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Probabilistic behavior analysis of a sandwiched buckled beam under Gaussian white noise with energy harvesting perspectives

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  • Mokem Fokou, I.S.
  • Nono Dueyou Buckjohn, C.
  • Siewe Siewe, M.
  • Tchawoua, C.

Abstract

In this paper, a sandwiched buckled beam with axial compressive force under Gaussian white noise is considered as a piezoelectric energy harvester. A stochastic averaging method is proposed to analytically predict the system’s response, the stability and the estimation of system’s reliability. By using the generalized harmonic transformation, the Itô differential equations with respect to the mechanical and electrical amplitude are derived through this technique. From these differential equations, we construct the Fokker–Plank–Kolmogorov equation for the electrical and mechanical subsystem where the solution of each equation in the stationary state is a probability density. The mean first passage time (MFPT) is numerically provided in order to study the attractor stability(stable equilibrium point observed in the effective potential) which give rise to the noise-enhanced stability(NES) phenomenon. The mean square response and voltage are obtained for different white noise intensities and others system parameters. The effects of linear damping and noise intensity on the mean square voltage are investigated. We notice that harvested energy can be enhanced by suitable choice of noise intensity and others system parameters. In additional, by combining the random signal with harmonic excitation, the stochastic resonance(SR) phenomenon is observed via the mean residence time(TMR) which give rise to the large amplitude of vibrations and consequently, an optimization of harvested energy. The agreements between the analytical method and those obtained numerically validate the effectiveness of analytical investigations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:92:y:2016:i:c:p:101-114
    DOI: 10.1016/j.chaos.2016.09.016
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    References listed on IDEAS

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    1. B. Spagnolo & A. Dubkov & N. Agudov, 2004. "Enhancement of stability in randomly switching potential with metastable state," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 40(3), pages 273-281, August.
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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. 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.
    3. 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).
    4. Yang, Tao & Cao, Qingjie, 2020. "Dynamics and high-efficiency of a novel multi-stable energy harvesting system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Tingting Zhang & Yanfei Jin, 2024. "Stochastic optimal control of a tri-stable energy harvester with the P-SSHI circuit under colored noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(1), pages 1-13, January.

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