The potential of electrical impedance on the performance of galloping systems for energy harvesting and control applications

Abstract

Performances of galloping-based piezoelectric systems for energy harvesting and control applications when considering complex electrical impedance are investigated. The aeroelastic system is composed of a unimorph piezoelectric cantilever beam with a square cylinder attached at its tip and subjected to a uniform flow speed. A quasi-steady representation is used to model the aerodynamic force. A nonlinear distributed-parameter model is developed when considering various scenarios of connections between electrical resistance, capacitance, and inductance. Theoretical strategies are developed in order to determine the relation between the onset speed of galloping and the components of the electrical impedance. The results show that the presence of the electrical capacitance and inductance is not beneficial in terms of improving the levels of the harvested power crossing the load resistance. On the other hand, it is shown that the inclusion of these electrical components may be useful for energy harvesting purposes when charging/discharging batteries. One of the important findings of this research study is that including an electrical inductance in connection to a load resistance is very beneficial for control purposes because a significant increase in the onset speed of instability can be obtained for well-defined values of the electrical components. Analytical predictions of these optimum values of the electrical inductance and resistance are determined and compared with numerical simulations. It is also demonstrated that supercritical Hopf bifurcations take place at this controlled optimal configuration without having any hysteresis and jumps when increasing and decreasing the wind speeds.