The effect of aspect ratio and mass ratio on the flow-induced flutter of a thin flexible sheet

Abstract

This study experimentally investigates the flow-induced flutter of a thin flexible sheet, focusing on how the sheet's aspect ratio and mass ratio affect its stability and flutter characteristics in the post-critical regime. The flutter frequency of the sheet was obtained using hotwire measurements, while flutter amplitude and mode shape were acquired through high-speed imaging. The flowfield around the flapping sheet was analyzed using particle image velocimetry (PIV). Based on experimental observations, we report the onset of flutter as a subcritical bifurcation with hysteresis. The dynamic characteristics of the sheet play a significant role in its flutter instability, with the onset and cessation of flutter occurring at a frequency close to the sheet's second-mode natural frequency. The results show that both aspect ratio and mass ratio significantly affect the critical wind speed and flutter characteristics in the post-critical regime. Both flutter frequency and amplitude decrease as the aspect ratio decreases. PIV measurements in various planes reveal the highly three-dimensional nature of the flow. Results from off-axis PIV show a pair of counter-rotating spiral vortices in the wake that oscillate and change orientation with the sheet's movement. Additionally, a theoretical analysis was conducted to derive an approximate analytical relationship between the aspect ratio and critical wind speed. Experimental results aligned well with theoretical predictions for sheets with low aspect ratios (aspect ratio ≤1) but deviated for sheets with higher aspect ratios (aspect ratio >1). The relevant scaling parameters have also been explored to represent the experimental data in a non-dimensional form.