An improved stability characterization for aeroelastic energy harvesting applications

Abstract

An enhanced stability characterization for aeroelastic energy harvesters is introduced by using both the normal form of the Hopf bifurcation and shooting method. Considering a triangular cylinder subjected to transverse galloping oscillations and a piezoelectric transducer to convert mechanical vibrations to electrical power, it is demonstrated that the nonlinear normal form is very beneficial to characterize the type of instability near bifurcation and determine the influence of structural and/or aerodynamic nonlinearities on the performance of the harvester. It is also shown that this tool is strong in terms of designing reliable aeroelastic energy harvesters. The results show that this technique can accurately predict the harvester’s response only near bifurcation, however, cannot predict the stable solutions of the harvester when subcritical Hopf bifurcation takes place. To cover these drawbacks, the shooting method is employed. It turns out that this approach is beneficial in determining the stable and unstable solutions of the system and associated turning points. The results also show that the Floquet multipliers, obtained as the by-product of this method, can be used to characterize the response’s type of the harvester. Thus, the normal form of the Hopf bifurcation and shooting method predictions can supplement each other to design stable and reliable aeroelastic energy harvesters.