Flow-induced oscillation of flexible bodies

Abstract

We present a combined theoretical and experimental investigation of two systems in which flexible bodies are induced to oscillate by steady flows. The first system we study consists of multiple thin sheets of paper in a steady flow, clamped at the downstream end, which we call the "clapping book". Pages sequentially lift off, accumulating in a stack of paper held up by the wind. When the elasticity and weight of the pages overcome the aerodynamic force, the book claps shut; this process then repeats. We investigate this system experimentally and theoretically, using the theory of beams in high Reynolds number flow, and test our predictions of the clapping period. The second system we consider is inspired by free-reed musical instruments, which produce sound by the oscillation of reeds, thin strips of metal tuned to specific pitches. Each reed is mounted above a slot on the upstream side of a support plate, a geometry that allows a steady flow to induce finite-amplitude oscillations. We study this system experimentally and propose models, also based on the theory of elastic beams in high Reynolds number flow. The relative merits of these models is assessed by comparing their predictions with experiments.