A novel three-dimensional (3D) multi-modal analytical method is proposed in the present study for investigating the dynamic mechanism of long-span bridge flutter. The multi-modal coupled flutter differential equations are derived in a practical manner utilizing the principle of virtual work in this method, and the explicit expressions of system damping and stiffness are established through the excitation-feedback mechanism. Consequently, this method can not only conveniently identify the critical point of 3D bridge flutter, but also provide a comprehensive understanding of the underlying mechanism involved in 3D bridge flutter. The well-known coupled aerodynamic damping related to flutter derivatives ${\mathit{\text{A}}}_{\text{1}}^{\ast }$ and ${\mathit{\text{H}}}_{\text{3}}^{\ast }$, which is principally responsible for the coupled flutter, is further subdivided in this study to reveal the intrinsic coupled mechanism of flutter participating modes: The aerodynamic coupled degree between a certain vertical bending mode and the fundamental torsional mode can be ascertained by evaluating the similarity factor between their mode shapes; the phase angle between a certain vertical bending mode and the fundamental torsional mode, which is largely dominated by the numerical relationship between natural and flutter frequency, determines whether the aerodynamic coupled effect associated with the two modes drives or restrains flutter.

本研究提出了一种新颖的三维（3D）多模态分析方法，用于研究大跨桥梁颤振的动力机制。该方法利用虚功原理实用地推导了多模态耦合颤振微分方程，并通过激励反馈机制建立了系统阻尼和刚度的显式表达式。因此，该方法不仅可以方便地识别3D桥梁颤振的临界点，而且可以全面了解3D桥梁颤振的潜在机制。著名的与颤振导数相关的耦合气动阻尼${\mathit{\text{A}}}_{\text{1}}^{*}$和${\mathit{\text{H}}}_{\text{3}}^{*}$是耦合颤振的主要原因，本文进一步细分，以揭示颤振参与模态的内在耦合机制：通过评估相似因子可以确定某一垂直弯曲模态与基本扭转模态之间的气动耦合程度它们的振型之间；特定垂直弯曲模式和基本扭转模式之间的相位角主要由固有频率和颤振频率之间的数值关系决定，决定与两种模式相关的气动耦合效应是驱动还是抑制颤振。