论文标题
无粘性流中膜稳定性的本本符分析
Eigenmode analysis of membrane stability in inviscid flow
论文作者
论文摘要
当将膜沉浸在无粘性流体流中并散发出尾随的涡旋 - 表唤醒时，我们研究了薄膜（零弯曲刚度）的薄膜（零弯曲刚度）的不稳定性。对于三个规范的边界条件，我们在最初的猜测中迭代解决了非线性特征值问题 - 两者都固定，一端固定和一个免费，并且均为免费。在几个数量级的膜质量密度上，我们发现通过散发或颤动（尤其是在较大的质量密度下，或一个或两端的自由）的不稳定性。最不稳定的本征量通常在较小的质量密度和较小的张力下变为“波动”，但具有非单调行为区域。我们发现，与最终的稳态大振幅运动的定性相似性，我们发现与不稳定的时间步变模拟的良好一致性。
We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem iteratively with large ensembles of initial guesses, for three canonical boundary conditions---both ends fixed, one end fixed and one free, and both free. Over several orders of magnitude of membrane mass density, we find instability by divergence or flutter (particularly at large mass density, or with one or both ends free). The most unstable eigenmodes generally become "wavier" at smaller mass density and smaller tension, but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.
