Use of targeted energy transfer to delay K\'{a}rm\'{a}n vortex shedding and suppress vortex-induced vibration in flow past a cylinder

For two-dimensional flow past a circular cylinder whose motion is constrained by a linear spring to be perpendicular to the mean flow, we report computations showing that ``targeted energy transfer'' using a nonlinear energy sink (NES; consisting of a mass, a linear damper, and an essentially nonlinear spring) not only can reduce the amplitude of the cylinder motion, but can also increase the critical Reynolds number (\textit{Re}) at which the K\'{a}rm\'{a}n vortex street first appears. Absent the NES, the critical \textit{Re} at which vortex shedding (and hence cylinder motion) sets in is determined as a function of the stiffness of the linear spring. Over a wide range of stiffness, the NES is shown to delay the onset to higher \textit{Re}.