Hydrodynamic forces in array of uniform and non-uniform cantilever beams

Abstract

In this paper, we have implemented the three-dimensional Boundary Element Method (BEM) to solve the hydrodynamic forces in arrays of two, three, and five thin beams oscillating with small amplitudes in a fluid. We solve the unsteady Stokes equation by considering the oscillatory Stokeslet. The non-dimensional hydrodynamic function is validated through numerical solutions obtained using the Finite Element Method (FEM) at various frequency parameters and gap ratios. We analyse the influence of the relative phase and amplitude ratio of a uniform beam and a non-uniform two-beam array in terms of added mass and damping coefficients. Additionally, we compare the solution with experimental results available in the literature as a function of gap ratio. The analysis presented in this paper can be useful for optimizing arrays used in Atomic Force Microscope (AFM), biosensors, and energy harvesters.