Effect of a single gap on the dynamics of flexible plates*

Wind tunnel experiments and direct numerical simulations were conducted to investigate the impact of a single square perforation in the reconfigurations and unsteady dynamics of flexible rectangular plates at a porosity of 0.028. The analysis considered various Reynolds, Re, and Cauchy, Ca, numbers and the relative location of the perforation along the vertical axis of the plates. High-frequency force balance was used to obtain the unsteady aerodynamics force. Particle tracking velocimetry (PTV) and particle image velocimetry (PIV) were used to characterize the flexible plate deformation and flow field around the plates. Results show the modulation of the single perforation on the unsteady dynamics of the plate. Despite that the perforation imposed minor changes in mean reconfiguration, it significantly reduced tip fluctuation of the plates with perforations near the base. PTV shows two regimes where tip fluctuation sharply increases as a function of Ca and perforation location. Spectral analysis shows that the increase of tip motions is linked to the synchronization of the flow-induced frequency, fv, with the bending and twisting mode frequency depending on Ca. A plate softening effect may be produced for specific perforation locations. We propose a simple formulation for estimating fv considering the effective porosity and Vogel exponent, which is particularly useful for quantifying critical lock-in velocity for flexible plates.