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Chaos in the fractionally damped broadband piezoelectric energy generator

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Abstract

Piezoelectric materials play a significant role in harvesting ambient vibration energy. Due to their inherent characteristics and electromechanical interaction, the system damping for piezoelectric energy harvesting can be adequately characterized by fractional calculus. This paper introduces the fractional model for magnetically coupling broadband energy harvesters under low-frequency excitation and investigates their nonlinear dynamic characteristics. The effects of fractional-order damping, excitation amplitude, and frequency on dynamic behaviors are proposed using the phase trajectory, power spectrum, Poincare map, and bifurcation diagram. The numerical analysis shows that the fractionally damped energy harvesting system exhibits chaos, periodic motion, chaos and periodic motion in turn when the fractional order changes from 0.2 to 1.5. The period doubling route to chaos and the inverse period doubling route from chaos to periodic motion can be clearly observed. It is also demonstrated numerically and experimentally that the magnetically coupling piezoelectric energy harvester possesses the usable frequency bandwidth over a wide range of low-frequency excitation. Both high-energy chaotic attractors and large-amplitude periodic response with inter-well oscillators dominate these broadband energy harvesting.

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Acknowledgments

This project is being jointly supported by the National Natural Science Foundation of China (Grant No. 51075317), Program for New Century Excellent Talents in University (Grant No. NCET-12-0453), and International Cooperation Project in Shaanxi Province (Grant No. 2011KW-21).

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Authors and Affiliations

  1. Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University, Xi’an, 710049, China

    Junyi Cao & Shengxi Zhou

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109-2140, USA

    Daniel J. Inman

  3. School of Engineering, University of California, Merced, 5200 North Lake Rd., Merced, CA, 95343, USA

    Yangquan Chen

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  1. Junyi Cao
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  2. Shengxi Zhou
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  3. Daniel J. Inman
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Correspondence to Junyi Cao.

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Cao, J., Zhou, S., Inman, D.J. et al. Chaos in the fractionally damped broadband piezoelectric energy generator. Nonlinear Dyn 80, 1705–1719 (2015). https://doi.org/10.1007/s11071-014-1320-6

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  • DOI: https://doi.org/10.1007/s11071-014-1320-6

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