Three-dimensional reconfiguration of an elastic sheet with unidirectional side flaps

Abstract

Motivated by drag-based propulsion of crinoids, the shape reconfiguration of a feather-like elastic structure under both steady and unsteady translational motions is investigated. The simplified elastic structure consists of a centre rod to which numerous side flaps are attached by elastic hinges. These side flaps fold in only one direction to realize a dramatic reduction in the area of the structure during the recovery stroke. Compared with experimental measurements, analytical methods developed to couple the dynamics of the centre rod and the side flaps successfully predict the drag force and three-dimensional reconfiguration of the elastic structure during both power and recovery strokes. A dimensionless speed given by the ratio of inertial fluid force to elastic bending force is proposed for the coupled deflections of the centre rod and side flaps, and is found to determine primarily the reconfiguration of the elastic structure. A reconfiguration number defined specifically for our model provides an appropriate characterization of the effect of side-flap folding on drag force reduction. Moreover, the ratio of drag forces between the power and recovery strokes is evaluated to find model conditions for the optimal force ratio.