lawrence A. Bergman,
Lawrence A. Bergman
Department of Aerospace Engineering,
University of Illinois,
Urbana, IL 61801
University of Illinois,
Urbana, IL 61801
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Alexander F. Vakakis
Alexander F. Vakakis
Department of Mechanical Science
and Engineering,
University of Illinois,
Urbana, IL 61801
and Engineering,
University of Illinois,
Urbana, IL 61801
Search for other works by this author on:
Antoine Blanchard
Department of Aerospace Engineering,
University of Illinois,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
University of Illinois,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
Lawrence A. Bergman
Department of Aerospace Engineering,
University of Illinois,
Urbana, IL 61801
University of Illinois,
Urbana, IL 61801
Alexander F. Vakakis
Department of Mechanical Science
and Engineering,
University of Illinois,
Urbana, IL 61801
and Engineering,
University of Illinois,
Urbana, IL 61801
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 1, 2017; final manuscript received May 30, 2017; published online June 14, 2017. Assoc. Editor: Walter Lacarbonara.
J. Appl. Mech. Aug 2017, 84(8): 081003 (19 pages)
Published Online: June 14, 2017
Article history
Received:
March 1, 2017
Revised:
May 30, 2017
Citation
Blanchard, A., Bergman, L. A., and Vakakis, A. F. (June 14, 2017). "Passive Suppression Mechanisms in Laminar Vortex-Induced Vibration of a Sprung Cylinder With a Strongly Nonlinear, Dissipative Oscillator." ASME. J. Appl. Mech. August 2017; 84(8): 081003. https://doi.org/10.1115/1.4036942
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