This study presents a multimode coupled nonlinear flutter analysis method for long-span bridges with consideration of vibration-amplitude-dependent flutter derivatives. By converting the equation of motion into a complex eigenvalue problem, a double layer iterative method (DLIM) is proposed to determine the real iterative frequency as well as the participation of each structural mode shape to the flutter response for a given wind speed and vibration amplitude. The accuracy of the proposed scheme is cross-validated with a classical bimodal analysis method. Two suspension bridges, characterized by a soft type and a hard type nonlinear flutter, respectively, are used to examine the performance of the proposed method. Modal properties (i.e., damping ratio and frequency), as functions of wind speed and vibration amplitude, can be estimated such that the nonlinear flutter response including the critical wind speed and vibration amplitude can be accurately quantified. At last, the coupling effect among different structural modes and its further influence on the genesis and evolution of the nonlinear flutter are also discussed.

本研究提出了一种考虑振动幅度相关颤振导数的大跨度桥梁多模耦合非线性颤振分析方法。通过将运动方程转换为复杂的特征值问题，提出了一种双层迭代法（DLIM）来确定真实的迭代频率以及每个结构振型对给定风速和振动幅值的颤振响应的参与. 所提出方案的准确性与经典的双峰分析方法进行了交叉验证。两个悬索桥，分别以软型和硬型非线性颤振为特征，用于检查所提出方法的性能。模态特性（即阻尼比和频率），作为风速和振动幅度的函数，可以估计，从而可以准确量化包括临界风速和振动幅度在内的非线性颤振响应。最后还讨论了不同结构模式之间的耦合效应及其对非线性颤振发生和演化的进一步影响。