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Probabilistic response analysis of nonlinear vibration energy harvesting system driven by Gaussian colored noise

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  • Liu, Di
  • Xu, Yong
  • Li, Junlin

Abstract

A new quasi-conservative stochastic averaging method is proposed to analyze the Probabilistic response of nonlinear vibration energy harvesting (VEH) system driven by exponentially correlated Gaussian colored noise. By introducing a method combining a transformation and the residual phase, the nonlinear vibration electromechanical coupling system is equivalent to a single degree of freedom system, which contains the energy-dependent frequency functions. Then the corresponding drift and diffusion coefficients of the averaged Ito^ stochastic differential equation for the equivalent nonlinear system are derived, which are dependent on the correlation time of Gaussian colored noise. The probability density function (PDF) of stationary responses is derived through solving the associated Fokker–Plank–Kolmogorov (FPK) equation. Finally, the mean-square electric voltage and mean output power are analytically obtained through the relation between the electric voltage and the vibration displacement, and the output power has a linear square relationship with the electric voltage, respectively. The main results on probabilistic response of VEH system are obtained to illustrate the proposed stochastic averaging method, and Monte Carlo (MC) simulation method is also conducted to show that the proposed method is quite effective.

Suggested Citation

  • Liu, Di & Xu, Yong & Li, Junlin, 2017. "Probabilistic response analysis of nonlinear vibration energy harvesting system driven by Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 806-812.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:806-812
    DOI: 10.1016/j.chaos.2017.09.027
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    References listed on IDEAS

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    1. Mokem Fokou, I.S. & Nono Dueyou Buckjohn, C. & Siewe Siewe, M. & Tchawoua, C., 2016. "Probabilistic behavior analysis of a sandwiched buckled beam under Gaussian white noise with energy harvesting perspectives," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 101-114.
    2. Vocca, Helios & Neri, Igor & Travasso, Flavio & Gammaitoni, Luca, 2012. "Kinetic energy harvesting with bistable oscillators," Applied Energy, Elsevier, vol. 97(C), pages 771-776.
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    Cited by:

    1. Fezeu, G.J. & Fokou, I.S. Mokem & Buckjohn, C. Nono Dueyou & Siewe Siewe, M. & Tchawoua, C., 2020. "Resistance induced P-bifurcation and Ghost-Stochastic resonance of a hybrid energy harvester under colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Dongmei Huang & Shengxi Zhou & Zhichun Yang, 2019. "Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations," Complexity, Hindawi, vol. 2019, pages 1-20, December.
    3. Deng, Hang & Ye, Jimin & Huang, Dongmei, 2023. "Design and analysis of a galloping energy harvester with V-shape spring structure under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Liu, Di & Li, Junlin & Meng, Yu, 2019. "Probabilistic response analysis for a class of nonlinear vibro-impact oscillator with bilateral constraints under colored noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 179-188.
    5. Guo, Shu-Ling & Yang, Yong-Ge & Sun, Ya-Hui, 2021. "Stochastic response of an energy harvesting system with viscoelastic element under Gaussian white noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    6. Yang, Tao & Cao, Qingjie, 2020. "Dynamics and high-efficiency of a novel multi-stable energy harvesting system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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