Investigations on the stability and effectiveness of wing-based piezoaeroelastic systems with combined nonlinearities

An investigation on the effects of the existence of freeplay, polynomial stiffness and aerodynamic nonlinearities on the dynamical responses of flutter-based piezoaeroelastic energy harvesting systems is performed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived including structural and aerodynamic nonlinearities, namely stall effects. The aerodynamic loading used in this study is the unsteady representation, based on the Duhamel formulation. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay combined with structural hardening nonlinearities before and after the linear onset of flutter. Such nonlinearities must be considered in the modeling and design of piezoaeroelastic energy harvesters, the combination of it can result in the presence of several secondary bifurcations and multiple solution regions and, therefore, affect the overall efficiency of the system. It is shown that the existence of freeplay nonlinearity leads to the possibility of harvesting energy at lower speeds than the linear onset speed of instability. As the gap size of the freeplay nonlinearity increases, the polynomial quadratic term in structural nonlinearity minimally affects the performance of the energy harvester. Further, it is shown that the stall effect should be considered when the angle of attack is higher than 2 ∘ which significantly affect the higher Hopf bifurcations in the pitch degree of freedom.