Energy harvesting under combined aerodynamic and base excitations

Abstract

This paper investigates the transduction of a piezoaeroelastic energy harvester under the combination of vibratory base excitations and aerodynamic loadings. The harvester which consists of a rigid airfoil supported by nonlinear flexural and torsional springs is placed in an incompressible air flow and subjected to a harmonic base excitation in the plunge direction. Under this combined loading, the airfoil undergoes complex motions which strain a piezoelectric element producing a voltage across an electric load. To capture the qualitative behavior of the harvester, a five-dimensional lumped-parameter model which adopts nonlinear quasi-steady aerodynamics is used. A center manifold reduction is implemented to reduce the full model into one nonlinear first-order ordinary differential equation. The normal form of the reduced system is then derived to study slow modulation of the response amplitude and phase near the flutter instability. Below the flutter speed, the response of the harvester is observed to be always periodic with the air flow serving to amplify the influence of the base excitation on the response by reducing the effective stiffness of the system, and hence, increasing the RMS output power. Beyond the flutter speed, two distinct regions are observed. The first occurs when the base excitation is small and/or when the excitation frequency is not close to the frequency of the self-sustained oscillations induced by the flutter instability. In this case, the response of the harvester is two-period quasiperiodic with amplitude modulation due to the presence of two incommensurate frequencies in the response. This amplitude modulation reduces the RMS output power. In the second region, the amplitude of excitation is large enough to eliminate the quasiperiodic response by causing the two frequencies to lock into each other. In this region, the response becomes periodic and the output power increases exhibiting little dependence on the base excitation.