Energy harvesting under combined aerodynamic and base excitations

This paper investigates the transduction of a piezoaeroelas-tic energy harvester under combined base and aerodynamic loadings. The harvester consists of a typical rigid airfoil supported by hardening flexural and torsional springs. The airfoil is placed in an incompressible air flow and subjected to a harmonic base excitation in the plunge direction. Considering a nonlinear quasi-steady aerodynamic model, the response behavior and electric output of the harvester are analyzed near the flutter instability. A center manifold reduction is implemented to reduce the original five-dimensional system into one nonlinear first-order ordinary differential equation. Subsequently, the normal form of the reduced system is derived to study slow modulation of the voltage amplitude and phase. Several case studies are presented indicating a considerable improvement in the output voltage of the harvester under the combined loading even when the air speed is below the flutter velocity, i.e., even when the harvester cannot maintain steady-state periodic oscillations in the absence of the harmonic base excitation. It is also shown that, when the base-excitation amplitude is sufficiently large and its frequency is close to the frequency of the self-sustained limit-cycle oscillations emanating from the flutter instability, the periodic solution resulting from the base excitation entrains the self-sustained oscillations yielding a periodic output voltage. However, when the excitation frequency is far from the limit-cycle frequency, or the amplitude of base excitation is small, the voltage is two-period quasiperiodic.