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Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations

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  • Dongmei Huang
  • Shengxi Zhou
  • Zhichun Yang

Abstract

To improve energy harvesting performance, this paper investigates the resonance mechanism of nonlinear vibrational multistable energy harvesters under narrow-band stochastic parametric excitations. Based on the method of multiple scales, the largest Lyapunov exponent which determines the stability of the trivial steady-state solutions is derived. The first kind modified Bessel function is utilized to derive the solutions of the responses of multistable energy harvesters. Then, the first-order and second-order nontrivial steady-state moments of multistable energy harvesters are considered. To explore the stochastic bifurcation phenomenon between the nontrivial and trivial steady-state solutions, the Fokker–Planck–Kolmogorov equation corresponding to the two-dimensional Itô stochastic differential equations is solved by using the finite difference method. In addition, the mechanism of the stochastic bifurcation of multistable energy harvesters is analyzed for revealing their unique dynamic response characteristics.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:1050143
    DOI: 10.1155/2019/1050143
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    References listed on IDEAS

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    3. 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.
    4. Younesian, Davood & Alam, Mohammad-Reza, 2017. "Multi-stable mechanisms for high-efficiency and broadband ocean wave energy harvesting," Applied Energy, Elsevier, vol. 197(C), pages 292-302.
    5. Xu, Pengfei & Jin, Yanfei & Zhang, Yanxia, 2019. "Stochastic resonance in an underdamped triple-well potential system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 352-362.
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    Cited by:

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    2. Lu Wang & Zutang Wu & Shuai Liu & Qian Wang & Junjie Sun & Yun Zhang & Guangzhao Qin & Dejiang Lu & Ping Yang & Libo Zhao & Zhuangde Jiang & Ryutaro Maeda, 2022. "Uniform Stress Distribution of Bimorph by Arc Mechanical Stopper for Maximum Piezoelectric Vibration Energy Harvesting," Energies, MDPI, vol. 15(9), pages 1-10, April.
    3. Yang, Fan & Gao, Mingyuan & Wang, Ping & Zuo, Jianyong & Dai, Jun & Cong, Jianli, 2021. "Efficient piezoelectric harvester for random broadband vibration of rail," Energy, Elsevier, vol. 218(C).

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