Stochastic dynamics of a piezoelectric energy harvester with fractional damping under Gaussian colored noise excitation

•The mathematical model of a piezoelectric energy harvester with fractional damping is presented.•The stochastic averaging method is utilized to construct the theoretical results.•The influences of fractional orders and system parameters on the mean square voltage are analyzed.•The heat maps of relative error are presented to investigate the effectiveness of the stochastic averaging method. This paper introduces the fractional damping for a piezoelectric energy harvester subjected to Gaussian colored noise and investigates the dynamic response by the stochastic averaging method. To successfully achieve this goal, the original system is decoupled into the equivalent stochastic system through variable transformation at first. Then the stochastic averaging approach is employed to construct the theoretical results. Furthermore, the feasibility and performance of the stochastic averaging method are evaluated with the assistance of the numerical results from Monte Carlo simulation. Finally, we concentrate on discussing the effect of fractional orders and system parameters on the mean square voltage and analyzing the effectiveness of the stochastic averaging method for the piezoelectric energy harvesting system by heat maps of the relative error in a quantitative perspective.