Abstract
In this paper, we investigate the problem for a classical piezoelectric vibration energy harvester. Exact theoretical solution to the problem is derived and compared to the solutions proposed in the literature. Asymptotic expansions of the solution are explored in the hope of finding a plausible simpler approximation of the solution and corresponding output performance measures. Dependence of the output performance measures upon the electromechanical coupling factor is therefore studied. Some tips are then provided for the design of piezoelectric energy harvester.
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Acknowledgements
The authors would like to thank the financial support from the National Natural Science Foundation of China (NSFC) under Contract Number 51705112. The research presented in this paper is also supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ18E050007.
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Appendix
Appendix
whose solution is expressed by
in which
In terms of \(Q_k\) (\(k \ge 0\)), we have the following iterative relation
and the initial two values \(Q_0\) and \(Q_1\):
Hence it is shown that for \(k \ge 0\),
As a result, we obtain that for \(k \ge 1\),
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Zhou, M., Zhao, H. Revisit to the theoretical analysis of a classical piezoelectric vibration energy harvester . Arch Appl Mech 90, 2379–2395 (2020). https://doi.org/10.1007/s00419-020-01727-x
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DOI: https://doi.org/10.1007/s00419-020-01727-x