Effective design and characterization of flutter-based piezoelectric energy harvesters with discontinuous nonlinearities

Abstract

A comprehensive study on the design and nonlinear characterization of a two-degree of freedom piezoaeroelastic energy harvesting system with freeplay and multi-segmented nonlinearities in the pitch degree of freedom is explored and discussed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived and the unsteady representation based on the Duhamel formulation is employed to represent the aerodynamic loads. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay and multi-segmented nonlinearities before and after the linear onset of flutter. Such nonlinearities can be introduced to piezoaeroelastic energy harvesters for performance enhancement through the possible existence of subcritical Hopf bifurcation and aperiodic responses due to the grazing and grazing/sliding bifurcations. It is shown that the existence of discontinuous effects result in the possibility of harvesting energy at lower speeds than the linear onset speed of instability due to the activation of the subcritical Hopf bifurcation. Additionally, the increase of the strength of the multi-segmented nonlinearities leads to the existence of aperiodic responses with the presence of several bifurcations limiting the system's dynamics at low pitch angles with limiting stall issues. It is proved that an effective design with harvesting energy at low wind speeds can be carried out for wing-based energy harvesters by carefully selecting the linear stiffness of the pitch degree of freedom, gap and type of the multi-segmented discontinuity, and electrical load resistance.