Aquatic locomotion by an elastically mounted flexible foil actuated by an oscillating force
An analytical formulation of the fluid-structure interaction of a flexible foil driven by an oscillating force actuating on its elastically mounted leading edge, so that it can heave, pitch and deform passively with the hydrodynamic forces, is used to investigate the aquatic locomotion of a body, responsible for the whole drag and thrusted by the oscillating flexible foil. The small-amplitude theoretical model is validated with previous theoretical and experimental results for a body propelled by a rigid plate oscillating with a prescribed heaving motion and passive pitch. The inclusion of passive heave and deformation allows to expand the parametric ranges for optimal self-propulsion conditions in terms of length travelled by flapping cycle (stride length) and locomotion efficiency. In addition to the known optimal locomotion condition localized near the resonance of the torsional spring on which the foil is elastically mounted, which here is modulated by its coupling with the resonances of the translational spring and of the structural deformation of the foil, another even better local optimal locomotion condition is found near the translational spring branch of the elastic support resonance that occurs at lower stiffnesses of both springs. Unlike the local maximum of efficiency close to the natural frequency associated with the torsional spring branch, which increases with the stiffness of the foil, being the highest for a rigid foil, the larger local maximum associated with the translational spring branch increases as the stiffness of the foil decreases.