Dynamic modeling and structural optimization of a bistable electromagnetic vibration energy harvester

Bei Zhang, Qichang Zhang, Wei Wang*, Jianxin Han, Xiaoli Tang, Fengshou Gu, Andrew D. Ball

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A novel bistable electromagnetic vibration energy harvester (BEMH) is constructed and optimized in this study, based on a nonlinear system consisting mainly of a flexible membrane and a magnetic spring. A large-amplitude transverse vibration equation of the system is established with the general nonlinear geometry and magnetic force. Firstly, the mathematical model, considering the higher-order nonlinearities given by nonlinear Galerkin method, is applied to a membrane with a co-axial magnet mass and magnetic spring. Secondly, the steady vibration response of the membrane subjected to a harmonic base motion is obtained, and then the output power considering electromagnetic effect is analytically derived. On this basis, a parametric study in a broad frequency domain has been achieved for the BEMH with different radius ratios and membrane thicknesses. It is demonstrated that model predictions are both in close agreement with results from the finite element simulation and experiment data. Finally, the proposed efficient solution method is used to obtain an optimizing strategy for the design of multi-stable energy harvesters with the similar flexible structure.

Original languageEnglish
Article number2410
Issue number12
Publication statusPublished - 23 Jun 2019

Bibliographical note

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Funding: This research was funded by the National Natural Science Foundation of China, grant 11872044, 11772218 and 11702192; the International Exchanges Cost Share 2018 China (NSFC-RS) award (IEC\NSFC\181496); the Tianjin Research Programme of Application Foundation and Advanced Technology grant 17JCYBJC18900 and the National Key Research and Development Program of China grant 2018YFB0106200.


  • Design
  • Dynamic response
  • Electromagnetic vibration energy harvester
  • Nonlinear Galerkin method
  • Optimization
  • Output power


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