Vibration Control for Long-Span Bridges: A Systematic Study on Pulley-Block Tuned Mass Damper Inerter (PBTMDI) System

In this paper, a pulley block (PB) is incorporated into the Tuned Mass Damper Inerter (TMDI) system. The pulley block system can not only amplify the relative displacement between the bridge and the mass block, but also transfer this displacement to the longitudinal direction of the bridge. Therefore, the spring in the PBTMDI can be placed outside the TMDI, and the static deformation of the spring is no longer limited by the height of the box girder, which greatly facilitates the applicability of TMDI. First, the governing equations for the bridge-PBTMDI system are derived. When the deformation of the pulley block’s cable is negligible, the PBTMDI is essentially a TMDI, and a parameter [Formula: see text] is proposed to evaluate whether the deformation can be ignored. Subsequently, based on the reduction ratio of the dynamic amplification factor (DAF), the influences of the PBTMDI’s parameters, such as stiffness ratio, mass ratio, inertance ratio, and pulley block magnification factor, are investigated, and the robustness and static deformation of the PBTMDI are also examined. Finally, two numerical cases for vortex-induced vibration (VIV) and buffeting vibration are conducted to further illustrate the performance of PBTMDI. The result shows that the PBTMDI has the same buffeting control effect and VIV control effect compared to TMDI. In addition, the pulley block system can completely solve the static deformation issue of springs of TMDI and amplify the damping coefficient, spring stiffness, and inerter coefficient.