Optimization and performance analysis of a track tristable nonlinear energy sink subjected to impulsive, harmonic and sea wave excitations

• The analytical analysis and vibration reduction performance of a track tristable nonlinear energy sink (TTNES) are conducted under impulsive excitations. • The approximate analysis and vibration reduction performance of a TTNES are carried out under harmonic excitations. • A TTNES is applied to vibration mitigation of an offshore platform under sea wave excitations. A traditional track nonlinear energy sink (TNES) is very sensitive to input energy. In order to extend effective energy threshold range of a TNES, a track tristable nonlinear energy sink (TTNES) with rotational inertia is proposed. Firstly, motion equations of a linear structure coupled with a TTNES are derived. The TTNES can translate into the track bistable NES (TBNES) and the track monostable NES (TMNES, traditional TNES) by adjusting track shape parameters. Secondly, equilibrium stability and bifurcation of a TTNES are determined. Then, analytical analysis and vibration reduction performance of a TTNES are conducted under impulsive excitations. In addition, approximate analysis and vibration reduction performance of a TTNES are carried out under harmonic excitations. Finally, a TTNES is applied to vibration mitigation of an offshore platform under sea wave excitations. The results show the TTNES exhibits better vibration reduction performance and higher robustness than traditional TNES when subjected to impulsive and harmonic excitations. In addition, the TTNES can effectively reduce the response of an offshore platform under sea wave excitations. This research provides the necessary theoretical basis for designing and applying the TTNES.