Edge clearance effects on the added mass and damping of beams submerged in viscous fluids

Submerged structures that vibrate with a free boundary in close proximity to a comparatively rigid wall are commonly found in engineered systems. The confinement of the fluid in the gap can strongly influence the fluid added mass and damping associated with the structural vibration. Here, this influence is studied for submerged slender beams vibrating parallel to a wall, with small clearance between a lengthwise edge of the beam and the wall. The fluid-structure system is modeled using the Fourier transformed Stokes equations in two dimensions for incompressible viscous fluids. Added mass and damping are calculated with the use of a hydrodynamic function across a large range of Reynolds numbers and edge clearances. Relative to a previously studied case in which beams vibrate transversely to a rigid wall, the effects of the clearance gap in the present configuration - while significantly milder - are also more complicated. The results indicate that for a given Reynolds number, there is often a discrete gap height that maximizes fluid added mass or damping. This is in contrast to many other configurations where added mass and damping increase monotonically for fixed Reynolds number and increasing fluid confinement. A high-order polynomial is fit to the numerical results to facilitate their practical use. Experiments conducted in both water and vegetable oil validate the theoretical results across a wide parameter space.