The study of the dynamics of cantilevered thin flexible plates in reverse axial flow – also known as inverted flags – has become of significant interest, partly due to their energy harvesting potential. This paper presents fresh experimental results, aiming to enhance our understanding of the dynamics of inverted flags, particularly concerning stability and global dynamics sensitivity to various system parameters, such as the aspect ratio (i.e. height-to-length ratio) and flag material. This is achieved through testing flags of various dimensions, made from different materials. The dynamics of the system is presented in the form of bifurcation diagrams in which the flag tip angle is shown as a function of the dimensionless flow velocity. The frequency content of oscillatory motions is presented in the form of spectrograms. Also, time-histories, phase-plane portraits, as well as power spectral density and probability density function plots are presented for different flow regimes. Interesting dynamical features, such as small- and large-amplitude flapping, static divergence, large-amplitude buckling, and chaotic motions, have been observed experimentally, some for the first time. It is shown that for flags of very low aspect ratio the undeflected static equilibrium is stable prior to a subcritical pitchfork bifurcation. For flags of large aspect ratio, on the other hand, the undeflected static equilibrium becomes unstable via a supercritical pitchfork bifurcation leading to static divergence (buckling) at a sufficiently high flow velocity; at higher flow velocities, past the pitchfork bifurcation, a supercritical Hopf bifurcation materializes leading to flapping motion around the deflected static equilibrium; at even higher flow velocities, flapping motion becomes symmetric around the undeflected static equilibrium. Interestingly, it is found that heavy flags may exhibit large-amplitude flapping right after the initial static equilibrium, provided that they are subjected to a sufficiently large disturbance. In addition to experiments, nonlinear analytical models for the two asymptotic cases of zero and infinite aspect ratios are outlined, the results of which are used for comparison with the experimental results. Theory and experiments are found to be in reasonably good agreement.

对悬臂薄柔性板在反向轴向流动（也称为倒置标志）中的动力学的研究已经引起了广泛的兴趣，部分原因是它们具有能量收集的潜力。本文提出了新鲜的实验结果，旨在加深我们对倒置标志的动力学的理解，特别是关于稳定性和全局动力学对各种系统参数（例如长宽比（即长宽比）和标志材料）的敏感性。这是通过测试由不同材料制成的各种尺寸的标记来实现的。系统的动力学以分叉图的形式表示，其中标志的尖端角度显示为无因次流速的函数。振荡运动的频率内容以频谱图的形式表示。另外，时间历史 给出了针对不同流态的相平面图以及功率谱密度和概率密度函数图。有趣的动力学特征，如小振幅和大振幅拍打，静态发散，大振幅屈曲和混沌运动，已通过实验观察到，其中一些是首次观察到。结果表明，对于长径比非常低的标志，未弯曲的静态平衡在亚临界干草叉分叉之前是稳定的。另一方面，对于长宽比较大的标记，未偏转的静态平衡会由于超临界的干草叉分叉而变得不稳定，从而在足够高的流速下导致静态发散（屈曲）。在较高的流速下，经过干草叉分叉，超临界霍普夫分叉的形成导致围绕偏转的静态平衡的拍打运动。在更高的流速下，拍打运动围绕未偏转的静态平衡变得对称。有趣的是，发现如果重标记受到足够大的干扰，它们可能会在初始静态平衡后立即表现出大幅度的震荡。除实验外，还概述了两种纵横比为零和无限大的渐近情况的非线性分析模型，其结果用于与实验结果进行比较。发现理论和实验相当吻合。我们发现，如果重标记受到足够大的干扰，则在初始静态平衡之后，它们可能会表现出大幅度的震荡。除实验外，还概述了两种纵横比为零和无限大的渐近情况的非线性分析模型，其结果用于与实验结果进行比较。发现理论和实验相当吻合。我们发现，如果重标记受到足够大的干扰，则在初始静态平衡之后，它们可能会出现大幅度的拍动。除实验外，还概述了两种纵横比为零和无限大的渐近情况的非线性分析模型，其结果用于与实验结果进行比较。发现理论和实验相当吻合。