Three-Dimensional Analysis of Shape-Morphing Cantilever Oscillations in Viscous Fluids

In this paper, we study the linear flexural oscillations of a cantilever beam undergoing chord-wise shape-morphing deformation in a quiescent, Newtonian, viscous fluid. The shape-morphing deformation is prescribed for the beam cross section to an arc of a circle by specifying a periodic maximum curvature continuously along the axis of the structure. This particular strategy is investigated as a possible way to manipulate fluid-structure interaction mechanisms by modifying the hydrodynamic interactions in the vicinity of the submerged structure. Since we focus on the linear vibration of the beam, the fluid flow is described using three-dimensional unsteady Stokes hydrodynamics. By solving the linear unsteady Stokes problem in the frequency domain with a Stokeslet method, we identify the effect of the proposed shape-morphing strategy on the propulsion performance by estimating thrust, lift, and hydrodynamic power dissipation for a range of prescribed deformations. We verify the results obtained from our boundary element method against results from the existing literature. Our findings show a possible improvement in propulsion characteristics and minimization of hydrodynamic power dissipation, for an optimum level of shape-morphing deformation which is aspect ratio-dependent. Results from this study can aid in designing and operating cantilever-based underwater actuation systems for which the multi-objective goal of power losses reduction and propulsion performance improvement is sought.