Finite amplitude vibrations of cantilevers of rectangular cross sections in viscous fluids

In this paper, we study finite amplitude vibrations of a cantilever beam of rectangular cross section immersed in a viscous fluid under harmonic base excitation. Fluid–structure interactions are modeled through a complex hydrodynamic function that describes added mass and damping effects in response to moderately large oscillation amplitudes. The hydrodynamic function is identified from the analysis of the two-dimensional flow physics generated by a rigid rectangle undergoing harmonic oscillations in a quiescent fluid. Computational fluid dynamics is used to investigate the effects of three salient non-dimensional parameters on the flow physics and inform the formulation of a tractable expression for the hydrodynamic function. Theoretical results are validated against experimental findings on underwater vibration of compliant beams of varying cross sections.