Spanwise variations in membrane flutter dynamics

Abstract

We study the large-amplitude flutter of rectangular membranes in 3-D inviscid flows. The membranes’ deformations vary significantly in both the chordwise and spanwise directions. Many previous studies used 2D flow models and neglected spanwise variations, so here we focus on cases with significant spanwise nonuniformity. We determine when such cases occur and how the dynamics vary over the parameter space of membrane mass and pretension for two sets of boundary conditions and two values of both the Poisson ratio and the membrane aspect ratio. With spanwise symmetric and asymmetric initial perturbations, the motions differ for long times but eventually reach the same steady state in most cases.

At large times, spanwise symmetric and asymmetric oscillations are seen, with the latter more common. Oscillations are often in the form of “side-to-side” and other standing wave motions along the span, as well as traveling wave motions, particularly with free side-edges. Motions are generally nonperiodic and more spatially complex with a large membrane mass, and sometimes periodic at small-to-moderate membrane mass. A large Poisson ratio gives somewhat smoother spatial and temporal features in the dynamics at a given pretension. Increasing the aspect ratio makes the deflection more uniform along the span. With different chordwise and spanwise pretensions we find motions that are qualitatively similar to cases with isotropic pretensions between the anisotropic values.