A novel lever-arm tuned mass damper inerter (LTMDI) for vibration control of long-span bridges

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.