A customizable cam-typed bistable nonlinear energy sink

Abstract

A novel cam-typed bistable nonlinear energy sink (CBNES) is first proposed in this paper. The CBNES achieves a customized design of the ideal configuration of BNES by introducing a cam-roller-spring negative stiffness mechanism (CRS-NSM). The design criteria for continuous and smooth bistable cam profiles are studied, and the extreme values of dimensionless stiffness and pre-compression are predicted. Furthermore, the periodic and quasi-periodic dynamics of the system are studied by using the complexification-averaging (CA-X) method. By combining Slow Invariant Manifold (SIM) and phase trajectory, the energy dissipations of different response types of the CBNES are predicted. The SMR and chaotic response have the best and lowest targeted energy transfer (TET) efficiency, respectively. The saddle-node (S-N) and Holf bifurcation characteristics of the periodic fixed points are analyzed to predict the possibility of SMR occurrence. The analysis of the amplitude frequency curve with the variation of system parameters indicates that weak negative stiffness and intermediate cubic stiffness are more beneficial to vibration suppression. The highlight is that the excitation thresholds of SMR are predicted by using analytical and numerical methods, and the influences of system parameters on the thresholds are analyzed. The deviation between the analytical and numerical results will decrease with increasing damping. Finally, the correctness of the analytical results is verified through a series of fixed-frequency experiments. The proposed CBNES provides a valuable potential solution for designing efficient and robust mechanical BNES physical implementations.