We investigate the dynamics of membranes that are held by freely-rotating rigid tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations in terms of deflection amplitudes, dominant periods, and numbers of local extrema of deflection along the membranes across the parameter space of membrane mass density, stretching modulus, pretension, and tether length. We determine the region of instability and the small-amplitude behavior by solving a nonlinear eigenvalue problem. We also consider an infinite periodic membrane model, which yields a regular eigenvalue problem, analytical results, and asymptotic scaling laws. We find qualitative similarities among all three models in terms of the oscillation frequencies and membrane shapes at small and large values of membrane mass, pretension, and tether length/stiffness.

我们研究了由流体流动中自由旋转的刚性系绳固定的膜的动力学。系留边界条件允许某些参数值的周期性和混沌振荡运动。我们根据膜质量密度、拉伸模量、预紧力和系绳长度的参数空间，根据偏转幅度、主导周期和偏转局部极值的数量来表征振荡。我们通过解决非线性特征值问题来确定不稳定区域和小幅度行为。我们还考虑了一个无限周期膜模型，它产生了一个规则的特征值问题、分析结果和渐近缩放定律。