Enhanced stability identi cation and global response prediction of galloping energy harvesters

Abstract

For a better characterization of the type of instability and prediction of the unstable solutions of a galloping-based energy harvester, the normal form of the Hopf bifurcation and shooting method are employed. By attaching a piezoelectric transducer to the transverse degree of freedom of a triangular cylinder, mechanical vibrations can be converted to electrical energy. Using the nonlinear normal form, it is shown that this technique is beneficial to identify the type of instability near bifurcation and determine the impact of structural and/or aerodynamic nonlinearities on the levels of the harvested power. The results also showed that this approach is strong in terms of designing reliable gallopingbased energy harvesters. It is demonstrated that this technique can accurately predict the response of harvester 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 predicting the stable and unstable solutions of the harvester and associated turning points. It is also shown that the Floquet multipliers can be utilized to identify the response’s type of the aeroelastic system. This enhanced stability characterization which is based on both the nonlinear normal form and shooting method will have a strong impact in designing efficient aeroelastic energy harvesters.