Skip to main content
SpringerLink
Log in

Mathematical Model Development, Experimental Validation and Design Parameter Study of A Folded Two-Degree-of-Freedom Piezoelectric Vibration Energy Harvester

  • Regular Paper
  • Published:
International Journal of Precision Engineering and Manufacturing-Green Technology Aims and scope Submit manuscript

Abstract

A folded two-degree-of-freedom piezoelectric vibration energy harvester has been proposed by several researchers including the authors. It is characterized by the reversal of the modal sequence, which enhances the electrical output power near a target operating frequency with very little eigenfrequency separation. However, no appropriate mathematical models have yet been developed, though a well-developed one would clarify the physical behaviors and allow efficient investigations of the effects of design parameters. In this work, a rigorous mathematical model based on the continuous Euler–Bernoulli beam theory is proposed for the first time. It is validated by both a finite element analysis and by experimental measurements. The validated mathematical model is then employed for a design parameter study with four design parameters, in this case the length of each component beam and the magnitude of each proof mass. For certain selected cases from the design parameter study sets, prototypes are fabricated and their performances are measured for verification of the design parameter study. Some useful observations are also drawn from the design parameter study for the design of a high-performance folded two-degree-of-freedom piezoelectric vibration energy harvester. Through all of the results presented in this work, it is shown that the proposed mathematical model will serve as an effective tool for the analysis and design of a folded two-degree-of-freedom piezoelectric vibration energy harvester.

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

Similar content being viewed by others

References

  1. Roundy, S., Wright, P. K., & Rabaey, J. (2003). A study of low level vibrations as a power source for wireless sensor nodes. Computer Communications, 26(11), 1131–1144.

    Article  Google Scholar 

  2. Priya, S. and Inman, D. J., “Energy Harvesting Technologies,” Springer, 2009.

  3. Erturk, A. and Inman, D. J., “Piezoelectric Energy Harvesting,” John Wiley & Sons, 2011.

  4. Liu, H., Zhong, J., Lee, C., Lee, S.-W., & Lin, L. (2018). A comprehensive review on piezoelectric energy harvesting technology: Materials, mechanisms, and applications. Applied Physics Reviews, 5(4), 041306.

    Article  Google Scholar 

  5. Kim, H. S., Kim, J.-H., & Kim, J. (2011). A review of piezoelectric energy harvesting based on vibration. International Journal of Precision Engineering and Manufacturing, 12(6), 1129–1141.

    Article  Google Scholar 

  6. Erturk, A., & Inman, D. J. (2009). An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Materials and Structures, 18(2), 025009.

    Article  Google Scholar 

  7. Sodano, H. A., Park, G., & Inman, D. J. (2004). Estimation of electric charge output for piezoelectric energy harvesting. Strain Journal, 40(2), 49–58.

    Article  Google Scholar 

  8. Erturk, A., & Inman, D. J. (2008). Issues in mathematical modeling of piezoelectric energy harvesters. Smart Materials and Structures, 17(6), 065016.

    Article  Google Scholar 

  9. Kim, J. E., & Kim, Y. Y. (2011). Analysis of piezoelectric energy harvesters of a moderate aspect ratio with a distributed tip mass. Journal of Vibration and Acoustics, 133(4), 041010.

    Article  Google Scholar 

  10. Kim, J. E., Kim, H., Yoon, H., Kim, Y. Y., & Youn, B. D. (2015). An energy conversion model for cantilevered piezoelectric vibration energy harvesters using only measurable parameters. International Journal of Precision Engineering and Manufacturing-Green Technology, 2(1), 51–57.

    Article  Google Scholar 

  11. Sun, C., Qin, L., Li, F., & Wang, Q.-M. (2009). Piezoelectric energy harvesting using single crystal Pb(Mg1/3Nb2/3)O3-XPbTiO3(PMN-PT) device. Journal of Intelligent Material Systems and Structures, 20(5), 559–568.

    Article  Google Scholar 

  12. Challa, V. R., Prasad, M. G., & Fisher, F. T. (2009). A coupled piezoelectric-electromagnetic energy harvesting technique for achieving increased power output through damping matching. Smart Materials and Structures, 18(9), 095029.

    Article  Google Scholar 

  13. Kim, H., Lee, S., Cho, C., Kim, J. E., Youn, B. D., & Kim, Y. Y. (2015). An experimental method to design piezoelectric energy harvesting skin using operating deflection shapes and its application for self-powered operation of a wireless sensor networks. Journal of Intelligent Material Systems and Structures, 26(9), 1128–1137.

    Article  Google Scholar 

  14. Rupp, C. J., Evgrafov, A., Maute, K., & Dunn, M. L. (2009). Design of piezoelectric energy harvesting system: A topology optimization approach based on a multilayer plates and shells. Journal of Intelligent Material Systems and Structures, 20(16), 1923–1939.

