  We study the large-amplitude flutter of membranes (of zero bending rigidity)
with vortex-sheet wakes in 2D inviscid fluid flows. We apply small initial
deflections and track their exponential decay or growth and subsequent
large-amplitude dynamics in the space of three dimensionless parameters:
membrane pretension, mass density, and stretching modulus. With both ends
fixed, all the membranes converge to steady deflected shapes with single humps
that are nearly fore-aft symmetric, except when the deformations are
unrealistically large. With leading edges fixed and trailing edges free, the
membranes flutter with very small amplitudes and high spatial and temporal
frequencies at small mass density. As mass density increases, the membranes
transition to periodic and then increasingly aperiodic motions, and the
amplitudes increase and spatial and temporal frequencies decrease. With both
edges free, the membranes flutter similarly to the fixed-free case but also
translate vertically with steady, periodic, or aperiodic trajectories, and with
nonzero slopes that lead to small angles of attack with respect to the oncoming
flow.
