Nonlinear flutter control of long-span bridge decks by underwater heave plates: Hydro-aero damping balance and design regimes

Underwater heave plates (UHPs) offer a removable passive strategy for improving the flutter stability of sea-crossing long-span bridges, yet the nonlinear mechanism governing their control performance remains insufficiently understood. In particular, the combined effects of plate mass, hydrodynamic damping, cable tension–slack behavior and amplitude-dependent aerodynamic negative damping have not been incorporated into a unified computational framework. This study formulates a computationally tractable nonlinear hydro-aero damping-balance model for bridge decks equipped with suspended UHPs. The model couples self-excited aerodynamic forces with amplitude-dependent flutter derivatives, Morison-type hydrodynamic loading and suspended-cable tension–slack behavior. An iterative time-domain procedure is developed to update the oscillation amplitude, flutter frequency, aerodynamic derivatives and hydrodynamic coefficients until a converged controlled flutter state is reached. The model is validated against coupled wind-tunnel and water-tank experiments. Full-scale analyses show that UHPs can increase increase the critical wind speed for flutter divergence by more than 45% for all representative deck sections examined, with the increase exceeding 70% for the bluff section. The non-monotonic dependence of control efficiency on plate mass is explained by a damping-balance mechanism: increasing mass enhances hydrodynamic damping but also shifts the deck toward larger post-critical amplitudes, where aerodynamic negative damping intensifies. This damping-balance perspective provides a useful basis for interpreting the effects of plate aspect ratio, deck frequency and deck section, and for guiding UHP parameter design in bridge flutter control.