Large-amplitude membrane flutter in inviscid flow

We study the dynamics of thin membranes---extensible sheets with negligible bending stiffness---fixed at both ends and aligned with a uniform inviscid background flow. This is a benchmark fluid-structure interaction that has previously been studied mainly in the small-deflection limit, to identify the flutter behavior of membranes. Recent work has also considered applications of thin membranes to shape-morphing airfoils. First, we characterize growth rates and frequencies at small amplitude with respect to mass ratio and membrane pretension. We find general agreement with previous work in the locations of divergence and flutter, but we find an increased range of unstable motions. Our method is able to compute stable large-amplitude motions, but only at sufficiently large stretching modulus. We describe how the membranes' motions and frequencies change in the transition from small- to large- amplitude motions. We also describe transitions from periodic to chaotic dynamics as pretension is decreased and mass ratio is increased.