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The undesirable vortex-induced vibration (VIV) may seriously influence the fatigue life and serviceability of bridge structures. It is important to take countermeasures to suppress the adverse VIV of long-span bridges. In the present study, a novel inerter-based system, namely the tuned mass damper inerter (TMDI), is proposed to control the VIV of the main deck of long-span bridges. In this system, an inerter device, which is able to transform the linear motion into the high-speed rotational motion and thus significantly amplifies the physical mass of the system, is incorporated into the conventional tuned mass damper (TMD) system to further improve the performance of TMD. An applicable layout of the TMDI inside the bridge deck is introduced and the governing equations of the structure-TMDI system subjected to VIV are established. The optimization of the TMDI parameters with the consideration of nonlinear …