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Tuned mass damper inerter (TMDI) has become a popular choice for vibration control in flexible structures, including long-span bridges, due to its superior performance compared to traditional tuned mass dampers (TMDs), such as improved control effect and smaller static displacement. However, the control effect of TMDI is heavily reliant on the spanning distance of inerter, which typically generates a significant internal additional moment due to the force imbalance, limiting the practical application of TMDI on flexible structures. For this reason, a novel lever-arm TMDI (LTMDI) is proposed in this study, to suppress the vibrations of long-span bridges. The non-dimensional governing equations of the bridge-LTMDI system are established in modal coordinates, and the closed-form solutions of the optimum frequency and damping ratios of LTMDI are derived based on the classical fixed-point theory. Parametric studies are conducted to investigate the influences of the fulcrum position, modal shape ratio, mass ratio, inertance ratio and asymmetric mode on the control effectiveness. Moreover, for comparison, the control effectiveness of LTMDI is further compared to those of the TMD and TMDI. Finally, a long-span bridge is selected as an example to demonstrate the effectiveness of LTMDI in reducing vortex-induced vibration (VIV). The results show that the LTMDI has superior control effect and space feasibility as compared to the TMD and TMDI in both frequency and time domains. The derived analytical formulas can accurately determine the optimal parameters, providing a simple yet efficient guideline for the application of LTMDI in flexible structures. [ABSTRACT FROM AUTHOR]

• A novel lever-arm TMDI is proposed for vibration control of long-span bridges. • The influences of design parameters are systematically investigated. • Empirical design formulas are proposed. • Control performance is validated in both frequency and time domains. In this study, the lever mechanism is incorporated with the tuned mass damper inerter (TMDI) to further promote the practical application of TMDI in long-span bridges. Four potential configurations of the lever-arm tuned mass damper inerter (LTMDI) are first established, and the corresponding governing equations are derived. Then, the optimum configuration of LTMDI is identified by minimizing the peak of non-dimensional displacement frequency response function (FRF). Subsequently, the influences design parameters, such as mass ratio, inertance ratio, lever mass ratio, and spanning distance of the inerter are investigated. Based on the results, empirical design formulas of design parameters are proposed and verified. Finally, a cable-stayed bridge is adopted as a numerical case to further illustrate the performance of LTMDI in terms of response reduction and robustness. The results show that the involving of the lever into TMDI is an effective mechanism for implementing the inerter's spanning in long-span bridges. With this mechanism, it is practically feasible to achieve a high effectiveness, low space requirement and more robustness control device for long-span bridges. The developed design formulas have a high accuracy, which can provide reliable support for the design of the LTMDI in engineering applications. [ABSTRACT FROM AUTHOR]