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This study investigates the parameters design of the tuned mass damper (TMD) for mitigating the vortex-induced vibration (VIV) of long-span bridges, which includes the selection of vortex-induced force models and robustness problem. The critical damping ratio of the bridge obtained by wind tunnel tests is used as the control objective of the TMD for VIV mitigation. Two types of optimum design parameters of the TMD and equivalent damping ratios contributed by the TMD based on empirical linear and nonlinear models are discussed and compared. A flatness for the equivalent damping ratio curve versus system error is used to quantify the robustness of the TMD, and consequently a simplified formula for the optimum damping ratio of the TMD is given based on the flatness. The VIV mitigation of the Hong Kong–Zhuhai–Macao Bridge (HZMB) deep-water nonnavigable bridge is used to illustrate the parameters design of the TMD. The results show that the empirical linear model gives a conservative control evaluation and large damping ratio of the TMD compared to the empirical nonlinear model, and these differences result from their different controlled frequencies in the VIV mitigation. The flatness can both quantify the result of mistuning phenomenon of the TMD and consider its probability of occurrence. The proposed simplified formula avoids the difficulty in selecting the damping ratio of the TMD in the VIV mitigation of bridges. The frequency ratio and damping ratio of the TMD for the HZMB deep-water nonnavigable bridge are initially taken as 0.996% and 5.57% under the given mass ratio of 0.36%. The result of fatigue tests shows that the manufactured TMDs have sufficient performance stability on the VIV mitigation of the HZMB.
Dai et al. (Thu,) studied this question.