We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in 2D inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free, the membranes flutter with very small amplitudes and high spatial and temporal frequencies at small mass density. As mass density increases, the membranes transition to periodic and then increasingly aperiodic motions, and the amplitudes increase and spatial and temporal frequencies decrease. With both edges free, the membranes flutter similarly to the fixed-free case but also translate vertically with steady, periodic, or aperiodic trajectories, and with nonzero slopes that lead to small angles of attack with respect to the oncoming flow.

中文翻译：

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无粘流中的大振幅膜颤振

我们研究了二维无粘性流体流动中带有涡流片尾迹的膜（零弯曲刚度）的大振幅颤动。我们应用小初始偏转并跟踪它们的指数衰减或增长以及随后在三个无量纲参数空间中的大振幅动力学：膜预张力、质量密度和拉伸模量。在两端固定的情况下，所有膜会聚成稳定的偏转形状，带有几乎前后对称的单个驼峰，除非变形大得不切实际。由于前缘固定而后缘自由，膜以非常小的振幅和高空间和时间频率在小质量密度下颤动。随着质量密度的增加，膜过渡到周期性运动，然后逐渐增加非周期性运动，幅度增​​加，空间和时间频率降低。在两个边缘都自由的情况下，膜的颤动类似于固定自由的情况，但也会以稳定、周期性或非周期性的轨迹垂直平移，并且具有非零斜率，从而导致相对于迎面而来的流动的小迎角。