中文摘要：

研究了含分数阶阻尼的双稳态能量采集系统的相干共振。建立了带有分数阶阻尼的轴向受压梁压电能量采集系统动力学模型。对于分数阶方程，采用Euler-Maruyama-Leipnik方法进行求解，计算了不同阻尼阶数下的能量采集系统的信噪比、响应均值、跃迁数目等统计物理量。结果表明：此压电能量采集系统在随机激励下可以实现相干共振，阻尼阶数对相干共振的临界噪声强度和相干共振幅值有很大影响。

英文摘要：

In this paper, we investigate the coherence resonance of a piezoelectric energy harvester of beam subjected to an axial force. The fractional damping is considered. First, a nonlinear model of the energy harvesting system with fractional damping and random excitation is set up. The coupling equations of dynamics and electrics are derived. Euler-Maruyama-Leipnik method is used to solve the fractional order differential equations. The signal-to-noise ratios, mean responses, and other statistical quantities under the damping forces with different orders are computed. The results obviously show the appearance of coherence resonance. It can be seen that the reduction of fractional order not only reduces the critical value of noise level, thus leading to coherence resonance, but also increases the amplitude on the occurrence of coherence resonance. So it is possible to maximize harvest power for a given density or variance of random excitation by varying system parameters.