Nonlinear resonant vibration of a partially immersed beam in viscous fluid.

This article presents an experimental exploration of the nonlinear vibration of a partially immersed cantilever beam. A set of hypotheses was developed to study the influence of the geometry (immersion depth and volume of the fluid) and fluid properties (viscosity and density) on the nonlinear response of the beam, and a test matrix of combinations of different parameters was generated. From the nonlinear experiments, linear parameters such as resonant frequency, damping ratio, and nonlinear parameters such as nonlinear frequency shift and nonlinear damping ratio were extracted. Finally, a regression analysis was carried out to determine the statistical relationships between different parameters, and the linear parameters were compared against results reported in the literature. The results suggest that the volume of the fluid has no dependence on the vibrational response, and a coupling between immersion depth, viscosity, and density was observed.