Nonlinear oscillations of shape-morphing submerged structures: Control of hydrodynamic forces and power dissipation via active flexibility

Abstract

In this paper, we consider nonlinear oscillations of a shape-morphing plate submerged in a quiescent, Newtonian, viscous fluid. We investigate the two-dimensional problem arising from two prescribed concurrent periodic motions of the plate: a rigid oscillation along its transverse direction coupled to a shape-morphing deformation to an arc of a circle with prescribed maximum curvature. As opposed to existing literature concerned with passive flexible structures, this study focuses on actively prescribed deformations of the structure as a means to manipulate the vortex-shedding and convection patterns responsible for hydrodynamic forces and power dissipation during underwater oscillations. We elucidate the potential of the proposed shape-morphing strategy in regulating the added mass and damping effects along with the hydrodynamic power dissipation both in the linear and nonlinear hydrodynamic regime, by utilizing a linear boundary integral formulation as well as computational fluid dynamics simulations. Results show the possibility of minimizing the hydrodynamic power dissipation for optimal values of the imposed curvature, along with significant reduction of the hydrodynamic forces. A simplified semianalytical argument relates these novel effects to specific geometric properties of the plate motion. Findings from this study are directly relevant to cantilever-based sensing and actuation systems operating in fluids, where control and modulation of oscillation quality factors, hydrodynamic forces, and power losses is beneficial.