Experimental investigation of inclined cantilever beams in vertically falling soap films
Here we investigate the dynamic response of cantilever beam at various angles of attack using theory and experiments. The problem is motivated by separate wind tunnel experiments using energy producing piezoelectric cantilevers. Assuming small vibrational amplitudes, we utilize the Euler-Bernoulli beam theory to test semi-empirical correlations that are compared with measured quantities. To utilize the beam theory, we estimate the aerodynamic loading on the cantilever as the sum of a steady and harmonic component, each proportional to the aerodynamic pressure. Dynamically similar cantilever beams (5000 $<$ Re $<$ 25000) with varying flexural rigidity are studied in a vertically falling soap film experiment to visualize the wake and vortex shedding flow characteristics. High speed video and image analysis were used to estimate quantities such as the average displacement, vibration amplitude and frequency for the cantilevers. From the analysis we find the steady displacement force is linear with respect to the aerodynamic pressure. We define a coefficient which is the ratio of steady displacement force and aerodynamic pressure. We call this steady aerodynamic loading coefficient. We further show that there is a significant effect of inclination on this coefficient. Furthermore, this coefficient was found to be dependent on the flexible nature of the cantilever beam. The wake structure and the vortex shedding are visualized and analyzed for the vortex shedding frequency which is plotted against the frequency of beam vibrations. We also explore the relationship between the Strouhal, Reynolds numbers and angle of attack.