Skip to main content

Advertisement

SpringerLink
Log in

Modeling and analysis of magnetically coupled piezoelectric dual beam with an annular potential energy function for broadband vibration energy harvesting

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Conventional piezoelectric cantilever-based vibration energy harvesters have narrow bandwidth. In this article, we develop a dual-beam piezoelectric energy harvester featuring an annular potential energy function that can harvest vibration energy over a wide spectrum under small amplitude excitations. The proposed harvester contains two conventional piezoelectric cantilevers placed orthogonal to each other which are coupled by repulsive magnetic force. We demonstrate analytically and numerically that a new annular potential energy function can be built with proper configuration. In the new annular stable state, the harvester can detour around the potential barrier rather than jump over it, yielding large amplitude voltage outputs throughout a wide spectrum. Case studies were carried out, and it is proved that the proposed annular stable harvester has a bandwidth of 3.9 Hz and a voltage output performance 3.01 times better than that of a conventional bistable one under excitations of 3 m/s2. The nonlinear dynamics of the proposed harvester are analyzed in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Data availability

All necessary data needed to generate the results obtained in this study have been included in the article.

References

  1. Kim, H.S., Kim, J.H., Kim, J.: A review of piezoelectric energy harvesting based on vibration. Int. J. Precis. Eng. Manuf. 12, 1129–1141 (2011). https://doi.org/10.1007/s12541-011-0151-3

    Article  Google Scholar 

  2. Erturk, A., Inman, D.J.: An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct. 18, 025009 (2009). https://doi.org/10.1088/0964-1726/18/2/025009

    Article  Google Scholar 

  3. Challa, V.R., Prasad, M.G., Shi, Y., Fisher, F.T.: A vibration energy harvesting device with bidirectional resonance frequency tunability. Smart Mater. Struct. 17, 015035 (2008). https://doi.org/10.1088/0964-1726/17/01/015035

    Article  Google Scholar 

  4. Tang, L., Yang, Y., Soh, C.K.: Toward broadband vibration-based energy harvesting. J. Intell. Mater. Syst. Struct. 21, 1867–1897 (2010). https://doi.org/10.1177/1045389X10390249

    Article  Google Scholar 

  5. Al-Ashtari, W., Hunstig, M., Hemsel, T., Sextro, W.: Frequency tuning of piezoelectric energy harvesters by magnetic force. Smart Mater. Struct. 21, 035019 (2012). https://doi.org/10.1088/0964-1726/21/3/035019

    Article  Google Scholar 

  6. Liu, C., Jing, X.: Nonlinear vibration energy harvesting with adjustable stiffness, damping and inertia. Nonlinear Dyn. 88, 79–95 (2017). https://doi.org/10.1007/s11071-016-3231-1

    Article  Google Scholar 

  7. Liu, H., Lee, C.K., Kobayashi, T., Tay, C.J., Quan, C.G.: Investigation of a MEMS piezoelectric energy harvester system with a frequency-widened-bandwidth mechanism introduced by mechanical stoppers. Smart Mater. Struct. 21, 035005 (2012). https://doi.org/10.1088/0964-1726/21/3/035005

    Article  Google Scholar 

  8. Tang, L., Yang, Y.: A nonlinear piezoelectric energy harvester with magnetic oscillator. Appl. Phys. Lett. 101, 094102 (2012). https://doi.org/10.1063/1.4748794

    Article  Google Scholar 

  9. Lan, C., Qin, W.: Enhancing ability of harvesting energy from random vibration by decreasing the potential barrier of bistable harvester. Mech. Syst. Signal Process. 85, 71–81 (2017). https://doi.org/10.1016/j.ymssp.2016.07.047

    Article  Google Scholar 

  10. Ramlan, R., Brennan, M.J., Mace, B.R., et al.: Potential benefits of a non-linear stiffness in an energy harvesting device. Nonlinear Dyn. 59, 545–558 (2010). https://doi.org/10.1007/s11071-009-9561-5

