# Research on the Coupled Bending-Torsional Flutter Mechanism for Ideal Plate
## 1 Introduction
Both types of flutter are self-excited oscillations caused by torsional aerodynamic damping, specifically, a mechanism known as the \"torsional negative damping drive\", which induces flutter in bluff body sections. [PERSON] [18] used the \"step-by-step solution\" method to analyze the torsional coupling flutter of the Akashi Kaikyo Bridge and the torsional flutter of the Suramadu Bridge. [PERSON] [19; 20; 21] utilized the \"incentive feedback\" mechanism to separate the modal analysis of bending-torsion-coupled vibration. They identified the aerodynamic damping associated with both vertical and torsional modes. The research findings on the \"incentive feedback\" mechanism reveal how the self-excited, lift-induced vertical bending system responds to torsional displacement. The self-excited moments caused by vertical vibrations act as aerodynamic negative damping in the torsional vibration system. This interaction can lead to the divergence of the torsional vibrations in the bridge structure. The vertically vibrating system, influenced by coupled self-excited lift, enters a divergent state that causes torsional coupling flutter in the bridge structure. This phenomenon, known as the \"torsional negative damping drive\" mechanism, is responsible for the torsional coupling flutter of the bridge. [PERSON] [22; 23; 24] conducted research on the mechanisms of coupled flutter and torsional flutter, using the theory known as \"coupled flutter closure solution\". He transformed the time-domain vibration equations into complex-domain vibration equations through Laplacetransformation, considering the characteristics of very small structural damping ratios. He simplified the terms related to complex frequencies, and then decoupled them using the bending-torsion amplitude ratio function. Finally, based on the real and imaginary parts of the vibration equations, he identified the vertical and torsional modal damping ratios and modal frequencies. His research revealed that torsional negative damping results in torsional-axial coupling flutter, which aligns with the analysis conclusion regarding the \"incentive feedback\" mechanism. However, the existing \"incentive feedback\" theory fails to strictly adhere to the vibration equation when performing modal decoupling of the coupled vibration system through the \"incentive feedback\" mechanism. Moreover, the process of flutter aerodynamic damping identification necessitates a cyclic search for the vibration frequency, leading to low identification efficiency. In this paper, we explore the influence of direct aerodynamic damping and direct aerodynamic stiffness on the intrinsic damping and stiffness of the structure, building on the \"incentive feedback\" mechanism of flutter and previous research findings [19; 20; 21]. A flutter equation system is developed, and we perform modal decoupling of the coupled vibration system using the \"incentive feedback\" mechanism to identify the modal damping and modal stiffness. Compared to the previous analysis theory of the \"incentive feedback\" mechanism for flutter, this paper, while adhering to the flutter vibration equation, omits the cyclic search process for identifying flutter aerodynamic damping, thereby improving computational efficiency.