The hysteresis in flutter amplitude of almost ideally flat flexible membranes

Fluid flow along a flexible membrane which is clamped at its leading edge can lead to self-excited oscillations, also referred to as flutter. Interestingly, the critical fluid velocity that is required to initiate flutter is typically higher than the velocity below which a fluttering membrane stops moving. Systematic investigations of this hysteresis have been impeded in past studies because experimentally measured critical flow velocities can be highly sensitive to flatness defects in the membranes. The present study investigates the hysteresis in flutter amplitude of specimens whose flatness defects are negligible with respect to their thickness, as quantified by means of stereophotogrammetry. We present how the two dimensionless parameters mass ratio and aspect ratio determine the critical velocities of onset and ceasing of flutter. Remarkably, significant hysteresis is observed also in slender flags. Based on the observations, a hypothesis for the origin of the hysteresis in flutter amplitude is derived, which is valid for cases where flatness defects are not dominant. This hypothesis is further supported qualitatively by low-order modeling with ordinary differential equations.