Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid

In this paper, we study flexural vibrations of two thin beams that are coupled through an otherwise quiescent viscous fluid. While most of the research has focused on isolated beams immersed in placid fluids, inertial and viscous hydrodynamic coupling is ubiquitous across a multitude of engineering and natural systems comprising arrays of flexible structures. In these cases, the distributed hydrodynamic loading experienced by each oscillating structure is not only related to its absolute motion but is also influenced by its relative motion with respect to the neighbouring structures. Here, we focus on linear vibrations of two identical beams for low Knudsen, Keulegan-Carpenter and squeeze numbers. Thus, we describe the fluid flow using unsteady Stokes hydrodynamics and we propose a boundary integral formulation to compute pertinent hydrodynamic functions to study the fluid effect. We validate the proposed theoretical approach through experiments on centimetre-size compliant cantilevers that are subjected to underwater base-excitation. We consider different geometric arrangements, beam interdistances and excitation frequencies to ascertain the model accuracy in terms of the relevant non-dimensional parameters.