We computationally investigate coupling of a nonlinear rotational dissipative element to a sprung circular cylinder allowed to undergo transverse vortex-induced vibration (VIV) in an incompressible flow. The dissipative element is a ‘nonlinear energy sink’ (NES), consisting of a mass rotating at fixed radius about the cylinder axis and a linear viscous damper that dissipates energy from the motion of the rotating mass. We consider the Reynolds number range $20\leqslant Re\leqslant 120$, with $Re$ based on cylinder diameter and free-stream velocity, and the cylinder restricted to rectilinear motion transverse to the mean flow. Interaction of this NES with the flow is mediated by the cylinder, whose rectilinear motion is mechanically linked to rotational motion of the NES mass through nonlinear inertial coupling. The rotational NES provides significant ‘passive’ suppression of VIV. Beyond suppression however, the rotational NES gives rise to a range of qualitatively new behaviours not found in transverse VIV of a sprung cylinder without an NES, or one with a ‘rectilinear NES’, considered previously. Specifically, the NES can either stabilize or destabilize the steady, symmetric, motionless-cylinder solution and can induce conditions under which suppression of VIV (and concomitant reduction in lift and drag) is accompanied by a greatly elongated region of attached vorticity in the wake, as well as conditions in which the cylinder motion and flow are temporally chaotic at relatively low $Re$.

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We study the nonlinear fluid-structure interaction of an elastically supported rigid circular cylinder in a laminar flow. Periodic shedding of counter-rotating vortices from either side of the cylinder results in vortex-induced vibration of the cylinder. We demonstrate the passive suppression of the limit cycle oscillation (LCO) of the cylinder with the use of an essentially nonlinear element, the nonlinear energy sink (NES). The computational study is performed at a Reynolds number (Re) of 100; Re is defined based on the cylinder diameter and inlet velocity. The variational multiscale residual-based stabilized finite-element method is used to compute approximate solutions of the incompressible Navier-Stokes equations. The NES is comprised of a small mass, an essentially nonlinear spring, and a linear damper. With appropriate values for the NES parameters, the coupled system of flow-cylinder-NES exhibits resonant interactions, resulting in targeted energy transfer (TET) from the flow via the cylinder to the NES, where the energy is dissipated by the linear damper. The NES interacts with the fluid via the cylinder by altering the phase relation between the lift force and the cylinder displacement; this brings about significant reduction in the LCO amplitude of the cylinder for several set of values of the NES parameters.