Dynamic performance of the energy harvester with a fractional-order derivative circuit

Vibration energy harvesters are expected to replace chemical batteries and achieve self-power for low-power electronic devices, and their design has attracted significant attention. In previous studies, circuits consistent with the constitutive relationship with integer derivatives were frequently used, but fractional-order derivative circuits have received less attention. Because of the dissipation effects, such as internal friction and thermal memory, the fractional-order derivative is an effective mathematical approach for determining such nonconservative behaviors. In this study, the dynamic performance of a vibration energy harvester with a fractional-order derivative circuit in a random environment was investigated. Both linear and nonlinear vibration energy harvesters were evaluated using the linear random vibration theory and the equivalent linearization technique. The effects of the system parameters on the mean output power were analyzed, and the optimal system parameters, such as the oscillation frequency of the circuit and the coupling coefficient, were determined. Furthermore, the relationships between the optimal parameters and the order of the fractional derivative were established. Our study will potentially guide future designs of vibration energy harvesters.