    Article  MATH  Google Scholar 

  11. Kulah, H., Najafi, K.: Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications. IEEE Sens. J. 8, 261–268 (2008). https://doi.org/10.1109/JSEN.2008.917125

    Article  Google Scholar 

  12. Fu, H., Yeatman, E.M.: Rotational energy harvesting using bi-stability and frequency up-conversion for low-power sensing applications: theoretical modeling and experimental validation. Mech. Syst. Signal Process. 125, 229–244 (2019). https://doi.org/10.1016/j.ymssp.2018.04.043

    Article  Google Scholar 

  13. Shahruz, S.M.: Design of mechanical band-pass filters for energy scavenging. J. Sound Vib. 292, 987–998 (2006). https://doi.org/10.1016/j.jsv.2005.08.018

    Article  Google Scholar 

  14. Xu, J., Tang, J.: Multi-directional vibration energy harvesting by internal resonance. Appl. Phys. Lett. 107, 21 (2015). https://doi.org/10.1063/1.4936607

    Article  Google Scholar 

  15. Xu, C., Zhao, L.: Investigation on the characteristics of a novel internal resonance galloping oscillator for concurrent aeroelastic and base vibratory energy harvesting. Mech. Syst. Signal Process. 173, 109022 (2022). https://doi.org/10.1016/j.ymssp.2022.109022

    Article  Google Scholar 

  16. Xiong, L., Tang, L., Mace, B.R.: A comprehensive study of 2:1 internal-resonance-based piezoelectric vibration energy harvesting. Nonlinear Dyn. 91, 1817–1834 (2018). https://doi.org/10.1007/s11071-017-3982-3

    Article  Google Scholar 

  17. Sebald, G., Kuwano, H., Guyomar, D.: Simulation of a Duffing oscillator for broadband piezoelectric energy harvesting. Smart Mater. Struct. 20, 075022 (2011). https://doi.org/10.1088/0964-1726/20/7/075022

    Article  Google Scholar 

  18. Stanton, S.C., McGehee, C.C., Mann, B.P.: Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Phys. D 239, 640–653 (2010). https://doi.org/10.1016/j.physd.2010.01.019

    Article  MATH  Google Scholar 

  19. Cottone, F., Vocca, H., Gammaitoni, L.: Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601 (2009). https://doi.org/10.1103/PhysRevLett.102.080601

    Article  Google Scholar 

  20. Erturk, A., Hoffmann, J., Inman, D.J.: A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett. 94, 254102 (2009). https://doi.org/10.1063/1.3159815

    Article  Google Scholar 

  21. Erturk, A., Inman, D.J.: Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling. J. Sound Vib. 330, 2339–2353 (2011). https://doi.org/10.1016/j.jsv.2010.11.018

    Article  Google Scholar 

  22. Litak, G., Friswell, M.I., Adhikari, S.: Magnetopiezoelastic energy harvesting driven by random excitations. Appl. Phys. Lett. 96, 214103 (2010). https://doi.org/10.1063/1.3436553

    Article  Google Scholar 

  23. Masana, R., Daqaq, M.F.: Relative performance of a vibratory energy harvester in mono- and bi-stable potential. J. Sound Vib. 330, 6036–6052 (2011). https://doi.org/10.1016/j.jsv.2011.07.031

    Article  Google Scholar 

  24. Leadenham, S., Erturk, A.: Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances. Smart Mater. Struct. 24, 055021 (2015). https://doi.org/10.1088/0964-1726/24/5/055021

    Article  Google Scholar 

  25. Kim, P., Seok, J.: Dynamic and energetic characteristics of a tri-stable magnetopiezoelastic energy harvester. Mech. Mach. Theory 94, 41–63 (2015). https://doi.org/10.1016/j.mechmachtheory.2015.08.002

