Probabilistic response of a fractional-order hybrid vibration energy harvester driven by random excitation

The stochastic response of a fractional-order hybrid vibration energy harvester is investigated in this paper. Equivalent system can be derived by the variable transformation. Then, the probability density functions of mechanical states are obtained by the stochastic averaging technique. The good agreement between numerical simulation and analytical results demonstrates the effectiveness of the proposed method. Mean square voltage, mean square current, and mean output power are presented to illustrate the device output performance. Results imply that the hybrid vibration energy harvesting system can generate higher mean output power than that from a separate piezoelectric system and an electromagnetic system.