  The influence of the bending rigidity of a flexible heaving wing on its
propulsive performance in a two-dimensional imposed parallel flow is
investigated in the inviscid limit. Potential flow theory is used to describe
the flow over the flapping wing. The vortical wake of the wing is accounted for
by the shedding of point vortices with unsteady intensity from the wing's
trailing edge. The trailing-edge flapping amplitude is shown to be maximal for
a discrete set of values of the rigidity, at which a resonance occurs between
the forcing frequency and a natural frequency of the system. A quantitative
comparison of the position of these resonances with linear stability analysis
results is presented. Such resonances induce maximum values of the mean
developed thrust and power input. The flapping efficiency is also shown to be
greatly enhanced by flexibility.
