Tuned Mass Damper Inerter for Nonlinear Flutter Control of Long-Span Bridges: Optimal Design

The conventional flutter control target of long-span bridges focuses on enhancing the critical wind speed. However, in recent years, most bridge decks have been discovered to exhibit nonlinear limit cycle oscillation (LCO) and their postcritical LCO amplitudes grow slowly with wind speed. In reality, for long-span bridges, the postcritical LCO with safe amplitudes should be acceptable within the design wind speed. Besides, considering the installation space issue of TMD in long-span bridges with low frequency, a tuned mass damper inerter (TMDI) is adopted to control nonlinear flutter in this study, and a novel control target for nonlinear flutter is proposed, where the bridge amplitudes shall not exceed the safety threshold and the TMDI stroke shall not exceed the maximum allowable space when wind speeds are within the design wind speed. To obtain the minimum TMDI mass ratio (i.e., the most economical TMDI) that can achieve the novel control target, a TMDI parameter optimization method that considers nonlinear aeroelastic effects (i.e., considers nonlinear behavior of the wind–bridge–TMDI fully coupled system) is developed based on the gradient-based optimizer. Through a case study, the control effectiveness of the TMDI on nonlinear flutter is analyzed, and the control robustness of the TMDI for the offset of bridge structural parameters is discussed. The results show that the designed TMDI, developed using the optimization method in this study, can achieve the control target while simultaneously meeting the spatial feasibility, economy, and a certain level of robustness requirements.