The ABH effect shows potential application in vibration energy harvesting due to its wave localization property. In this study, the stochastic response of output voltage of ABH energy harvester has been investigated under Gaussian white noise excitation. The high dimensional Fokker–Planck–Kolmogorov equation of this piezoelectric coupling systems is given by using Gaussian Expansion method and dimension reduction method is used to convert it to one-dimensional first-order partial differential equation. Finally, the Lax-Friedrichs scheme is developed to solve the partial differential equation to obtain the probability density of output voltage. The results between calculated probability distribution and that of Monte Carlo simulation shows good accuracy of propose method. Finally, a comprehensive parametric analysis has been performed on this stochastic system and some conclusions are given.

中文翻译：

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高斯白噪声激励下声学黑洞压电能量收集器的随机分析

ABH 效应由于其波局域化特性而显示出在振动能量收集方面的潜在应用。在本研究中，研究了高斯白噪声激励下 ABH 能量采集器输出电压的随机响应。利用高斯展开法给出了该压电耦合系统的高维Fokker-Planck-Kolmogorov方程，并利用降维法将其转换为一维一阶偏微分方程。最后，提出Lax-Friedrichs格式求解偏微分方程，得到输出电压的概率密度。计算得到的概率分布与蒙特卡洛模拟结果之间的结果表明，该方法具有良好的准确性。最后，对该随机系统进行了全面的参数分析，并给出了一些结论。