Stochastic averaging for nonlinear vibration energy harvesting system

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• 作者：Ming Xu ; Xiaoling Jin ; Yong Wang ; Zhilong Huang
• 关键词：Nonlinear vibration energy harvesting ; Stochastic averaging ; Mean ; square electric voltage ; Mean output power ; Generalized harmonic transformation
• 刊名：Nonlinear Dynamics
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：78
• 期：2
• 页码：1451-1459
• 全文大小：490 KB
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• 作者单位：Ming Xu (1)
  Xiaoling Jin (2)
  Yong Wang (2)
  Zhilong Huang (2)
  
  1. Institute of Fluid Mechanics, China Jiliang University, Hangzhou, 310018, China
  2. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China
  
• ISSN：1573-269X

文摘

A stochastic averaging technique for the nonlinear vibration energy harvesting system to Gaussian white noise excitation is developed to analytically evaluate the mean-square electric voltage and mean output power. By introducing the generalized harmonic transformation, the influence of the external circuit on the mechanical system is equivalent to a quasi-linear stiffness and a quasi-linear damping with energy-dependent coefficients, and then the equivalent nonlinear system with respect to the mechanical states is completely established. The It? stochastic differential equation with respect to the mechanical energy of the equivalent nonlinear system is derived through the stochastic averaging technique. Solving the associated Fokker–Plank–Kolmogorov equation yields the stationary probability density of the mechanical states, and then the mean-square electric voltage and mean output power are analytically obtained through the approximate relation between the electric quantity and the mechanical states. The agreements between the analytical results and those from the moment method and from Monte Carlo simulations validate the effectiveness of the proposed technique.