Reconfiguration and oscillations of a vertical, cantilevered-sheet subject to vortex-shedding

TL;DR

This study investigates the dynamic behavior of a flexible sheet in a water flow, revealing how vortex shedding influences its static shape and oscillations, with a simple model capturing key oscillation features.

Contribution

It introduces a model for sheet tip oscillations under vortex forcing and explores the complex dynamic phenomena including lock-in and flow-induced vibrations.

Findings

Static deflection approximated by equilibrium of forces.

Upstream vortices hinder reconfiguration.

Model accurately predicts tip oscillation amplitudes.

Abstract

The dynamics of a thin low-density polyethylene sheet subject to periodic forcing due to B\'enard-K\`arm\`an vortices in a long narrow water channel is investigated here. In particular, the time-averaged sheet deflection and its oscillation amplitude are considered. The former is first illustrated to be well-approximated by the static equilibrium between the buoyancy force, the elastic restoring force, and the profile drag based on the depth-averaged water speed. Our observations also indicate that the presence of upstream vortices hinder the overall reconfiguration effect, well-known in an otherwise steady flow. For the sheet tip oscillations, a simple model based on torsional-spring-mounted flat plate correctly captures the measured tip amplitude over a wide range of sheet physical properties and flow conditions. Furthermore, a rich phenomenology of structural dynamics including vortex-forced-vibration, lock-in with the sheet natural frequency, flow-induced vibration due to the sheet wake, multiple-frequency and modal response is reported.