Stochastic analysis of an acoustic black hole piezoelectric energy harvester under Gaussian white noise excitation

•The FPK equation of ABH energy harvester is established.•The dimension reduction method is used to converted the high dimension FPK equation.•The Lax-Friedrichs scheme is used and its stability condition is also given. The ABH effect shows potential application in vibration energy harvesting due to...

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Bibliographic Details
Published in:Applied mathematical modelling 2024-07, Vol.131, p.22-32
Main Authors: Du, Weiqi, Xiang, Zijian, Qiu, Xiaobiao
Format: Article
Language:English
Subjects:
Acoustic black hole
Dimension reduction
Energy harvesting
Stochastic analysis
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Summary:•The FPK equation of ABH energy harvester is established.•The dimension reduction method is used to converted the high dimension FPK equation.•The Lax-Friedrichs scheme is used and its stability condition is also given. 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.
ISSN:0307-904X
DOI:10.1016/j.apm.2024.04.015