AIM Seminar: Membrane flutter in inviscid fluid flow

We develop different models to study the flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in two- and three-dimensional inviscid flows. For 2D flows, we use a nonlinear, time-stepping method to study large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching rigidity. With a linearized version of the membrane-vortex-sheet model we also investigate the instability of a membrane by solving a nonlinear eigenvalue problem iteratively, for three boundary conditions---both ends fixed, one end fixed and one free, and both free. We further consider a simple physical setup: a membrane held by tethers with hinged ends, that interpolates between the fixed--fixed and free--free cases. We additionally study an infinite membrane model mounted on a periodic array of Hookean springs. This model allows us to compute asymptotic scaling laws for how the frequencies, growth rates, and eigenmodes depend on membrane pretension and mass density. Finally, we develop a nonlinear model and computational method to study large-amplitude membrane flutter in 3D inviscid flow for 12 different boundary conditions.