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The origin of hysteresis in the flag instability

Published online by Cambridge University Press:  08 December 2011

Christophe Eloy ,
Nicolas Kofman  and
Lionel Schouveiler
Christophe Eloy*
Affiliation:
IRPHE, CNRS & Aix-Marseille Université, 49 rue Joliot-Curie, 13013 Marseille, France Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA
Nicolas Kofman
Affiliation:
IRPHE, CNRS & Aix-Marseille Université, 49 rue Joliot-Curie, 13013 Marseille, France
Lionel Schouveiler
Affiliation:
IRPHE, CNRS & Aix-Marseille Université, 49 rue Joliot-Curie, 13013 Marseille, France
*
†Email address for correspondence: Christophe.Eloy@irphe.univ-mrs.fr
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Abstract

The flapping flag instability occurs when a flexible cantilevered plate is immersed in a uniform airflow. To this day, the nonlinear aspects of this aeroelastic instability are largely unknown. In particular, experiments in the literature all report a large hysteresis loop, while the bifurcation in numerical simulations is either supercritical or subcritical with a small hysteresis loop. In this paper, the discrepancy is addressed. First, weakly nonlinear stability analyses are conducted in the slender-body and two-dimensional limits, and, second, new experiments are performed with flat and curved plates. The discrepancy is attributed to inevitable planeity defects of the plates in the experiments.

JFM classification

Nonlinear Dynamical Systems: Bifurcation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 583 - 593
Copyright
Copyright © Cambridge University Press 2011

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