A zero linear stiffness tristable nonlinear energy sink

The effectiveness of NES-based vibration control is characterized by its inherent frequency adaptability and energy-range robustness. However, conventional NESs are effective only within a limited energy range, whereas existing tristable NESs (TNESs), despite extending the energy range through their tristable characteristics, reintroduce local linear stiffness at stable equilibria, thereby compromising their essential nonlinearity and broadband adaptability. To address this limitation, this study proposes a zero linear stiffness TNES (ZLS-TNES) model, which maintains tristable characteristics while ensuring zero linear stiffness at all equilibrium points. The ZLS-TNES is realized through a cam-roller-spring mechanism, with the desired cam profile generated via an inverse design methodology. The slow invariant manifold and the nonlinear normal modes of the coupled system are derived to reveal the dynamic mechanisms. Systematic parametric investigations unveil a hierarchical activation mechanism involving two distinct energy thresholds: the first triggers intra-well strongly modulated response equivalent to a conventional NES, while the second activates high energy inter-well “snap-through” motions. Consequently, compared with the conventional NES, the proposed ZLS-TNES exhibits a significantly wider effective vibration mitigation amplitude range due to this dual-threshold hierarchical feature. Furthermore, the frequency self-adaptability of the TNES and ZLS-TNES is compared by varying the linear stiffness of the primary system. The results indicate that the ZLS-TNES achieves improved broadband adaptive capability by eliminating the positive linear stiffness at the stable equilibria of the conventional TNESs. Therefore, this study elucidates the hierarchical activation mechanism of the ZLS-TNES and presents a robust methodology to address the inherent limitations of conventional NESs and TNESs in terms of energy-level coverage and frequency adaptability.