Effective damping zone of nonlinear energy sinks

Although the nonlinear energy sink (NES) has the characteristic of wideband vibration reduction, there is no unified reference standard for the excitation frequency range and amplitude range where NES can achieve damping effect. In this paper, the response characteristics of the dynamic system composed of a NES and a linear oscillator under harmonic excitation are analyzed by using the method of Complexification-Averaging (CxA), multiple scales, and Runge–Kutta (R–K) method. In addition, the conditions that need to be satisfied for the excitation frequency and amplitude to achieve damping effect of NES are obtained. This study presents that the necessary condition for NES to achieve vibration reduction effect is that the excitation frequency and amplitude reach a certain threshold. The minimum frequency at which NES can have a damping effect is provided. Moreover, the effective damping zone of NES in the parameter space of excitation frequency-excitation amplitude is given. In particular, this paper identifies effective damping zones where thresholds do not exist, invalid zones where NES does not work, and deterioration zones where NES worsens the vibration of the linear oscillator. Therefore, the in-depth study of the effective damping zone of NES in this work is helpful to understand the vibration suppression characteristics of NES. Graphical abstract