Design Strategy of Nonlinear Energy Sink Inerter for Vortex-Induced Vibration Mitigation of Long-Span Bridges

Nonlinear energy-sink inerters (NESIs) combine the features of conventional nonlinear energy sinks (NESs) and an adjustable inerter to provide broadband vibration mitigation while requiring less mass than an NES alone. This makes NESI units particularly effective for mitigating vibration in large-scale structures. However, the effects of inherent supplementary forces (e.g., that of weight) of an NESI system cannot be easily compensated for through static displacement, which results in complex nonlinear effects of stiffness in NES-related systems influenced by gravitational effects, which weakens the capacity of an inerter to mitigate vibration to some extent. Previous studies have shown that using an NESI with quasi-zero stiffness (QZS) can eliminate these effects of supplementary forces. This approach also demonstrated low static displacement and strong robustness in mitigating vortex-induced vibrations (VIVs) in long-span bridges. Given its numerous design parameters and strong nonlinear characteristics, such enhanced NESI systems pose some notable challenges in identifying design parameters for desired control performance. In this study, we developed empirical parameter design strategies to support the application of enhanced NESI systems to mitigate VIVs in long-span bridges. According to empirical models, the optimal damping coefficient remains invariant to alterations in the magnitude of excitation, whereas the optimal stiffness decreases exponentially with increasing excitation intensity. The proposed design methodology successfully eliminated VIVs in long-span bridges, which validates the reliability and effectiveness of the approach. A parameter combination with a high inertance ratio is recommended to achieve the minimum static deflection, which constitutes 10% of the height of the girders.