Flapping states of an elastically anchored plate in a uniform flow with applications to energy harvesting by fluid-structure interaction

Linear stability analysis of an elastically anchored flat plate in a uniform flow is investigated both analytically and numerically. The analytical formulation explicitly takes into account the effect of the wake on the plate by means of Theodorsen's theory. Three different parameters non-trivially rule the observed dynamics: mass density ratio between plate and fluid, spring elastic constant, and distance between the plate center of mass and the spring anchor point on the plate. We found relationships between these parameters which rule the transition between stable equilibrium and fluttering. The shape of the resulting marginal curve has been successfully verified by high Reynolds number numerical simulations. Finally, the limiting case corresponding to a simply supported rigid rod is also analyzed and the resulting flapping instability traced back to a simple resonance condition. Our findings are of interest in applications related to energy harvesting by fluid-structure interaction, a problem that has recently attracted a great deal of attention. The main aim in that context is to identify the optimal physical/geometrical system configuration leading to large sustained motion, which is the source of energy one aims to extract.