Research on vibration suppression of nonlinear energy sink with linear damping and geometrically nonlinear damping

Nonlinear energy sink (NES) is a passive control device that can absorb a wide band, and it has the advantages of lightweight and strong robustness, which can play a very important role in vibration suppression. In this paper, the dynamic modeling and research on vibration suppression of NES with linear damping and geometrically nonlinear damping are carried out, and the effects of NES parameters on the vibration reduction effect are investigated. For the study of dynamic bifurcation, the slowly varying equation of the system is obtained by using the complex variable average method, and the effects of NES parameters on the number of fixed points and stability of the system are analyzed according to the slowly varying equation. At the same time, the effects of excitation amplitude and excitation frequency on the system response amplitude are also investigated. For the study of strongly modulated response (SMR), the slowly varying equation is further analyzed by using the multi-scale method, and the conditions for SMR phenomenon in the system are described by slow invariant manifold and phase portraits. By studying the slow manifold, the detuned parameter interval for the system to appear SMR is derived. For vibration reduction performance analysis, the effects of NES parameters on vibration reduction performance are analyzed from the perspectives of energy and amplitude-frequency response, and the influence laws of various parameters on vibration suppression are revealed. The vibration reduction performance of different NES is compared and analyzed, and it is concluded that the new NES proposed in this paper has better vibration reduction performance.