Analysis of nonlinear damping parallel nonlinear energy sink vibration reduction performance under strong excitation

The vibration reduction performance of NES is greatly affected by the excitation. When the excitation is too high, the system may experience bifurcation, leading to the vibration reduction failure of NES. For the above issues, a nonlinear damping parallel energy sink (NDPNES) is proposed in this paper, which utilizes damping to increase with the increase of relative motion between the NES and the controlled system to ensure efficient vibration reduction performance under strong excitation. At the same time, without increasing the total mass, to improve the stability of the NES through mass configuration. Firstly, the mathematical model of NDPNES was established, and the slowly varying equation of the system was obtained based on the complex variable averaging (CX-A) method. Then, the amplitude frequency characteristics of the controlled system were obtained, and the stability was analyzed using Lyapunov stability theorem, at the same time, the analytical results were verified by numerical methods. Afterwards, the influence of parameters on the vibration reduction performance of NDPNES was analyzed. Finally, the performance of the proposed scheme under transient and steady-state excitation was verified using numerical methods. The results indicate that, compared to existing Cubic stiffness NES (CNES), the proposed NDPNES has better vibration reduction performance and stability under strong excitation. The proposed scheme is of great significance for vibration control of machinery (such as mining machinery, engineering machinery, etc.) operating in strong excitation environments.