Design of piezoaeroelastic energy harvesters

We design a piezoaeroelastic energy harvester consisting of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. We choose the linear springs to produce the minimum flutter speed and then implement a linear velocity feedback to reduce the flutter speed to any desired value and hence produce limit-cycle oscillations at low wind speeds. Then, we use the center-manifold theorem to derive the normal form of the Hopf bifurcation near the flutter onset, which, in turn, is used to choose the nonlinear spring coefficients that produce supercritical Hopf bifurcations and increase the amplitudes of the ensuing limit cycles and hence the harvested power. For given gains and hence reduced flutter speeds, the harvested power is observed to increase, achieve a maximum, and then decrease as the wind speed increases. Furthermore, the response undergoes a secondary supercritical Hopf bifurcation, resulting in either a quasiperiodic motion or a periodic motion with a large period. As the wind speed is increased further, the response becomes eventually chaotic. These complex responses may result in a reduction in the generated power. To overcome this adverse effect, we propose to adjust the gains to increase the flutter speed and hence push the secondary Hopf bifurcation to higher wind speeds.