Modeling and performance of electromagnetic energy harvesting from galloping oscillations

The modeling and performance of a galloping-based electromagnetic energy harvester are investigated. To convert galloping oscillations into electrical energy, an electromagnetic transducer is used. A set of representative coupled equations that account for the transverse displacement of the bluff body and the induced electromagnetic current are constructed. The galloping force is modeled by using the quasi-steady approximation. The effects of the electrical load resistance on the coupled damping and onset speed of galloping are determined through a linear analysis. It is shown that the electrical load resistance strongly affects the coupled damping and hence the onset speed of galloping of the harvester. For high values of the electrical load resistance, it is demonstrated that the load resistance has a negligible impact on the onset speed of galloping. A nonlinear analysis is then performed to investigate the effects of the electrical load resistance and wind speed on the harvester's outputs. The nonlinear normal form is first derived and validated with numerical predictions in order to characterize the type of instability for various cross-section geometries. The results show that a very good agreement is obtained between the normal form solutions and numerical predictions near Hopf bifurcation. It is also shown that, for well-defined values of wind speeds, both the transverse displacement amplitude and the generated voltage are increasing with the electrical load resistance. On the other hand, there is an optimum value of the electrical load resistance, which varies with the wind speed, at which the levels of the harvested power are maximized.