Analytical Optimization and Performance Evaluation of Tuned Inerter‐Negative‐Stiffness Dampers (TINSD) for Seismic Response Control in Long‐Span Bridges With Floating Systems (LBFSs)

ABSTRACT This paper proposes using a composite control device, termed tuned inerter‐negative‐stiffness dampers (TINSDs), for the longitudinal seismic control of long‐span bridges with floating systems (LBFSs), and comprehensively investigates its optimization and control effectiveness. Initially, an analytical model for LBFS coupled with TINSD, referred to as the LBFS‐TINSD system, is established, followed by the derivation of the corresponding equations of motion. Subsequently, two optimization strategies, namely, displacement‐ and energy‐oriented optimizations, are formulated to determine the design parameters of TINSD. By ignoring inherent damping, closed‐form solutions for the optimal design parameters of TINSD are derived, and their accuracy is confirmed by contrasting them with numerical solutions. Parametric studies are then performed to investigate the influences of the stiffness ratio and inherent damping ratio of LBFS on the optimal design parameters of TINSD, while comparative analyses are conducted to investigate both optimization strategies. Finally, case studies are performed to numerically illustrate the effectiveness of TINSD in mitigating the responses of a classical cable‐stayed bridge under different types of ground motions. In addition, the seismic control performances of TINSD are also compared with its counterparts, that is, tuned viscous mass damper (TVMD) and negative stiffness amplifying damper (NSAD). The results demonstrate that the energy‐oriented optimization achieves a more balanced performance in terms of girder displacement, girder acceleration, and energy dissipation compared to the displacement‐oriented optimization, albeit with a slight increase in control force. Furthermore, the TINSD exhibits superior performance over TVMD and NSAD, significantly reducing peak girder displacement response.