Multimode coupled nonlinear flutter analysis for long-span bridges based on a time-varying flutter derivative model

Accurate assessment of the three-dimensional (3D) nonlinear flutter response of full-bridge systems is regarded as a prerequisite for the future implementation of wind-resistant design standards that employ the amplitude threshold of the limit-cycle oscillations (LCOs) as the criterion for nonlinear flutter. To satisfy this requirement, a time-frequency hybrid model of three-degree-of-freedom coupled nonlinear self-excited forces was developed on the basis of time-varying flutter derivatives (FDs), and a 3D multimode coupled nonlinear flutter analysis method suitable for long-span bridges was proposed. Using two long-span bridges with markedly different natural mode shapes as case studies, the proposed method was systematically applied to examine the effects of multimode coupling on nonlinear flutter responses and static equilibrium positions of the main girders. Structural modes that exert a critical influence on nonlinear flutter were further identified, their contributions were quantified, and the underlying mechanisms were revealed. The results indicate that multimode coupling effects primarily reduce system stability through the enhancement of aerodynamic negative damping. Neglecting the effects of multimode coupling leads to substantial misestimation of the nonlinear flutter response, the critical flutter wind velocity, and the equilibrium position of the main girder. Moreover, the natural mode shapes of the bridge deck, particularly the purity of its first-order symmetric torsional mode, are demonstrated to be key factors governing multimode coupled flutter behavior.