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 fixedfree 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

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We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3-D) inviscid fluid flow. We apply small initial perturbations and track their decay or growth to large-amplitude steady-state motions. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension and stretching rigidity. With free side edges we find good agreement with previous 2-D results that used different discretization methods. We find that the 3-D dynamics in the 12 cases naturally forms four groups based on the conditions at the leading and trailing edges. The deflection amplitudes and oscillation frequencies have scalings similar to those in the 2-D case. The conditions at the side edges, although generally less important, may have small or large qualitative effects on the membrane dynamics – e.g. steady vs unsteady, periodic vs chaotic or the variety of spanwise curvature distributions – depending on the group and the physical parameter values.

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We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly, and then considering the limit as the smoothing tends to zero. The analysis is generalized to derive a simple model for the behaviour at a junction between an arbitrary number of viscidas, which is then coupled to the governing equation for each viscida. We thus obtain a general theory, consisting of $N$ partial differential equations and $3J$ algebraic conservation laws, for a system of $N$ viscidas connected at $J$ junctions. This approach provides a framework to understand the fabrication of microstructured optical fibres containing closely spaced holes separated by interconnected thin viscous struts. We show sample solutions for simple networks with $J=2$ and $N=2$ or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses.