Abstract The flutter of a rigid panel is considered as a super/subcritical Hopf bifurcation. However, the initial conditions of such characteristics have not been extensively explored. In this study, a 2-DOF rigid rectangular panel was tested in a wind tunnel at zero angle of attack to investigate the flutter stability, with and without external excitations, in the Reynolds number range of 6.15–8.21×104. Coupled flutter occurs abruptly and evolves into four stages as the inflow wind velocity reaches a critical flutter velocity, Ucr. A hysteresis loop is observed when the wind velocity is decreased from Ucr to 0.75Ucr. External excitations are applied to the test model stepwise in the hysteresis region to examine the stability conditions. The critical excitation amplitude, Acr, is determined, which corresponded to the unstable limit cycle of the subcritical Hopf bifurcation. A fitted equation of the bifurcation is provided to correlate the flutter amplitude and the critical excitation amplitude with wind speed. PIV measurements show the flow field evolution around the panel during the entire flutter occurrence process. The size of the leading-edge vortex expands as the oscillation amplitude increases, then convects to the trailing edge and eventually sheds into the wake region. Wake patterns of each flutter stage were illustrated and analyzed using the Dynamic Mode Decomposition (DMD) method.

中文翻译：

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外部激励对二自由度刚性矩形板颤振特性的影响

摘要 刚性板的颤振被认为是超/亚临界Hopf分岔。然而，这些特性的初始条件尚未得到广泛探索。在这项研究中，一个 2-DOF 刚性矩形板在风洞中以零攻角进行测试，以研究在雷诺数范围为 6.15-8.21×104 的情况下，有和没有外部激励的颤振稳定性。当流入风速达到临界颤振速度 Ucr 时，耦合颤振突然发生并演变为四个阶段。当风速从 Ucr 降低到 0.75Ucr 时，观察到滞后回线。外部激励在滞后区域逐步应用于测试模型，以检查稳定性条件。临界激励振幅 Acr 确定，这对应于亚临界 Hopf 分岔的不稳定极限循环。提供了分岔的拟合方程，以将颤振幅度和临界激励幅度与风速相关联。PIV 测量显示在整个颤振发生过程中面板周围的流场演变。前缘涡的大小随着振荡幅度的增加而扩大，然后对流到后缘并最终落入尾流区域。使用动态模式分解 (DMD) 方法说明和分析每个颤振阶段的尾流模式。PIV 测量显示在整个颤振发生过程中面板周围的流场演变。前缘涡的大小随着振荡幅度的增加而扩大，然后对流到后缘并最终落入尾流区域。使用动态模式分解 (DMD) 方法说明和分析了每个颤振阶段的尾流模式。PIV 测量显示在整个颤振发生过程中面板周围的流场演变。前缘涡的大小随着振荡幅度的增加而扩大，然后对流到后缘并最终落入尾流区域。使用动态模式分解 (DMD) 方法说明和分析了每个颤振阶段的尾流模式。