Modulation of Nonlinear Hydrodynamic Damping in Finite Amplitude Underwater Oscillations of Flanged Structures

In this paper, we study the fluid-structure interaction problem of the harmonic oscillations of a flanged lamina in a quiescent, Newtonian, viscous fluid. Here, the flanges are introduced to elicit specific vortex-structure interactions, with the ultimate goal of modulating the nonlinear hydrodynamic damping experienced by the oscillating structure. The hydrodynamic forcing, incorporating added mass and hydrodynamic damping effects, is evaluated through boundary element method and computational fluid dynamics simulations. This allows to identify a model for the hydrodynamic forces in the form of a complex-valued function of three nondimensional parameters, describing oscillation frequency and amplitude and flange size. We find that the presence of the flanges results into larger fluid entrainment during the lamina oscillation, thus affecting the added mass. Further, we highlight the existence of a minimum in the hydrodynamic damping which is governed by complex dynamics of vortex-structure interaction. This peculiar phenomenon is discussed from physical grounds by analysis of the pertinent hydrodynamic fields. Finally, we propose a tractable form for the hydrodynamic function, to be used in the study of large amplitude underwater flexural vibrations of flanged structures.