Stochastic analysis of a nonlinear electromagnetic energy harvesting system with fractional damping under additive and multiplicative stochastic excitation

Electromagnetic energy harvester has been widely concerned in recent years due to its advantages of small size and high sensing frequency. In this paper, the stochastic behaviors of a nonlinear electromagnetic energy harvesting system (NEEH) with fractional damping are investigated under the additive and multiplicative stochastic excitation. Firstly, by applying the stochastic average method to the NEEH system, the mean square of the output current, and the steady-state probability density of vibration amplitude, displacement and velocity are obtained. Meanwhile, the validity of the theoretical results is verified by comparing with the numerical results given by the Monte Carlo method. Secondly, by investigating the theoretical and numerical results, the influences of noise intensity and fractional order on the NEEH system are explored. It is obvious that a higher output voltage can be obtained by the larger intensity of the stochastic excitation, and the smaller coefficient and fractional order of the fractional damping.