Theoretical Analysis of the Galloping Energy Harvesters under Bounded Random Parameter Excitation

In this paper, the response properties of galloping energy harvesters under bounded random parameter excitation are studied theoretically. The first-order approximate solution of the galloping energy harvester is derived by applying the multi-scales method. The expression for the largest Lyapunov exponent that determines the trivial solution is derived, and the corresponding simulation diagrams, including the largest Lyapunov exponent diagrams and time domain diagrams, verify our results. Then the steady-state response moments of the nontrivial solution are studied using the moment method, and the analytical expressions for the first-order and second-order moments of the voltage amplitude are obtained, respectively. The corresponding results show that wind speed enhances the steady-state response moments of the voltage amplitude. Meanwhile, the voltage output can be controlled by adjusting the cubic coefficient. To further verify the response characteristics of the galloping energy harvester, the stationary probability density functions of the displacement and velocity are obtained by the Monte-Carlo simulation method. The results show that the wind speed enhances the displacement of the bluff and the damping ratios should be reduced as much as possible to improve the performance. What's more, the piezoelectric materials also impact the performance of the energy harvester.