This study investigates the application of a Tuned Inerter Damper (TID) to control excessive relative displacements in pier-bridge systems under extreme lateral loads. Using frequency-domain analysis and fixed-point theory, optimal TID frequency and damping ratios are derived. The TID transforms the system into a three-degree-of-freedom model with a frequency response containing four fixed points. The optimization is conducted in two stages: first, equating the magnitudes of two low-frequency fixed points (P and Q) yields the optimal frequency ratio; second, equalizing the magnitudes at P, Q, and an auxiliary point M provides the optimal damping ratio via numerical solution. Results indicate that for a given inertance ratio, the optimal parameters stabilize as the substructure-to-superstructure frequency ratio increases, regardless of mass ratio. Based on this, a simplified two-step design method is proposed, incorporating fitted equations and parameter tables for efficient TID design without extensive computation. Numerical simulations demonstrate that the optimized TID effectively reduces resonant displacement peaks and improves decay rates, thereby enhancing seismic performance. The presented framework offers a practical and novel basis for the aseismic design of pier-bridge systems.
Tong et al. (Thu,) studied this question.