Theoretical and experimental investigations of the dynamics of cantilevered flexible plates subjected to axial flow

Abstract

In this paper, the dynamics of cantilevered flexible plates subjected to axial flow is investigated theoretically and experimentally. A nonlinear equation of motion of the plate based on the inextensibility assumption, coupled with an unsteady lumped vortex model for the aerodynamic part is used to analyze the instability and post-critical dynamical behaviour of this fluid–structure system theoretically. Experiments have been conducted in a 3 ft×2 ft (914 mm×610 mm) cross-section wind tunnel, using polypropylene carbonate (PPC) films, thin brass plates, polyethylene terephthalate (PET) sheets, and type 304 stainless steel sheets, with maximum dimensions 224 mm×168 mm. In the experiments, time traces, power spectral densities (PSDs), phase-plane plots, Poincaré maps, probability density functions (PDFs) and autocorrelations are used to characterize the motions of the system. Periodic and chaotic oscillations have been observed in the experiments. It has also been observed that flutter arises via a subcritical bifurcation involving hysteresis for large aspect ratio plates; this hysteresis does not occur for low aspect ratio plates. The hysteresis phenomenon is considered to be due to spanwise deformation of the plates. The effect of aspect ratio on critical flow velocity is investigated. The experimental critical flow velocities for flutter onset are in good agreement with the theoretically predicted values.