Stochastic Optimization of Multiple Tuned Inerter Dampers for Mitigating Seismic Responses of Bridges with Friction Pendulum Systems

Friction pendulum systems (FPSs) are increasingly being used for bridge seismic isolation, and the isolated response is generally achieved at the expense of inducing large bearing displacements. Setting up a tuned inerter damper (TID) is an approach for improving seismic performance. Nevertheless, the optimization and performance enhancement of multiple TIDs to mitigate the seismic responses of bridges isolated with the FPSs are limited. In this study, the stochastic optimization of multiple TIDs for controlling stochastically excited bridges with FPS bearings was pursued. By describing the hysteretic characteristics of the FPS using the Bouc–Wen model, augmented systems of the bridge model, FPS bearings, and TIDs were formulated and combined with the modeling of stochastic excitation as filtered Gaussian white noise. A stochastic optimization procedure of multiple TIDs for controlling the bridge response considering the nonlinearity of the FPS bearings is proposed and illustrated using examples of continuous bridges. The effects of FPS friction on the optimization and robustness of the TID parameters were identified. A parametric study was performed to determine the mechanism of TID performance enhancement depending on the number of TIDs, multiple modes of tuning, and inertance distribution. Numerical results indicate that the TIDs designed via stationary-stochastic-global (SSG) optimization significantly reduced the responses of the isolated bridge, and the performance was improved by increasing the TID number. Considering the multi-mode contributions to the transversal responses, the performance of spatially distributed TIDs can be substantially enhanced by adding the TID inertance as a design parameter.