Resonance response analysis of nonlinear vibration energy harvesting system under bounded noise excitation

Volume 15, Issue 1, pp 1--13 http://dx.doi.org/10.22436/jnsa.015.01.01

Publication Date: May 26, 2021 Submission Date: March 26, 2021 Revision Date: April 16, 2021 Accteptance Date: April 26, 2021

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Authors

Di Liu - School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, P. R. China. Qianqian Fu - School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, P. R. China.

Abstract

In this paper, the resonance response of piezoelectric vibration energy harvester (VEH) driven by bounded noise is discussed through the quasi-conservative stochastic averaging method. A nonlinear transformation based on the total energy is firstly established to transform piezoelectric VEH system from an electromechanical coupled nonlinear system into a single-degree-of-freedom (SDOF) system. Then the SDOF system is rewritten as It\^o stochastic system about the energy and residual phase under the case of p:q resonance through the quasi-conservative stochastic averaging method. And the joint probability density function (JPDF) of the stationary response is obtained by solving the corresponding two-dimensional Fokker-Planck-Kolmogorov (FPK) equation using the finite difference method. Meanwhile, the mean-square electric voltage and the mean output power are further analytically given through the JPDF. Finally, the resonance response of piezoelectric VEH system is analyzed in detail in case of the primary resonance, and the Monte Carlo (MC) simulation technique is adopted to validate the effectiveness of the finite difference method.

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Keywords

• Nonlinear vibration energy harvesting
• resonance response
• bounded noise
• quasi-conservative stochastic averaging method
• finite difference method

MSC

•  70L05
•  34C15
•  34C29

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