Abstract The cubic or third-power (TP) nonlinear energy sink (NES) has been proven to be an effective method for vibration suppression, owing the occurrence of targeted transfer (TET). However, TET is unable triggered by low initial input, and thus TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type with fractional nonlinearity, e.g., one-third-power (OTP) p...