Passive Suppression of Vortex-Induced Vibration of a Cylinder at $Re=100$

For a Reynolds number (\textit{Re}) based on cylinder diameter of 100 and a ratio of cylinder density to fluid density of 10, we investigate the use of an essentially nonlinear approach to passive suppression of vortex-induced vibration (VIV) of a rigid circular cylinder restrained by a linear spring, and constrained to move perpendicular to the mean flow. The variational multiscale residual-based stabilized finite-element method used to compute approximate solutions of the incompressible Navier-Stokes equations about the moving cylinder is coupled to a simple model of a ``nonlinear energy sink'' (NES), an essentially nonlinear oscillator consisting of a mass, a linear damper, and a strongly nonlinear spring. The NES promotes nearly one-way transfer of energy from the primary structure (the cylinder) to itself, resulting in reduction of the amplitude of the limit cycle oscillation by as much as 75{\%}, depending on the parameters characterizing the NES. Various mechanisms of VIV suppression by the NES are discussed, along with results showing the effectiveness, over a range of \textit{Re}, of passive suppression using an NES whose parameters were selected to work well at $Re=100$.