    Article  Google Scholar 

  15. Wickenheiser, A. M., & Garcia, E. (2010). Power optimization of vibration energy harvesters utilizing passive and active circuits. Journal of Intelligent Material Systems and Structures, 21(13), 1343–1361.

    Article  Google Scholar 

  16. Tang, L., Yang, Y., & Soh, C. K. (2010). Toward broadband vibration-based energy harvesting. Journal of Intelligent Material Systems and Structures, 21(18), 1867–1897.

    Article  Google Scholar 

  17. Nguyen, M. S., Yoon, Y.-J., & Kim, P. (2019). Enhanced broadband performance of magnetically coupled 2-DOF bistable energy harvester with secondary intrawell resonance. International Journal of Precision Engineering and Manufacturing-Green Technology, 6(3), 521–530.

    Article  Google Scholar 

  18. Ma, P. S., Kim, J. E., & Kim, Y. Y. (2010). Power-amplifying strategy in vibration-powered energy harvesters. Proceedings of the SPIE, 7643, 76430O. https://doi.org/10.1117/12.848903

    Article  Google Scholar 

  19. Aldraihem, O., & Baz, A. (2011). Energy harvester with a dynamic magnifier. Journal of Intelligent Material Systems and Structures, 22(6), 521–530.

    Article  Google Scholar 

  20. Tang, X., & Zuo, L. (2011). Enhanced vibration energy harvesting using dual-mass systems. Journal of Sound and Vibration, 330(21), 5199–5209.

    Article  Google Scholar 

  21. Ou, Q., Chen, X., Gutschmidt, S., Wood, A., Leigh, N., & Arrieta, A. F. (2011). An experimentally validated double-mass piezoelectric cantilever model for broadband vibration-based energy harvesting. Journal of Intelligent Material Systems and Structures, 23(2), 117–126.

    Article  Google Scholar 

  22. Tang, L., & Yang, Y. (2012). A multiple-degree-of-freedom piezoelectric energy harvesting model. Journal of Intelligent Material Systems and Structures, 23(14), 1631–1647.

    Article  Google Scholar 

  23. Kim, J. E. & Kim, Y. Y., “Energy harvester,” KOR Patent, No. 10-1061591, August 26, 2011.

  24. Kim, J. E., & Kim, Y. Y. (2013). Power enhancing by reversing mode sequence in tuned mass-spring unit attached vibration energy harvester. AIP Advances, 3(7), 072103.

    Article  Google Scholar 

  25. Wu, H., Tang, L., Yang, Y., & Soh, C. K. (2013). A novel two-degrees-of-freedom piezoelectric energy harvester. Journal of Intelligent Material Systems and Structures, 24(3), 357–368.

    Article  Google Scholar 

  26. Wu, H., Tang, L., Yang, Y., & Soh, C. K. (2014). Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester. Journal of Intelligent Material Systems and Structures, 25(14), 1875–1889.

    Article  Google Scholar 

  27. Hu, Y., & Xu, Y. (2014). A wideband vibration energy harvester based on a folded asymmetric gapped cantilever. Applied Physics Letters, 104(5), 053902.

    Article  Google Scholar 

  28. Guan, Q. C., Ju, B., Xu, J. W., Liu, Y. B., & Feng, Z. H. (2013). Improved strain distribution of cantilever piezoelectric energy harvesting devices using H-shaped proof masses. Journal of Intelligent Material Systems and Structures, 24(9), 1059–1066.

    Article  Google Scholar 

  29. Piezo Systems, Inc. Available from https://support.piezo.com/article/62-material-properties (cited on 14 January, 2019)

Download references

Acknowledgements

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1D1A1B03028192) and also by the Center for Advanced Metamaterials (CAMM) funded by Korean Ministry of Science, ICT and Future Planning as the Global Frontier Project (CAMM-2014M3A6B3063711).

Author information

Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Daegu Catholic University, 13-13 Hayang-ro, Hayang-eup, Gyeongsan-si, Gyeongsangbuk-do, 38430, Republic of Korea

    Jae Eun Kim

  2. Institute of Technology, Hyundai Motors, 10 Suji-ro, 112bun-gil, Yongin-si, Gyeonggi-do, 16858, Republic of Korea

    Sowon Lee

  3. School of Mechanical and Aerospace Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    Yoon Young Kim

Authors
  1. Jae Eun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sowon Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoon Young Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoon Young Kim.

Ethics declarations

Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, J.E., Lee, S. & Kim, Y.Y. Mathematical Model Development, Experimental Validation and Design Parameter Study of A Folded Two-Degree-of-Freedom Piezoelectric Vibration Energy Harvester. Int. J. of Precis. Eng. and Manuf.-Green Tech. 6, 893–906 (2019). https://doi.org/10.1007/s40684-019-00149-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40684-019-00149-7

Keywords

Search

Navigation