论文标题
三维无粘性流中的膜颤动
Membrane flutter in three-dimensional inviscid flow
论文作者
论文摘要
我们开发了一种模型和数值方法，以研究矩形膜（零弯曲刚度）的大幅度扑动，在三维（3D）Inviscid流体流中，将尾随的涡流唤醒放在尾随的涡旋式唤醒中。我们应用小的初始扰动，并将其衰减或生长跟踪到大振幅稳态运动。对于膜边缘的边界条件的12个组合，我们计算稳定性阈值以及随后在膜质量密度，预位和拉伸刚性的三参数空间上的随后的大振幅动力学。在自由边缘的情况下，我们发现使用了使用不同离散方法的先前2D结果一致。我们发现，在12个情况下的3D动力学自然会根据领先和尾随边缘的条件自然形成四组。挠度振幅和振荡频率的尺度与2D情况相似。侧边缘的条件虽然通常不太重要，但可能会对膜动力学产生微小或大的定性作用，例如稳定与不稳定，周期性与混乱或各种跨度曲率分布的变化 - 取决于组和物理参数值。
We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3D) inviscid fluid flow. We apply small initial perturbations and track their decay or growth to large-amplitude steady state motions. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension, and stretching rigidity. With free side edges we find good agreement with previous 2D results that used different discretization methods. We find that the 3D dynamics in the 12 cases naturally form four groups based on the conditions at the leading and trailing edges. The deflection amplitudes and oscillation frequencies have scalings similar to those in the 2D case. The conditions at the side edges, though generally less important, may have small or large qualitative effects on the membrane dynamics -- e.g. steady versus unsteady, periodic versus chaotic, or the variety of spanwise curvature distributions -- depending on the group and the physical parameter values.
