Stochastic averaging of energy harvesting systems

被引：53
|
作者：
Jiang, Wen-An [1 ]
Chen, Li-Qun [1 ,2 ,3 ]
机构：
[1] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China
[2] Shanghai Univ, Dept Mech, 99 Shang Da Rd, Shanghai 200444, Peoples R China
[3] Shanghai Univ, Shanghai Key Lab Mech Energy Engn, Shanghai 200072, Peoples R China
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2016年 / 85卷
关键词：
Energy harvesting; Stochastic averaging method; Gaussian white noise; Parametric excitation; Monte Carlo simulation;
D O I：
10.1016/j.ijnonlinmec.2016.07.002
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
A stochastic averaging method is proposed for nonlinear energy harvesters subjected to external white Gaussian noise and parametric excitations. The Fokker-Planck-Kolmogorov equation of the coupled electromechanical system of energy harvesting is a three variables nonlinear parabolic partial differential equation whose exact stationary solutions are generally hard to find. In order to overcome difficulties in solving higher dimensional nonlinear partial differential equations, a transformation scheme is applied to decouple the electromechanical equations. The averaged Ito equations are derived via the standard stochastic averaging method, then the FPK equations of the decoupled system are obtained. The exact stationary solution of the averaged FPK equation is used to determine the probability densities of the displacement, the velocity, the amplitude, the joint probability densities of the displacement and velocity, and the power of the stationary response. The effects of the system parameters on the output power are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulations. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：174 / 187
页数：14
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