Micro-amplitude vibration suppression of a bistable nonlinear energy sink constructed by a buckling beam

Effective reduction of micro-amplitude vibration has always been a serious challenge. The nonlinear energy sink (NES) has been proven to be able to reduce vibration at a wide frequency. However, the energy threshold of the NES prevents it from suppressing micro-vibrations. In this paper, a bistable nonlinear energy sink (BNES) based on a buckling beam oscillator is constructed. The threshold of the NES is lowered by the nonlinear dynamic behavior of jumping between wells of the bistable oscillator. The motion equations of the discrete–continuous system are derived by using Hamilton's principle. The approximate analytical solution is obtained and verified numerically. The results show that even when the primary system has a micro-amplitude resonance, the nonlinear cross-well vibration of the BNES can still reduce the vibration. The robustness of the BNES is stronger than that of the tuned mass damper (TMD). The optimal parameters of the BNES are obtained with particle swarm optimization (PSO) algorithm. The result of parameter optimization shows that the energy threshold of the nonlinear energy sink can be effectively lowered. In short, the method based on nonlinear dynamics in this paper provides an effective reduction strategy for micro-vibration in engineering. Graphical abstract: [Figure not available: see fulltext.].