Aeroelastic energy harvesting in flutter condition increases with combined nonlinear stiffness and nonlinear piezoelectrical coupling

The dynamic behaviour of an aeroelastic energy harvester using a piezoelectric transducer is studied. An important question in applications of energy harvesting is how to increase the efficiency of energy conversion. The study of both mechanical and electrical nonlinear terms has proven important in this context, both to provide more accurate models and to aid the design of purposely nonlinear systems. Here, the influence of plunge cubic nonlinear stiffness and nonlinear piezoelectrical coupling is investigated with respect to flutter speed, mechanical and electrical power. Different combinations of nonlinear terms are explored and compared to the linear case. The influence of the nonlinear coefficients and of the parameters of the electrical domain on the behaviour of the system are analysed analytically via the method of multiple scales (MMS) and numerically via a fourth-order Runge–Kutta method (RK). A Poincaré section method is proposed to determine the period of oscillations of the nonlinear systems at flutter. The results indicate that nonlinear stiffness has more influence in increasing flutter speed, and nonlinear piezoelectrical coupling has more influence in increasing electrical power. More energy is transferred from the pitch motion than from the plunge motion. Flutter speed, mechanical and electrical power increase with nonlinear stiffness, indicating that neglecting this characteristic can lead to underestimation of flutter speed and harvested energy.