A tristable nonlinear energy sink - Zeng, You-cheng; Ding, Hu (International journal of mechanical sciences, 2023)
•The tristable characteristics are applied to the design of the nonlinear energy sink (NES).•A tristable NES (TNES) constructed by the clamping beam and magnets is proposed.•Chaotic inter-well oscillations of the TNES can dissipate energy of the main system. The tristable characteristics are mostly used in the field of energy harvesting and vibration isolator, but are rarely devoted to in the field of vibration absorption. In this paper, a tristable nonlinear energy sink (TNES) model is proposed for vibration absorption. The TNES is constructed by fixing a magnet in the middle of the clamping pre-pressure beam, and setting a magnet on both sides of the fixed magnet. By adjusting the magnet position, the proposed TNES can be transformed into bistable NES (BNES) and monostable NES (MNES). The TNES is coupled with the linear oscillator (LO), and the differential equation of motion of the coupled system is obtained with the Hamiltonian principle. The approximate analytical method and the numerical method are mutually verified. The vibration reduction efficiency of the TNES under harmonic excitation is presented. The influence of the parameters of the TNES on the dynamics and vibration reduction efficiency is studied. The optimal parameters of the TNES are obtained by the particle swarm optimization (PSO) algorithm. Compared with the corresponding bistable NES and monostable NES, it shows that the tristable NES has obvious advantages in vibration suppression efficiency. The effects of the TNES barrier depths and the excitation amplitude on the vibration reduction efficiency are revealed. The TNES can dissipate energy through chaotic inter-well oscillation between three stable positions, and achieve the purpose of effectively suppressing vibration. [Display omitted]