    Article  Google Scholar 

  26. Yang, T., Cao, Q.: Dynamics and performance evaluation of a novel tristable hybrid energy harvester for ultra-low level vibration resources. Int. J. Mech. Sci. 156, 123–136 (2019). https://doi.org/10.1016/j.ijmecsci.2019.03.034

    Article  Google Scholar 

  27. Zhou, S., Cao, J., Inman, D.J., Lin, J., Liu, S., Wang, Z.: Broadband tristable energy harvester: modeling and experiment verification. Appl. Energy 133, 33–39 (2014). https://doi.org/10.1016/j.apenergy.2014.07.077

    Article  Google Scholar 

  28. Yang, W., Towfighian, S.: Internal resonance and low frequency vibration energy harvesting. Smart Mater. Struct. 26, 095008 (2017). https://doi.org/10.1088/1361-665X/aa791d

    Article  Google Scholar 

  29. Yang, W., Towfighian, S.: A parametric resonator with low threshold excitation for vibration energy harvesting. J. Sound Vib. 446, 129–143 (2019). https://doi.org/10.1016/j.jsv.2019.01.038

    Article  Google Scholar 

  30. Lin, W., et al.: A nonlinear magnetic and torsional spring coupling piezoelectric energy harvester with internal resonance. Smart Mater. Struct. 31, 115007 (2022). https://doi.org/10.1088/1361-665X/ac9657

    Article  Google Scholar 

  31. Yang, W., Towfighian, S.: A hybrid nonlinear vibration energy harvester. Mech. Syst. Signal Process. 90, 317–333 (2017). https://doi.org/10.1016/j.ymssp.2016.12.032

    Article  Google Scholar 

  32. Wang, Z., et al.: Nonlinear broadband piezoelectric vibration energy harvesting enhanced by inter-well modulation. Energy Convers. Manag. 246, 114661 (2021). https://doi.org/10.1016/j.enconman.2021.114661

    Article  Google Scholar 

  33. Yang, W., Towfighian, S.: Low frequency energy harvesting with a variable potential function under random vibration. Smart Mater. Struct. 27, 114004 (2018). https://doi.org/10.1088/1361-665X/aacbaf

    Article  Google Scholar 

  34. Zhang, Y., Ding, C., Wang, J., et al.: High-energy orbit sliding mode control for nonlinear energy harvesting. Nonlinear Dyn. 105, 191–211 (2021). https://doi.org/10.1007/s11071-021-06616-8

    Article  Google Scholar 

  35. Fang, S., Chen, K., Xing, J., Zhou, S., Liao, W.H.: Tuned bistable nonlinear energy sink for simultaneously improved vibration suppression and energy harvesting. Int. J. Mech. Sci. 212(3), 106838 (2021). https://doi.org/10.1016/j.ijmecsci.2021.106838

    Article  Google Scholar 

  36. Tang, L., Yang, Y., Soh, C.K.: Improving functionality of vibration energy harvesters using magnets. J. Intell. Mater. Sys. Struct. 23, 1433–1449 (2012). https://doi.org/10.1177/1045389X12443016

    Article  Google Scholar 

  37. Andò, B., Baglio, S., Maiorca, F., Trigona, C.: Analysis of two dimensional, wide-band, bistable vibration energy harvester. Sens. Actuator A Phys. 202, 176–182 (2013). https://doi.org/10.1016/j.sna.2013.02.025

    Article  Google Scholar 

  38. ANSI/IEEE.176–1987 (1988) IEEE standard on piezoelectricity. https://doi.org/10.1109/IEEESTD.1978.8941331

  39. Yung, K.W., Landecker, P.B., Villani, D.D.: An analytic solution for the force between two magnetic dipoles. Magn. Electr. Sep. 9, 39–52 (1998). https://doi.org/10.1155/1998/79537

