Suppression of vortex-induced vibrations using bistable nonlinear energy sink

The use of conventional cubic nonlinear energy sink (NES) to mitigate vortex-induced vibrations has been widely investigated. Recently, bistable NES (BNES) has gained considerable attention owing to its ability to execute large amplitude inter-well motion and thus enhance energy transfer. But, the efficacy of BNES to mitigate self-excited vibrations in general and vortex-induced self-excited vibrations in particular seems to have received little interest. The present study proposes the use of BNES to mitigate the vibration of an elastically mounted circular cylinder subjected to a flow field. The van der Pol equation with acceleration coupling is used to model the wake behavior. The BNES is appended to the linear structure. Analytical and numerical investigations are performed to understand the mechanism of energy transfer and to demonstrate the advantages of BNES over conventional cubic NES. Numerical studies reveal that the BNES is more effective in reducing vibration amplitude in the lock-in region. Like cubic NES, the inclusion of BNES de-stabilizes the large amplitude synchronized orbits in the lock-in region. The ability of BNES to exhibit inter-well chaotic motion is shown to cause larger vibration mitigation when compared with cubic NES. The transition from the intra-well periodic to inter-well chaotic motion is further investigated by Melnikov analysis, and the critical response amplitude needed for the same is arrived at. The complex-averaging (CX-A) method combined with the method of multiple scales (MMS) is used to derive the slow invariant manifold (SIM) from the slow-flow dynamics. The SIM topology, together with the projected time history, is used to demonstrate the advantages of BNES over cubic NES in vortex-induced vibration suppression. The effect of mass ratio, negative linear stiffness, non-dimensional damping, and stiffness ratio on the topology of SIM is investigated. Based on this parameter study, optimal BNES parameters for effective vibration suppression are suggested.