Study on excitation threshold of strong modulation response and vibration suppression performance of bistable nonlinear energy sink

The dynamics and vibration reduction performance of bistable nonlinear energy sink (BNES) are studied in this paper. First, the negative stiffness of BNES is realized by geometric nonlinearity, and the dynamics model of the system is established. The slow flow equation of the system under 1:1 main resonance is analyzed based on the complexification-averaging (CX-A) method, and the boundary conditions of saddle node bifurcation and Hopf bifurcation are analyzed. Second, the slow invariant manifold (SIM) of the BNES is studied based on multiscale analysis, and the excitation threshold of strongly modulated response (SMR) is analyzed; the analysis results are verified by the numerical method. The results show that the analytical solution is highly consistent with the numerical solution, and the error is less than 1%. Finally, the influence of structural parameters on the vibration reduction performance is analyzed and optimized. The vibration reduction performance of BNES and CNES is compared, and the results show that the BNES has better vibration reduction performance in the full frequency band.