Article Sidebar

Published: 17/12/2025
Abstract Views: 0
Views PDF: 0
Issue
No. 97 (2025)
Section
Articles
How to Cite
Nguyen, N. H., Nguyen, V. M., Nguyen, N. L., & Anh Tran, T. (2025). Phase portrait analysis of a cantilevered piezoelectric-electromagnetic energy harvester. Journal of Water Resources & Environmental Engineering, 97, 85-90. https://dev.vojs.vn/index.php/jwree/article/view/19

Phase portrait analysis of a cantilevered piezoelectric-electromagnetic energy harvester

Ngoc Hung Nguyen1,2, Van Manh Nguyen3, Ngoc Linh Nguyen4, Tuan Anh Tran5,6,
1 Faculty of Engineering Mechanics and Automation, VNU University of Engineering and Technology, Vietnam National University, Vietnam
2 Department of Science and Technology of Thanh Hoa Province, Vietnam
3 Faculty of Mechanical Engineering, Hanoi University of Civil Engineering, Vietnam
4 Faculty of Mechanical Engineering, Thuyloi University, Vietnam
5 Anh
6 Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi, Vietnam

Main Article Content

Abstract

This paper investigates a piezoelectric-electromagnetic hybrid energy harvester (PEM-HEH) which has only been developed recently where a linear electromagnetic harvester is attached to the free end of a cantilevered piezoelectric bimorph. First, the electromechanical model of PEM-HEH is introduced based on Euler–Bernoulli theory and Lagrange’s equations. It is demonstrated the coupling between the linear transverse motion of the piezoelectric bimorph and the nonlinear axial motion of the magnet inside the electromagnetic harvester. It turns out that the combination of two linear harvesters leads to a frequency-doubling effect in a nonlinear system. Next, a sample test is implemented to verify the characteristics of the nonlinearity of the system in phase portrait. Finally, relevant conclusions could be drawn.

Article Details

Keywords

Cantilevered piezoelectric bimorph, linear electromagnetic harvester, piezoelectric-electromagnetic hybrid energy harvester, frequency-doubling, phase portrait

References

Ahmad M. M., Khan F. U. (2020), “Review of vibration‐based electromagnetic- piezoelectric hybrid energy harvesters”, International Journal of Energy Research, p. 1–40,
doi:10.1002/er.6253.
Erturk A., Inman D. J. (2011), “Piezoelectric Energy Harvesting”, John Wiley & Sons.
Fan Y., Niu M.-Q., Ghayesh M. H., Amabili M., Chen L.-Q. (2024), “Nonlinear vibration energy harvesting via parametric excitation: Snap-through with time-varying potential wells”, Mechanical Systems and Signal Processing, 220, 111625,
doi:10.1016/j.ymssp.2024.111625.
Fang S., Zhou S., Yurchenko D., Yang T., Liao W. H. (2022), “Multistability phenomenon in signal processing, energy harvesting, composite structures, and metamaterials: A review”, Mechanical Systems and Signal Processing, 166, 108419,
doi:10.1016/j.ymssp.2021.108419.
Zheng R., Nakano K., Hu H., Su D., Cartmell M. P. (2014), “An application of stochastic resonance for energy harvesting in a bistable vibrating system”, Journal of Sound and Vibration, 333(12), p. 2568–2587,
doi:10.1016/j.jsv.2014.01.020.
Li P., Gao S., Niu S., Liu H., Cai H. (2014), “An analysis of the coupling effect for a hybrid piezoelectric and electromagnetic energy harvester”, Smart Materials and Structures, 23(6), 065016,
doi:10.1088/0964-1726/23/6/065016.
Hung N. N., Viet L. D., Linh N. N. (2025), “On a doubled-frequency squared-amplitude hybrid energy harvester”, International Journal of Non-Linear Mechanics, 178, 105192,
doi:10.1016/j.ijnonlinmec.2025.105192.