Three-dimensional nonlinear flutter analysis of long-span bridges by multimode and full-mode approaches

Based on amplitude-dependent flutter derivatives (FDs), the present study established three-dimensional (3D) nonlinear flutter analysis methods, including a multimode and a full-mode approach, for long-span bridges. Then, by adopting the proposed methods, the influences of 3D effects, self-excited drag force, and multimode aerodynamic coupling effects on nonlinear flutter response were investigated. Besides, critical structural modes that have a great impact on nonlinear flutter were identified, their contributions were quantified and roles were clarified. The results show that the 3D effects of structural modes can reduce the system stability mainly by increasing the negative uncoupled aerodynamic damping. Thus, if the 3D effects are ignored, the stable amplitude of nonlinear flutter will be underestimated. For long-span bridges whose foundational symmetric torsional mode couples a minor lateral-bending mode shape, the added aerodynamic damping from self-excited drag force, especially the term of FD P1**1, can improve the stability of the system. Thus, it will overestimate the nonlinear flutter response if the self-excited drag force is ignored. Meanwhile, the aerodynamic coupling effect among different structural modes should be considered, otherwise the nonlinear flutter responses of long-span bridges may be misestimated significantly. For the nonlinear flutter dominated by the fundamental symmetric torsional modal branch, the symmetric vertical bending modes with a frequency lower than the fundamental symmetric torsional mode should be considered. Besides, the other higher-order structural mode coupled with relatively significant fundamental symmetric torsional mode shape is also worth being taken into account. The selection of structural modes is an important and experience-based work in the multimode method. Thus, the full-mode method, which can consider the potential higher-order structural modes that may have contributions to the 3D nonlinear flutter, is also needed, especially when the amplitude is large enough. Otherwise, the nonlinear flutter response may be underestimated by the multimode method.