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In this paper, we study finite amplitude bending vibrations of a slender thin beam immersed in a quiescent viscous liquid and oscillating near a solid surface. We focus on the regime of low Knudsen and squeeze numbers and moderately large Keulegan-Carpenter number, for which neither squeeze film models nor unsteady Stokes hydrodynamics are suitable to describe the flow physics. In this case, the distributed hydrodynamic loading experienced by the oscillating beam is represented by a complex-valued hydrodynamic function, which explicitly depends on the Keulegan-Carpenter number to account for convection-driven nonlinearities in the fluid-structure interaction. We conduct a parametric study on the two-dimensional computational fluid dynamics of a rigid lamina oscillating in the vicinity of a solid surface to establish a handleable semianalytical formula for the hydrodynamic function in terms of the key nondimensional parameters. We validate the proposed modeling approach through experiments on centimeter-size compliant cantilevers vibrating underwater under base excitation at varying distances from a rigid wall.