Efficacy of Optimized Negative Stiffness and Inerter-Assisted TMDs in Bridge Deck Flutter Control

This study introduces a negative stiffness tuned mass damper (NSTMD) and its inerter-assisted variant (NSTMDI) as novel passive devices for bridge deck flutter control. Rational function approximation of the self-excited forces enables time-domain modeling of the aeroelastic system. A genetic algorithm–based multiobjective optimization framework is developed to maximize flutter speed while minimizing auxiliary mass block stroke, leading to Pareto-optimal designs. A combined performance index (CPI), based on weighted min–max normalization of the two objectives, provides a single transparent metric for selecting practically implementable designs from the Pareto set. Tuned mass dampers (TMDs), NSTMD, and NSTMDI achieve maximum flutter speed enhancements of approximately 22%, 30%, and 31%, respectively. The corresponding mass block stroke for NSTMDI is nearly two times lower than that of NSTMD and more than five times lower than that of TMD, underscoring the superior efficiency of the combined negative stiffness and inerter-assisted configuration. Negative stiffness effectively stabilizes the torsional mode, shifting the critical instability to the vertical mode at higher wind speeds, while the inerter enhances energy dissipation and reduces stroke demand. Although the controlled divergence speed is slightly lower than that of the uncontrolled system for NSTMD and NSTMDI, the overall stability margin improves appreciably because flutter, which governs the onset of instability, occurs at higher wind speeds. For a common target flutter speed, both NSTMD and NSTMDI yield lower RMS responses, shorter settling times, and smaller mass block strokes than TMD at preflutter conditions. The effective control moment acts predominantly out of phase with torsional velocity, providing enhanced damping, while NSTMD and NSTMDI generate significantly higher peak control moments than TMD, resulting in stronger and faster stabilization. Robustness analyses under structural and aeroelastic uncertainties, together with detuning of the optimal control parameters, confirm the superior efficacy of the NSTMDI for bridge deck flutter control.