Dynamic stability and performance analysis of a galloping-based piezoelectric energy harvester for different order representations of the aerodynamic force

In the present work, a non-linear electromechanical distributed parameter model is proposed for galloping based piezoelectric energy harvester (GPEH) and the impact of different order polynomial representation of aerodynamic force coefficient on the dynamic behavior of the system is investigated. Both geometric and aerodynamic nonlinearity (till9thorder polynomial) is introduced in the proposed model. The derived model is universally valid for both series and parallel connection of piezoelectric bimorph patches. The dynamic responses of the system, for different order representations of aerodynamic force, are extensively studied and then compared with experimental results from the literature. It is shown that a minimum fill 7th order polynomial should be chosen for representing the galloping force coefficient in order to get a good agreement with experimental results. It is also shown from the model that the overall efficiency of the system is highest near the onset of galloping speed and decreases with an increase in wind speed. Further, a parametric study is done to find the effect of load resistance on the dynamic behavior of the system. It is seen that the error between experimental and predicted power decreases with an increase in the order of polynomial at a particular value of load resistance. The present analysis based on the proposed model emphasizes the importance of representation of aerodynamic force coefficients and geometric nonlinearity in predicting the accurate response for GPEH.