In this paper, a Duffing-type energy harvester with time delay circuit under narrow-band random excitation is studied by using the method of multiple scales. The analytical expressions of the steady-state responses near the principal resonance and their stable conditions are derived. Results show that the phenomenon of stochastic jump is found, and the operational bandwidth of the nonlinear energy harvester can be extended. The effects of frequency detuning, noise intensity, time delay, piezoelectric coupling, and time constant ratio on the dynamical behaviors are discussed. From the viewpoint of improving system performance and optimizing harvester design, a proper choose of time delay and feedback gain is proposed by the power conversion efficiency and the RMS voltage. It indicates that the negative feedback gain is favorable for an energy harvester to provide more electrical output power and miniaturize design. Moreover, the Monte Carlo simulations are given to verify the validity of the theoretical method.

本文采用多尺度法研究了一种在窄带随机激励下具有延时电路的达芬型能量采集器。推导了主共振附近的稳态响应及其稳定条件的解析表达式。结果表明，发现了随机跳变现象，可以扩展非线性能量采集器的工作带宽。讨论了频率失谐，噪声强度，时间延迟，压电耦合和时间常数比对动力学行为的影响。从提高系统的性能和优化设计收割机的角度出发，适当选择延迟时间和反馈增益由电源转换效率和RMS电压建议。这表明负反馈增益有利于能量收集器提供更多的电输出功率并最小化设计。此外，给出了蒙特卡洛模拟，以验证该理论方法的有效性。