Stochastic analysis of a galloping-random wind energy harvesting performance on a buoy platform

Abstract

A new concept of a galloping-random wind energy harvester, which is a galloping-based piezoelectric harvester mounted on a buoy platform is proposed. The galloping-random wind energy harvester can concurrently harvest galloping energy due to the aero-instability and stochastic vibration energy due to the ocean wave. The harvester performance is comprehensively investigated through wind tunnel experiments and theoretical investigation. The mathematical model of the system is formulated, and its aerodynamic galloping is then validated with wind tunnel experimental measurements. Based on the verified mathematical model of the galloping-random wind energy harvester, the stochastic average method is applied to analytically obtain the probability density functions of the system’s stochastic responses and the average harvested power. The fidelity of the analytical solution is also verified by the numerical integration using the Euler-Maruyama algorithm. The results show that a unique crater phenomenon is discovered in the joint PDF of the responses, owing to the concurrent galloping and stochastic vibrations. In this case, the energy harvester exhibits a periodic galloping response with a fluctuating amplitude. The annulus range is wider when the galloping response is dominant and becomes stronger. In addition, this study investigates the average power output in terms of the stochastic excitation intensity, structural natural frequency, aerodynamic mass ratio, and normalized electrical term, to provide the useful design guidelines. The results show that the strong stochastic excitation intensity is beneficial to broadband energy harvesting and especially provides a high advantage for the low wind speed. The low structural natural frequency and large aerodynamic mass ratio can improve the performance. The parametric study also uncovers the optimal electrical term that can significantly improve the broadband average power output.