Two-Dimensional Hydrodynamic Forces in an Array of Shape-Morphed Cantilever Beams

In this paper, we estimated the hydrodynamic force in an array of cantilever beams separated by a distance \(\bar{s}\) oscillating in a viscous fluid. The beam is assumed to be sufficiently long to consider 2D flow and has symmetric as well as asymmetric shape morphing curvature while oscillating in a fluid. The fluid-structure interaction problem is modelled by considering the unsteady Stokes equation. The resulting 1D boundary integral problem is solved by the boundary element method (BEM) numerically in MATLAB to obtain the desired pressure distribution on the beam. It is found that as the frequency oscillation of the rigid beam is increased, both the damping as well as added mass effects are decreased at different rates due to the gradual decrease in unsteady viscous layer. Finally, the hydrodynamic coupling effect on the beam is demonstrated at \(\beta =0.1\). However, for increase in the symmetric and asymmetric shape morphing parameters, the hydrodynamic decoupling appears lower than the gap ratio 5. The cantilever beam with optimal shape morphing parameter can be useful for the optimal designs of atomic force microscopy (AFM).