  A flexible foil undergoing pitching oscillations is studied experimentally in
a wind tunnel with different imposed free stream velocities. The chord-based
Reynolds number is in the range 1600--4000, such that the dynamics of the
system is governed by inertial forces and the wake behind the foil exhibits the
reverse B\'enard-von K\'arm\'an vortex street characteristic of flapping-based
propulsion. Particle Image Velocimetry (PIV) measurements are performed to
examine the flow around the foil, whilst the deformation of the foil is also
tracked. The first natural frequency of vibration of the foil is within the
range of flapping frequencies explored, determining a strongly-coupled dynamics
between the elastic foil deformation and the vortex shedding.
  Cluster-based reduced order modelling is applied on the PIV data in order to
identify the coherent flow structures. Analysing the foil kinematics and using
a control-volume calculation of the average drag forces from the corresponding
velocity fields, we determine the optimal flapping configurations for thrust
generation. We show that propulsive force peaks occur at dimensionless
frequencies shifted with respect to the elastic resonances that are marked by
maximum trailing edge oscillation amplitudes. The thrust peaks are better
explained by a wake resonance, which we examine using the tools of classic
hydrodynamic stability on the mean propulsive jet profiles.
