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Shock and Vibration
Volume 2016 (2016), Article ID 3584740, 11 pages
Research Article

Chaotic Dynamics-Based Analysis of Broadband Piezoelectric Vibration Energy Harvesting Enhanced by Using Nonlinearity

Science and Technology on Integrated Logistics Support Laboratory, National University of Defense Technology, Changsha 410073, China

Received 31 August 2015; Revised 22 October 2015; Accepted 27 October 2015

Academic Editor: Carlo Trigona

Copyright © 2016 Zhongsheng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear magnetic forces are always used to enlarge resonant bandwidth of vibration energy harvesting systems with piezoelectric cantilever beams. However, how to determine properly the distance between two magnets is one of the key engineering problems. In this paper, the Melnikov theory is introduced to overcome it. Firstly, the Melnikov state-space model of the nonlinear piezoelectric vibration energy harvesting (PVEH) system is built. Based on it, chaotic dynamics mechanisms of achieving broadband PVEH by nonlinearity are exposed by potential function of the unperturbed nonlinear PVEH system. Then the corresponding Melnikov function of the nonlinear PVEH system is defined, based on which two Melnikov necessary conditions of determining the distance are obtained. Finally, numerical simulations are done to testify the theoretic results. The results demonstrate that the distance is closely related to the excitation amplitude and frequency once geometric and material parameters are fixed. Under a single-frequency excitation, the nonlinear PVEH system can generate a periodic vibration around a stable point, a large-amplitude vibration around two stable points, or a chaotic vibration. The proposed method is very valuable for optimally designing and utilizing nonlinear broadband PVEH devices in engineering applications.