# Large-amplitude membrane flutter in inviscid flow

## TL;DR

This paper investigates the large-amplitude flutter behavior of membranes in inviscid flows, analyzing how different boundary conditions and physical parameters influence their stability, motion patterns, and steady states.

## Contribution

It provides a comprehensive analysis of membrane flutter dynamics in inviscid flow, highlighting the effects of boundary conditions and physical parameters on stability and motion.

## Key findings

- Membranes with fixed ends settle into symmetric steady shapes.
- Membranes with free edges exhibit flutter with varying amplitudes and frequencies.
- Increased mass density leads to more complex, less periodic membrane motions.

## Abstract

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.