Non-linear effects on the resonant frequencies of a cantilevered plate

In this paper, we address experimentally and theoretically the non-linear effects on the resonance of a periodically-forced cantilevered plate immersed in a fluid at rest. Experiments are performed with small aspect-ratio plates made of two different materials. When forced harmonically at their leading edges, these plates exhibit resonances for their first 3 structural modes. The frequencies at these resonances decrease when the forcing amplitude is increased, revealing the presence of non-linear effects. To model this phenomenon, a theoretical model is employed, which takes into account both resistive and reactive forces exerted by the fluid on the plate. By carrying out a weakly non-linear analysis, the frequencies at the resonances can then be determined. Model and experiments are in good agreement, showing that a weakly non-linear approach is suited to this kind of fluid-structure interaction and could be applied, in the future, to engineering problems such as energy harvesting with a fluttering plate or the biological problem of aquatic propulsion with a flexible fin.