The origin of hysteresis in the flag instability

TL;DR

This paper investigates the large hysteresis observed in the flag flutter instability, combining theoretical analyses and experiments, and attributes the discrepancy to plate imperfections.

Contribution

It provides a combined theoretical and experimental study addressing the origin of hysteresis in flag instability, highlighting the role of plate imperfections.

Findings

Weakly nonlinear stability analyses explain the bifurcation behavior.

Experimental results show plate imperfections influence hysteresis size.

Discrepancy between simulations and experiments is due to plate defects.

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, this 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.