Small amplitude oscillations of a shape-morphing plate immersed in a viscous fluid near a solid wall

Abstract

In this paper, we investigate small amplitude oscillations of a thin shape-morphing plate submerged in a quiescent, Newtonian, incompressible, viscous fluid in the vicinity of a solid wall. The plate undergoes prescribed, time-varying shape-morphing deformation in phase with the transverse oscillation, consisting of periodic curvature to an arc of a circle. As the presence of the solid wall in close proximity of the oscillating plate is known to significantly increase hydrodynamic damping on the structure due to squeeze film effects, shape-morphing is considered as a potential strategy to modulate and control hydrodynamic forces, as well as power dissipation. Via a rigorous formulation based on unsteady Stokes equations and the boundary element method, we show that the shape-morphing strategy is effective in reducing hydrodynamic forces on the structure as well as hydrodynamic power dissipation due to viscous effects. Additionally, such a reduction is enhanced as the gap between the oscillating plate and the solid wall is reduced. We present a comprehensive parametric study which investigates the effect of oscillation frequency, gap size, and imposed curvature on the hydrodynamic performance of the system and support our findings with asymptotics from inviscid flow theory and lubrication theory. These findings are of direct interest and applicability in several cantilever-based sensing and actuation systems, such as atomic force microscopy and microelectromechanical systems in liquids.