Fractional nonlinear energy sinks

The cubic or third-power (TP) nonlinear energy sink (NES) has been proven to be an effective method for vibration suppression, owing to the occurrence of targeted energy transfer (TET). However, TET is unable to be triggered by the low initial energy input, and thus the TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type of NES with fractional nonlinearity, e.g., one-third-power (OTP) nonlinearity, is proposed. The dynamic behaviors of a linear oscillator (LO) with an OTP NES are investigated numerically, and then both the TET feature and the vibration attenuation performance are evaluated. Moreover, an analogy circuit is established, and the circuit simulations are carried out to verify the design concept of the OTP NES. It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES. The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system. Additionally, significant energy transfer is usually accompanied with efficient energy dissipation. Consequently, the OTP NES can realize TET under low initial input energy, which should be a promising approach for micro-vibration suppression.