Multiple tuned inerter-based dampers for seismic response mitigation of continuous girder bridges

Tuned inerter-based dampers (TIBDs), such as the tuned viscous mass damper (TVMD) and tuned inerter damper (TID), have demonstrated better control performance compared with traditional dampers. To enhance the seismic performance of continuous girder bridges, multiple TIBDs are employed to protect the long-span highspeed railway (HSR) continuous girder bridges under the seismic excitation. The governing equations of the motion of the bridge with TIBDs are reformulated in state-space. Based on the H2 control strategy, the frequency ratio and damping ratio of TIBDs to tune multiple modes of bridges are optimized. The control performance of TIBDs with optimal parameters is evaluated and compared with that of the viscous dampers (VDs) in terms of mitigating the peak response and root mean square (RMS) response of the bridge. Meanwhile, through analyzing the power spectral density and dissipated energy of different dampers, the mitigation principle of TIBDs is explored. Results show that TIBDs with optimal parameters can effectively improve seismic performance of the long-span HSR continuous girder bridge. Nevertheless, VDs shows better effectiveness of vibration mitigation on some seismic responses at large inertance ratio in the transverse direction. In addition, the control efficiency of seismic mitigation is reduced for optimal TIBD compared with that for VD with the increase of inertance ratio. Note that the non-linear behavior of the ballasted track system for used HSR bridge model is not considered in the study. Therefore, the proposed analysis method and results obtained in this study can provide references for seismic response control in the linear continuous girder bridges using multiple TIBDs.