IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i5p1284-d506335.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/5/1284/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/14/5/1284/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lobaccaro, G. & Croce, S. & Lindkvist, C. & Munari Probst, M.C. & Scognamiglio, A. & Dahlberg, J. & Lundgren, M. & Wall, M., 2019. "A cross-country perspective on solar energy in urban planning: Lessons learned from international case studies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 108(C), pages 209-237.
    2. Gnatowska, Renata & Moryń-Kucharczyk, Elżbieta, 2019. "Current status of wind energy policy in Poland," Renewable Energy, Elsevier, vol. 135(C), pages 232-237.
    3. Huguet, Thomas & Badel, Adrien & Druet, Olivier & Lallart, Mickaël, 2018. "Drastic bandwidth enhancement of bistable energy harvesters: Study of subharmonic behaviors and their stability robustness," Applied Energy, Elsevier, vol. 226(C), pages 607-617.
    4. Gao, Mingyuan & Wang, Yuan & Wang, Yifeng & Wang, Ping, 2018. "Experimental investigation of non-linear multi-stable electromagnetic-induction energy harvesting mechanism by magnetic levitation oscillation," Applied Energy, Elsevier, vol. 220(C), pages 856-875.
    5. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz, 2019. "Evolution of the geometric structure of strange attractors of a quasi-zero stiffness vibration isolator," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 47-57.
    6. Zhou, Shengxi & Cao, Junyi & Inman, Daniel J. & Lin, Jing & Liu, Shengsheng & Wang, Zezhou, 2014. "Broadband tristable energy harvester: Modeling and experiment verification," Applied Energy, Elsevier, vol. 133(C), pages 33-39.
    7. Raynaud, D. & Hingray, B. & François, B. & Creutin, J.D., 2018. "Energy droughts from variable renewable energy sources in European climates," Renewable Energy, Elsevier, vol. 125(C), pages 578-589.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Margielewicz, Jerzy & Gąska, Damian & Haniszewski, Tomasz & Litak, Grzegorz & Wolszczak, Piotr & Borowiec, Marek & Sosna, Petr & Ševeček, Oldřich & Rubeš, Ondřej & Hadaš, Zdeněk, 2024. "Vibration energy harvesting system with cyclically time-varying potential barrier," Applied Energy, Elsevier, vol. 367(C).
    4. 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.
    5. Tomasz Haniszewski & Maria Cieśla, 2022. "Energy Harvesting in the Crane-Hoisting Mechanism," Energies, MDPI, vol. 15(24), pages 1-22, December.
    6. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Chen, Lin & Liao, Xin & Sun, Beibei & Zhang, Ning & Wu, Jianwei, 2022. "A numerical-experimental dynamic analysis of high-efficiency and broadband bistable energy harvester with self-decreasing potential barrier effect," Applied Energy, Elsevier, vol. 317(C).
    3. Eghbali, Pejman & Younesian, Davood & Farhangdoust, Saman, 2020. "Enhancement of the low-frequency acoustic energy harvesting with auxetic resonators," Applied Energy, Elsevier, vol. 270(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. 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).
    6. 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).
    7. Liu, Weiqun & Qin, Gang & Zhu, Qiao & Hu, Guangdi, 2018. "Synchronous extraction circuit with self-adaptive peak-detection mechanical switches design for piezoelectric energy harvesting," Applied Energy, Elsevier, vol. 230(C), pages 1292-1303.
    8. Huguet, Thomas & Badel, Adrien & Druet, Olivier & Lallart, Mickaël, 2018. "Drastic bandwidth enhancement of bistable energy harvesters: Study of subharmonic behaviors and their stability robustness," Applied Energy, Elsevier, vol. 226(C), pages 607-617.
    9. Zhang, Yulong & Wang, Tianyang & Luo, Anxin & Hu, Yushen & Li, Xinxin & Wang, Fei, 2018. "Micro electrostatic energy harvester with both broad bandwidth and high normalized power density," Applied Energy, Elsevier, vol. 212(C), pages 362-371.
    10. Qin, Jian & Zhang, Zhenquan & Huang, Shuting & Wang, Wei & Liu, Yanjun & Xue, Gang, 2024. "Energy capture performance enhancement of point absorber wave energy converter using magnetic tristable and quadstable mechanisms," Renewable Energy, Elsevier, vol. 221(C).
    11. Jakub Jurasz & Jerzy Mikulik & Paweł B. Dąbek & Mohammed Guezgouz & Bartosz Kaźmierczak, 2021. "Complementarity and ‘Resource Droughts’ of Solar and Wind Energy in Poland: An ERA5-Based Analysis," Energies, MDPI, vol. 14(4), pages 1-24, February.
    12. Pan, Yu & Lin, Teng & Qian, Feng & Liu, Cheng & Yu, Jie & Zuo, Jianyong & Zuo, Lei, 2019. "Modeling and field-test of a compact electromagnetic energy harvester for railroad transportation," Applied Energy, Elsevier, vol. 247(C), pages 309-321.
    13. Li, Zhongjie & Jiang, Xiaomeng & Yin, Peilun & Tang, Lihua & Wu, Hao & Peng, Yan & Luo, Jun & Xie, Shaorong & Pu, Huayan & Wang, Daifeng, 2021. "Towards self-powered technique in underwater robots via a high-efficiency electromagnetic transducer with circularly abrupt magnetic flux density change," Applied Energy, Elsevier, vol. 302(C).
    14. 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).
    15. Wang, Yifeng & Li, Shoutai & Gao, Mingyuan & Ouyang, Huajiang & He, Qing & Wang, Ping, 2021. "Analysis, design and testing of a rolling magnet harvester with diametrical magnetization for train vibration," Applied Energy, Elsevier, vol. 300(C).
    16. Zou, Donglin & Liu, Gaoyu & Rao, Zhushi & Cao, Junyi & Liao, Wei-Hsin, 2022. "Design of a high-performance piecewise bi-stable piezoelectric energy harvester," Energy, Elsevier, vol. 241(C).
    17. Grzegorz Litak & Piotr Wolszczak & Jacek Caban & Jerzy Margielewicz & Damian Gąska & Xiaoqing Ma & Shengxi Zhou, 2022. "Energy Harvesting Using a Nonlinear Resonator with Asymmetric Potential Wells," Energies, MDPI, vol. 15(24), pages 1-14, December.
    18. Mingyuan Gao & Yunwu Li & Jun Lu & Yifeng Wang & Ping Wang & Li Wang, 2018. "Condition monitoring of urban rail transit by local energy harvesting," International Journal of Distributed Sensor Networks, , vol. 14(11), pages 15501477188, November.
    19. Fan, Kangqi & Wang, Chenyu & Zhang, Yan & Guo, Jiyuan & Li, Rongchun & Wang, Fei & Tan, Qinxue, 2023. "Modeling and experimental verification of a pendulum-based low-frequency vibration energy harvester," Renewable Energy, Elsevier, vol. 211(C), pages 100-111.
    20. Gao, Mingyuan & Su, Chengguang & Cong, Jianli & Yang, Fan & Wang, Yifeng & Wang, Ping, 2019. "Harvesting thermoelectric energy from railway track," Energy, Elsevier, vol. 180(C), pages 315-329.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:14:y:2021:i:5:p:1284-:d:506335. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.