Closed‐form design formulas of TMDI for suppressing vortex‐induced vibration of bridge structures

Summary Tuned mass damper inerter (TMDI) is a promising device for structural vibration control. Existing design formulas for TMDI are derived based on an undamped single‐degree‐of‐freedom primary structure. When applied to vortex‐induced vibration (VIV) control of bridges, it may lead to a suboptimal design of TMDI, since VIV is characterized by nonlinear aeroelastic effect and sensitive to the structural damping. This study proposes closed‐form design formulas of TMDI that are suitable for VIV control of bridges. Governing equations of the bridge‐TMDI system are first established in modal coordinate. Based on these equations, the equivalent damping of TMDI to the bridge is derived. Then, the design formulas for TMDI frequency and damping ratio with predetermined TMDI mass, inertance, and inerter arrangement are developed to achieve the required equivalent damping of TMDI. The reliability of the proposed formulas is validated by utilizing the wind tunnel experimental data of a bridge. It is found that the effect of TMDI to the bridge can be treated as an increase of the structural damping. It is also found that the TMDI parameters will betray the optimum values if the VIV force model fails to correctly predict the required equivalent damping of TMDI. To eliminate this disadvantage, some design suggestions are presented. The comparison with existing TMDI design formulas and discussions on the application scope of the proposed formulas are also conducted. The proposed formulas can achieve a better control efficiency for the same predetermined TMDI parameters and have high accuracy within the scope of practical engineering applications.