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

Abstract

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 nondimensional parameters.

Harmonic oscillations of a thin lamina in a quiescent viscous fluid: A numerical investigation within the framework of the lattice Boltzmann method

“…Several analytical and numerical studies have been carried out on this topic during the last decades [19][20][21][22]. More recently, several authors have discussed the effect of various parameters such as the compressibility of the flow [23], the interplay between two solid bodies [24,25], the presence of a solid wall close to the beam [26][27][28] or the role of a shear-dependent viscosity [29].…”

Response of a fluid-immersed microcantilever close to a deformable body

“…It would also allow us to consider tipped microcantilevers (although this is perhaps less of an issue for glass fibres). It would also be useful to see how key spectral quantities such as the resonant frequency, and quality factor, change as a function of the nondimensional parameters, as in the multiple microcantilever studies of Intartaglia et al 5 At the moment, the computational cost makes this prohibitively expensive, and so it could be valuable to investigate what model reductions could be made. Also, consideration of viscoelastic, rather than purely elastic, microrheologies could be very valuable.…”

“…In a landmark theoretical paper, Sader 1 developed a model to describe the thermal response of an isolated microcantilever immersed in a viscous fluid, and later demonstrated its ability to faithfully reproduce spectra obtained experimentally. 3 Subsequent studies demonstrated how the finite-amplitude effects, [34][35][36] different modes of vibration, 37,38 the presence of neighbouring microcantilevers, 4,5,[7][8][9][10] or nearby rigid surfaces 2,[11][12][13][14][15][16]35,39,40 can all modify the microcantilever's frequency response via hydrodynamics.…”

Doubling the quality factor of cantilevers in liquid through fluid coupling-based actuation

“…This is the case with photothermal excitation [11], where the driving force is focused directly on the cantilever and not on other elements such as the substrate. The development of a physical model to describe our proposed fluid-coupling based actuation method will certainly require detailed simulation due to the complex relationship between the motion of both cantilevers and the surrounding fluid [15]. We leave this work for a future study and focus instead on a preliminary experimental analysis to introduce the concept.…”