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Multiple Solutions of the Tristable Energy Harvester

Author

Listed:
  • Grzegorz Litak

    (Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland)

  • Jerzy Margielewicz

    (Faculty of Transport and Aviation Engineering, Silesian University of Technology, Krasińskiego 8, 40-019 Katowice, Poland)

  • Damian Gąska

    (Faculty of Transport and Aviation Engineering, Silesian University of Technology, Krasińskiego 8, 40-019 Katowice, Poland)

  • Piotr Wolszczak

    (Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland)

  • Shengxi Zhou

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China)

Abstract

This paper presents the results of numerical simulations of a non-linear, tristable system for harvesting energy from vibrating mechanical devices. Detailed model tests were carried out in relation to the system consisting of a beam and three permanent magnets. Based on the derived mathematical model and assuming a range of control parameter variability, a three-dimensional image of the distribution of the largest Lyapunov exponent was plotted. On its basis, the regions of chaotic and predictable movement of the considered system exist have been established. With reference to selected plane of the largest Lyapunov exponent cross-sections, possible co-existing solutions were identified. To identify multiple solutions, a diagram of solutions (DS) diagram was used to illustrate the number of existing solutions and their periodicity. The proposed calculation tool is based on the so-called fixed points of Poincaré cross-section. In relation to selected values of the control parameter ω, coexisting periodic solutions were identified for which phase trajectories and basins of attraction were presented. Based on the model tests carried out, it was found that in order to efficiently harvest energy, appropriate transducer adjustment is required. Calibration of the transducer is necessary to obtain the greatest amplitude of vibration of the beam, which corresponds to the phase trajectory limited by external energy potential barriers. As expected, the average voltage induced on the electrodes of the piezoelectric transducer and the average electrical power recorded on the resistive element are directly proportional to the amplitude and average kinetic energy of the beam.

Suggested Citation

  • Grzegorz Litak & Jerzy Margielewicz & Damian Gąska & Piotr Wolszczak & Shengxi Zhou, 2021. "Multiple Solutions of the Tristable Energy Harvester," Energies, MDPI, vol. 14(5), pages 1-17, February.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:5:p:1284-:d:506335
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz & Wolszczak, Piotr & Yurchenko, Daniil, 2022. "Nonlinear dynamics of a new energy harvesting system with quasi-zero stiffness," Applied Energy, Elsevier, vol. 307(C).
    2. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz & Yurchenko, Daniil & Wolszczak, Piotr & Dymarek, Andrzej & Dzitkowski, Tomasz, 2023. "Influence of the configuration of elastic and dissipative elements on the energy harvesting efficiency of a tunnel effect energy harvester," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Joanna Iwaniec & Grzegorz Litak & Marek Iwaniec & Jerzy Margielewicz & Damian Gąska & Mykhaylo Melnyk & Wojciech Zabierowski, 2021. "Response Identification in a Vibration Energy-Harvesting System with Quasi-Zero Stiffness and Two Potential Wells," Energies, MDPI, vol. 14(13), pages 1-14, June.
    4. Tomasz Haniszewski & Maria Cieśla, 2022. "Energy Harvesting in the Crane-Hoisting Mechanism," Energies, MDPI, vol. 15(24), pages 1-22, December.
    5. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz & Haniszewski, Tomasz & Wolszczak, Piotr & Trigona, Carlo, 2023. "Influence of the potential barrier switching frequency on the effectiveness of energy harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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