Computational study of vortex-induced vibration of a sprung rigid circular cylinder with a strongly nonlinear internal attachment

For a Reynolds number (Re) based on cylinder diameter of 100, and a ratio of cylinder density to fluid density of 10, we investigate the effect of a strongly nonlinear internal attachment on the vortex-induced vibration (VIV) of a rigid circular cylinder restrained by a linear spring, and constrained to move perpendicularly 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 to itself from the primary structure (the cylinder), 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 nonlinear interaction of the NES with the cylinder undergoing VIV are discussed. Although no optimization of the NES is performed in this work, we demonstrate capacity for passive suppression of VIV and compare the performance of the NES to the tuned linear absorber of equal mass.