Optimal design of tuned mass damper inerter with a Maxwell element for mitigating the vortex-induced vibration in bridges

•A novel tuned mass-damper-inerter with a Maxwell element is proposed to mitigate the vortex-induced vibration in bridges.•The effect of the inerter location on the optimal M-TMDI parameters is considered.•The optimal M-TMDI parameters are developed in closed-form expression for the VIV mitigation. This paper investigates the optimal design of the Maxwell tuned mass-damper-inerter (M-TMDI) for mitigating the vortex-induced vibration (VIV) in bridges. The M-TMDI consists of a three-element tuned mass damper (TMD) and an inerter. Considering that the bridge deck is a multiple-degree-of-freedom (DOF) system, the inerter location is considered as a design variable of the M-TMDI in our study. The optimal parameters of a specific M-TMDI, in which the end of the inerter is connected to the fixed ground, are analytically given based on a two-DOF system. Furthermore, the optimal parameters of the M-TMDI with any inerter location on the bridge deck are developed in closed-form based on a multiple-DOF system. Finally, numerical analysis on a continuous steel box-girder bridge subjected to the VIV is performed to confirm the optimal design and superiority of the M-TMDI control. The result demonstrates that the optimally designed M-TMDI outperforms the TMD and three-element TMD in the transient amplitude mitigation, steady-state amplitude mitigation, stroke limitation, and static stretching reduction. The optimal control effect of the M-TMDI greatly depends on the defined effective mass ratio, which is function of the inerter location, mode shape, physical mass, and inertial mass.