Membrane flutter in three-dimensional inviscid flow

TL;DR

This study models and numerically analyzes large-amplitude flutter of 3D membranes in inviscid flow, revealing stability thresholds and dynamic behaviors across various boundary conditions and physical parameters.

Contribution

It introduces a novel 3D model and numerical method for membrane flutter, extending previous 2D results and classifying dynamics based on boundary conditions.

Findings

Good agreement with 2D results for free side edges

Identification of four dynamic groups based on boundary conditions

Scaling laws for deflection amplitudes and frequencies

Abstract

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 (3D) 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 2D results that used different discretization methods. We find that the 3D dynamics in the 12 cases naturally form 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 2D case. The conditions at the side edges, though generally less important, may have small or large qualitative effects on the membrane dynamics -- e.g. steady versus unsteady, periodic versus chaotic, or the variety of spanwise curvature distributions -- depending on the group and the physical parameter values.