Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a novel sort of forcing. We consider a circular flexible plate clamped at its center and subject t
o a uniform flow normal to its initial surface. As the flow velocity is gradually increased, the plate exhibits a rich variety of bending deformations: from a cylindrical taco-like shape, to isometric developable cones with azimuthal periodicity two or three, to eventually a rolled-up period-three cone. We show that this sequence of flow-induced deformations can be qualitatively predicted by a linear analysis based on the balance between elastic energy and pressure force work.
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.
