Theoretical investigation on vibration mitigation in a system with fractional nonlinear energy sinks

Recently, the fractional nonlinear energy sink (NES) has been proven to behave with excellent micro-vibration mitigation effect. However, only one-third power of the fractional NES was considered in the previous study, and its dynamic behaviors was studied simply through numerical simulations. Obviously, there is a lack of in-depth theoretical investigation on the fractional NES with different powers. This paper aims at drawing a complete picture of dynamic behaviors for the fractional NES with different powers, and deeply exploring the vibration mitigation mechanism of the fractional NES. Firstly, the motion equations of a host oscillator with the fractional NES are established. Then, the slow invariant manifold (SIM) of the fractional NES system under impulse is derived by the complexification-averaging (CX-A) method and verified by numerical analysis. Additionally, the frequency response of the fractional NES system under harmonic excitation is obtained by the harmonic balance method (HBM). Furthermore, the vibration mitigation characteristics of the fractional NES with different powers under both the impulse and harmonic excitation are investigated by numerical simulations. The results demonstrate that when the power is close to 1, the NES behaves similarly to a linear oscillator. As the power decreases, the fractional NES becomes able to perform excellent vibration mitigation effect. And decreasing power further could increases the threshold and widen the TET region. The fractional NES with a moderate power, such as 1/3, possesses a desirable micro-vibration mitigation performance, that is, it has a low threshold and a wide excitation range for vibration mitigation. These findings will facilitate the further investigation and application of the fractional NES.