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Large-amplitude membrane flutter in inviscid flow

Published online by Cambridge University Press:  26 March 2020

C. Mavroyiakoumou  and
S. Alben Open the ORCID record for S. Alben [Opens in a new window]
C. Mavroyiakoumou*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109, USA
S. Alben*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional 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 to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming flow.

JFM classification

Instability: Nonlinear instability Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A23
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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