  Linear stability analysis of an elastically anchored wing in a uniform flow
is investigated both analytically and numerically. The analytical formulation
explicitly takes into account the effect of the wake on the wing by means of
Theodorsen's theory. Three different parameters non-trivially rule the observed
dynamics: mass density ratio between wing and fluid, spring elastic constant
and distance between the wing center of mass and the spring anchor point on the
wing. 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 direct numerical
simulations. Our findings are of interest in applications related to energy
harvesting by fluid-structure interaction, a problem which 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 we aim to extract.

Fluid Dynamics