    Article  Google Scholar 

  40. Stanton, S.C., Owens, B.A.M., Mann, B.P.: Harmonic balance analysis of the bistable piezoelectric inertial generator. J Sound Vib. 331, 3617–3627 (2012). https://doi.org/10.1016/j.jsv.2012.03.012

    Article  Google Scholar 

  41. Wu, H., Tang, L., Yang, Y.: Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester. J. Intell. Mater. Syst. Struct. 25, 1875–1889 (2014). https://doi.org/10.1177/1045389X14541494

    Article  Google Scholar 

  42. Wu, Z., Harne, R.L., Wang, K.W.: Energy harvester synthesis via coupled linear-bistable system with multistable dynamics. J. Appl. Mech. 81, 061005 (2014). https://doi.org/10.1115/1.4026555

    Article  Google Scholar 

  43. Lan, C., Tang, L., Qin, W., Xiong, L.: Magnetically coupled dual-beam energy harvester: benefit and trade-off. J. Intell. Mater. Syst. Struct. 29, 1216–1235 (2017). https://doi.org/10.1177/1045389X17730927

    Article  Google Scholar 

Download references

Funding

National Natural Science Foundation of China (Grant Nos. 51905094 and 52275093), Fundamental Research Funds for the Central Universities (Grant No. 2242023K40013) and the “Zhishan” Scholars Programs of Southeast University (Grant No. 3222002205A2).

Author information

Authors and Affiliations

  1. School of Instrument Science and Engineering, Southeast University, Nanjing, 210096, Jiangsu, China

    Nan Shao, Zhuo Chen, Xian Wang, Chengxin Zhang, Jiawen Xu & Xiaosu Xu

  2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Ruqiang Yan

Authors
  1. Nan Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhuo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiawen Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiaosu Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ruqiang Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiawen Xu.

Ethics declarations

Conflict of interest

The author declares that he has no conflicts of interest to report regarding the present study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A

Appendix A

\({Q}_{i} (i=\mathrm{1,2},\mathrm{3,4},\mathrm{5,6})\) in Eqs. (20) and (21) can be expressed as:

$$ \begin{gathered} Q_{1} = \frac{1}{4}\left( {3A^{3} + 3AC^{2} + AD^{2} + 4AJ^{2} + 3AB^{2} + 12AI^{2} + 2BCD + 8CIJ} \right) \hfill \\ Q_{2} = \frac{1}{4}\left( {3 \, B^{3} + 3BD^{2} + BC^{2} + 4BJ^{2} + 3A^{2} B + 12 \, BI^{2} + 2ACD + 8DIJ} \right) \hfill \\ Q_{3} = \frac{1}{4}\left( {4I^{3} + 2C^{2} I + 2D^{2} I + 4IJ^{2} + 6A^{2} I + 6 \, B^{2} I + 4ACJ + 4BDJ} \right) \hfill \\ Q_{4} = \frac{1}{4}\left( {3C^{3} + 3A^{2} C + B^{2} C + 4CI^{2} + 3CD^{2} + 12CJ^{2} + 2ABD + 8AIJ} \right) \hfill \\ Q_{5} = \frac{1}{4}\left( {3D^{3} + 3B^{2} D + A^{2} D + 4DI^{2} + 3C^{2} D + 12DJ^{2} + 2ABC + 8BIJ} \right) \hfill \\ Q_{6} = \frac{1}{4}\left( {4J^{3} + 2A^{2} J + 2B^{2} J + 4I^{2} J + 6C^{2} J + 6D^{2} J + 4ACI + 4BDI} \right) \hfill \\ \end{gathered} $$
(A1a-f)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shao, N., Chen, Z., Wang, X. et al. Modeling and analysis of magnetically coupled piezoelectric dual beam with an annular potential energy function for broadband vibration energy harvesting. Nonlinear Dyn 111, 11911–11937 (2023). https://doi.org/10.1007/s11071-023-08503-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08503-w

Keywords

Search

Navigation