Resonance capture in vortex-induced vibration of a cylinder with a rotator

Abstract eng:
At the intermediate Reynolds number Re = 100, a two-dimensional, linearly-sprung, circular cylinder restricted to move in the cross-flow direction and incorporating a rotational nonlinear energy sink (NES; consisting of a mass freely rotating about the cylinder axis and whose angular motion is restrained by a linear viscous damper) can undergo repetitive cycles of slowly decaying oscillations — which can lead to significant vortex street elongation with partial stabilization of the wake — interrupted by chaotic bursts. We construct a reduced-order model of the fluid-structure interaction dynamics and employ analytical techniques to show that the strongly modulated response is the manifestation of a resonance capture into a slow invariant manifold (SIM) that leads to targeted energy transfer from the cylinder to the rotator. Capture into the SIM corresponds to transient cylinder stabilization, and escape from the SIM to chaotic bursts.

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