A novel multi-objective optimization of mass dampers for controlling the vortex-induced vibration in bridges

•The equations of motion of the bridge-damper system subjected to the vortex-induced force are established and solved by the Krylov-Bogoliubov method.•The vortex-induced amplitude of the girder is analytically given and the optimal design is implemented by taking the vortex-induced amplitude as the constraint condition.•Introducing two optimization objectives, the stroke index and the robustness index, a novel bi-objective optimization framework with constraints is proposed and solved by multiple objective particle swarm optimization (MOPSO).•A comparative analysis of three mass dampers with varying total mass ratios is performed. This paper investigates an optimization framework of the four mass dampers for controlling the vortex-induced vibration (VIV) in long-span bridges, including the tuned mass damper (TMD), the series double tuned mass dampers (DTMD) and the inerter-equipped tuned mass damper (ITMD). The equations of motion of the bridge-damper system subjected to the vortex-induced force are established. The vortex-induced amplitude of the girder is analytically given. Furthermore, the optimal design is implemented by taking the vortex-induced amplitude as the constraint condition. Introducing two optimization objectives, the stroke index and the robustness index, a novel bi-objective optimization framework with constraints is proposed and then solved by multiple objective particle swarm optimization (MOPSO). A comparative analysis of the four mass dampers with varying total mass ratios is performed. The results show that the vortex-induced amplitude of the girder is greatly reduced to satisfy the requirement after installing the four optimized mass dampers. Both performances of the two optimization objectives are improved with the increase of the total mass ratio. The inertial device parallel to the spring and dashpot provides no advantage in controlling the VIV in bridges. The DTMD has dramatic robustness to changes in the bridge natural frequency and cannot strongly amplify its stroke, especially under the condition of a small mass ratio. The framework provides an excellent balance between control effect and stability in the VIV of bridges for the optimal design of the mass dampers.