A fractionally damped vibration energy harvester excited by the wide-band random noise is investigated theoretically in this paper. Firstly, by introducing the generalized harmonic transformation, an equivalent uncoupled system only with respect to the mechanical states is established, while the external circuit and the fractional derivative damping are decoupled into damping and stiffness with amplitude-dependent coefficients, respectively. Then, a stochastic averaging operator technique is carried out to derive the stationary distribution of the mechanical states and furtherly obtain the mean square electric voltage (MSEV) and mean output power (MOP) of the energy harvester theoretically. Finally, the relationships between the fractional derivative and the MSEV and MOP are explored in detail to help improve the performance of the energy harvester.

本文从理论上研究了一种由宽带随机噪声激发的分数阻尼振动能量采集器。首先，通过引入广义谐波变换，建立了一个仅关于机械状态的等效非耦合系统，而外部电路和分数导数阻尼分别被解耦为具有振幅相关系数的阻尼和刚度。然后，通过随机平均算子技术推导出机械状态的平稳分布，进而从理论上得到能量采集器的均方电压（MSEV）和平均输出功率（MOP）。最后，