Nonlinear hydrodynamic damping of sharp-edged cantilevers in viscous fluids undergoing multi-harmonic base excitation

In this paper, we investigate finite amplitude polychromatic flexural vibration of a thin beam oscillating in a quiescent viscous fluid. We consider a cantilever beam with rectangular cross section undergoing periodic base excitation in the form of a triangular wave. Experiments are performed on centimeter-size beams in water to elucidate the effect of the amplitude and the frequency of the base excitation on the fluid structure interaction. The fundamental frequency of the excitation is selected to induce structural resonance and the shape of the cantilevers is parametrically varied to explore different flow regimes. Experimental results demonstrate the presence of a frequency-dependent nonlinear hydrodynamic damping which tends to enhance higher frequency harmonics as compared to the fundamental harmonic. Such filtering effect produced by the encompassing fluid increases with both the frequency and amplitude of the base excitation. Experimental results are interpreted through available theoretical models, based on the notion of the complex hydrodynamic function, and pertinent computational fluid dynamics findings.