Characteristic analysis and design of nonlinear energy sink with cubic damping considering frequency detuning

The nonlinear energy sink (NES) is a vibration energy absorber, which is of great significance in vibration reduction applications. In this study, the dynamic analysis of the NES with cubic nonlinear damping considering frequency detuning is investigated, and the effects of external harmonic force and NES parameters on the vibration reduction are given. Firstly, for a 1-dof NES system, through the analysis of the slow flow equation, the influence regularities of the frequency detuning coefficient and the NES parameter on bifurcation are obtained, and the corresponding truncation damping is revealed. For the 2-dof NES case, the effect of the mass distribution between NES on the bifurcation phenomenon of the system is given. For the 2-dof NES case considering frequency detuning, through the incremental harmonic balance method and Floquet theory, the analysis of the number and stability of the solutions is obtained. Secondly, utilizing the multi-scale method to analyze the response of the 1-dof NES case, the effects of the load amplitude variation on the frequency detuning interval are revealed. Meanwhile, using Poincare mapping to analyze the response of the 2-dof NES case, it is revealed that the responses of various parts of the system can be inconsistent, and the 2-dof NES could produce additional strongly modulated response than the 1-dof NES. Lastly, the energy spectrum is applied to verify the vibration reduction of the NES with cubic nonlinear damping, and it also indicates that the 2-dof NES has better vibration reduction.