Eigenmode analysis of membrane stability in inviscid flow

We study the stability of a thin membrane (of zero bending rigidity) with vortex sheet as nonlinear eigenvalue problem in parameter space mass (${R}_{1}$) and pretension (${T}_{0}$). With both ends fixed light membranes become unstable by divergence instability heavy lose flutter for ${T}_{0}$ that increases ${R}_{1}$. leading edge trailing free, or edges eigenmodes transition shape across boundary. find good quantitative agreement unsteady time-stepping simulations at small amplitude, but only qualitative similarities eventual steady-state large-amplitude motions.