A tristable nonlinear energy sink to suppress strong excitation vibration

As well known, the vibration reduction efficiency of the nonlinear energy sink (NES) is poor under strong excitation. In this paper, a tristable NES (TNES) is proposed. The TNES can degenerate into bistable and mono-stable NES by adjusting the geometric parameters of the springs. The governing equations of a linear oscillator coupled with the TNES under harmonic excitation are derived. The approximate analytical solution of the coupled system is obtained by using the harmonic balance method and verified numerically. The vibration suppression efficiency of TNES and NES is compared. The dynamic behavior of TNES under strong excitation is demonstrated. The results show that the nonlinear restoring force is softened due to the wide distribution of the three stable points of TNES. Therefore, compared with NES, the proposed TNES can suppress stronger excitation vibration. In addition, the low side barrier depth is conducive to TNES to perform chaotic inter-well oscillation, which can effectively suppress the strong excitation vibration and obtain good vibration reduction performance. As a result, the proposed TNES can eliminate the detached resonance curve and enlarge the effective range of the NES. Under relatively weak excitation, the vibration suppression efficiency of TNES is slightly lower than that of NES, although the TNES is also relatively significant. Therefore, this paper reveals the vibration suppression mechanism of TNES, and provides a way to effectively solve the problem of low vibration reduction efficiency of NES under strong excitation.