Airfoil-based piezoelectric energy harvesting by exploiting the pseudoelastic hysteresis of shape memory alloy springs

The modeling and analysis of an electromechanically coupled typical aeroelastic section with shape memory alloy springs for wind energy harvesting is addressed in this paper. An airfoil with two-degrees-of-freedom, namely pitch and plunge, is considered and piezoelectric coupling is added to the plunge degree-of-freedom. A load resistance is assumed in the electrical domain of the problem in order to estimate the electrical power output. Shape memory alloy coil springs are modeled in the pitch degree-of-freedom of the typical section. A nickel-titanium alloy that exhibits pseudoelasticity at room temperature is assumed. The constitutive model for the shape memory alloy is based on classical phenomenological models. The unsteady aerodynamic loads are obtained by Jones' approximation to Wagner's indicial function. The resulting nonlinear electroaeroelastic model is cast into a state-space representation and solved with a Runge-Kutta method. The effects of preload values of the shape memory springs and resistive power generation on the aeroelastic behavior of the wind energy harvester are investigated at the flutter boundary and in a post-flutter regime. The nonlinear kinetics of the austenite-to-martensite phase transformation changes the typical linear flutter behavior to stable limit-cycle oscillations over a range of airflow speeds. Such nonlinear aeroelastic behavior introduced by the hysteretic behavior of the SMA springs provides an important source of persistent electrical power.