Nonlinear Dynamics

, Volume 91, Issue 3, pp 1817–1834 | Cite as

A comprehensive study of 2:1 internal-resonance-based piezoelectric vibration energy harvesting

  • Liuyang Xiong
  • Lihua Tang
  • Brian R. Mace
Original Paper


This work exploits a 2:1 internal resonance mechanism to enhance broadband vibration energy harvesting. It is achieved by adding a properly tuned auxiliary oscillator to the primary energy harvesting oscillator coupled by a nonlinear magnetic force. A theoretical study is conducted on the nonlinear dynamic and energy harvesting performance of the proposed harvester by various analytical approximations, and the accuracy of these analytical models is investigated. Given harmonic base excitation, the output voltage frequency response is derived by the multi-scale method and harmonic balance method (HBM), which are then verified by equivalent circuit simulations and experiments. The necessity of taking into account the zeroth-order harmonic component in the HBM is verified and discussed. The HBM result without this component and the multi-scale method fail to accurately predict the nonlinear dynamic behaviour. With the validated HBM model and the equivalent circuit model, key features of internal resonance are revealed by investigating modal interaction and saturation phenomena under varying excitation. By and large, the operational bandwidth of the vibration energy harvester is enlarged due to the 2:1 internal resonance.


Energy harvesting Nonlinear internal resonance Multi-scale method Harmonic balance method Circuit simulation 



This work is financially supported by the PhD scholarship from China scholarship Council (no. 201506890009).


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of AucklandAucklandNew Zealand

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