Moment analysis of galloping energy harvesters with a parallel circuit under stochastic excitation

Abstract

In this paper, the stochastic response performance of a galloping energy harvester with a parallel circuit under Gaussian white noise excitation is analyzed. To overcome the complexity of the distributed parameter model and the two-degree-of-freedom characteristics of the harvester, firstly, the exact closed expressions for the mean square displacement, mean square voltage and mean output power are derived by the equivalent linearization method. The results obtained by the direct Monte Carlo simulations verify the accuracy of the theoretical analysis. Then, the conditions for the occurrence of the galloping phenomenon can be identified. The influences of dimensionless parameters and noise intensity on the statistical moments are discussed. The results show that most of the parameters have the same tendency to affect the mean square displacement and the mean square voltage. However, the electromechanical coupling term has the opposite effect on both of them. It is also shown that the mean output power decreases as the coefficients of the electromechanical coupling term and mechanical damping ratio increase, however, it increases dramatically with increasing the wind speed and the linear galloping force coefficient. In addition, utilizing the stationary probability density of the stochastic harvester, the influences of important parameters and noise intensity on the harvester’s performance are studied. It is observed that a larger level of noise intensity results in the greater peak value of the stationary probability density.