Performance assessment of tuned inerter damper (TID) for transversal seismic vibration mitigation in adjacent bridge pairs

For the urban highway systems with adjacent bridges of closely spaced bridges, transversal collision between these bridges might occur during earthquakes, in addition to the damage to each individual structure. This study employs a tuned inerter damper (TID) to mitigate the seismic responses of this coupled bridge system and proposes an energy-based index (Energy Dissipation Ratio, EDR) for the optimization of its design parameters. The mathematical model of the adjacent bridge-TID coupled system is first developed, where the bridge pairs are simplified and represented by cantilever columns with the mass of each bridge deck lumped at the top of the piers. Utilizing the Hamilton principle, the equation of motion (EOM) for the adjacent bridge-TID coupled system is derived, followed by the definition of the EDR based on the dissipated and input energy. Subsequently, a detailed parametric analysis is conducted concerning the variation of EDR, based on which the procedure determining the design parameters of the TID is established. In the time domain, the efficiency of this proposed procedure is demonstrated via an illustrative example employing nonlinear dynamic analysis. The results show that structural responses are effectively suppressed by the TID device with the design parameters determined according to EDR, specifically the Park-Ang damage index for adjacent piers accounting for pier top displacement and hysteretic energy, and the inter-pier relative displacement (i.e., a key indicator of collision potential). Additionally, investigations are further conducted demonstrating the efficiency of the TID over conventional viscous dampers (VD), as well as its robustness against the potential variations in the dynamic properties of bridges.