In this paper, the flapping dynamics and wake flow characteristics in the nonlinear hysteresis region are investigated experimentally by immersing a cantilevered flexible plate in uniform airflow. The experimental results show that the flapping mode of a cantilevered flexible plate in hysteresis region will be transited from periodical traveling wave mode to limited cantilever-like mode with the variation of Reynolds number. The flapping mode will greatly influence the kinetic parameters of a flexible plate and also wake flow characteristics. The comparison of Strouhal number values between flapping flexible plate and animals further indicates that the fluid dynamics between passive flapping and active swimming is similar to the obtained optimal propulsive efficiency. Flow visualization reveals that the Karman vortex street appears, vanishes and coherent structures of turbulent flow arise behind the stable flexible plate with increasing Reynolds number. Meanwhile, the measurements of pressure distribution in wake flow provide a good physical understanding of the energy-saving mechanism and the optimal arrangement in fish school. Moreover, the fast Fourier transform (FFT) spectra of fluctuating velocity indicate that the characteristics of wake flow are closely related to the flapping mode of flexible plate. The wake flow will come into strong harmonic excitation state when flapping mode transits into a limited cantilever-like mode.

中文翻译：

---

非线性迟滞区柔性板的扑动动力学和尾流特性研究

在本文中，通过将悬臂柔性板浸入均匀气流中，对非线性滞后区域的扑动动力学和尾流特性进行了实验研究。实验结果表明，随着雷诺数的变化，悬臂式柔性板在滞后区的扑动模式会从周期行波模式转变为有限的类悬臂模式。扑动模式将极大地影响柔性板的动力学参数以及尾流特性。拍动柔性板与动物之间的 Strouhal 数值比较进一步表明，被动拍动和主动游泳之间的流体动力学与获得的最佳推进效率相似。流动可视化显示卡门涡街出现，随着雷诺数的增加，湍流的消失和相干结构出现在稳定的柔性板后面。同时，尾流中压力分布的测量提供了对节能机制和鱼群优化布置的良好物理理解。此外，脉动速度的快速傅里叶变换（FFT）谱表明，尾流的特性与柔性板的扑动模式密切相关。当扑动模式转变为有限的类悬臂模式时，尾流将进入强谐波激励状态。尾流中压力分布的测量提供了对节能机制和鱼群优化布置的良好物理理解。此外，脉动速度的快速傅里叶变换（FFT）谱表明，尾流的特性与柔性板的扑动模式密切相关。当扑动模式转变为有限的类悬臂模式时，尾流将进入强谐波激励状态。尾流中压力分布的测量提供了对节能机制和鱼群优化布置的良好物理理解。此外，脉动速度的快速傅里叶变换（FFT）谱表明，尾流的特性与柔性板的扑动模式密切相关。当扑动模式转变为有限的类悬臂模式时，尾流将进入强谐波激励状态。