Bifurcation and Chaos Thresholds of Bistable Piezoelectric Vibration Energy Harvesting Systems

LI Hai-tao; QIN Wei-yang

doi:10.3879/j.issn.1000-0887.2014.06.007

Volume 35 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(6): 652-662

LI Hai-tao, QIN Wei-yang. Bifurcation and Chaos Thresholds of Bistable Piezoelectric Vibration Energy Harvesting Systems[J]. Applied Mathematics and Mechanics, 2014, 35(6): 652-662. doi: 10.3879/j.issn.1000-0887.2014.06.007

Citation:

PDF( 1603 KB)

Bifurcation and Chaos Thresholds of Bistable Piezoelectric Vibration Energy Harvesting Systems

doi: 10.3879/j.issn.1000-0887.2014.06.007

Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China(11172234)

Received Date: 2014-01-06
Rev Recd Date: 2014-04-03
Publish Date: 2014-06-11

Abstract

Abstract

Nonlinear dynamic performances such as homoclinic bifurcation and chaos were modeled and analyzed for bistable nonlinear vibration energy harvesting systems. According to bistability of the beam under axial loading, a model of the bistable nonlinear vibration energy harvester was established. Based on the Melnikov theory, a qualitative method was proposed to address homoclinic bifurcation of the bistable energy harvester under harmonic excitation, and the criteria for homoclinic bifurcation and the high-energy solution were derived from the Melnikov function through parameter optimization. Numerical simulation shows that the singlewell-to-doublewell transitions occur at the critical thresholds, which verifies the theoretical analysis. Research on the Melnikov method for nonlinear energy harvesting systems promises effective tools for the parametric design of high-performance energy harvesters.
- bistable energy harvester,
- Melnikov function,
- homoclinic bifurcation

FullText(HTML)

References(18)

References

[1]	Cottone F, Vocca H, Gammaitoni L. Nonlinear energy harvesting[J].Phys Rev Lett,2008,102(8): 080601.
[2]	崔岩, 王飞, 董维杰, 姚明磊, 王立鼎. 非线性压电式能量采集器[J]. 光学精密工程, 2012,20(12): 2737-2743.(CUI Yan, WANG Fei, DONG Wei-jie, YAO Ming-lei, WANG Li-ding. Nonlinear piezoelectric energy harvester[J].Optics and Precision Engineering,2012,20(12): 2737-2743.(in Chinese))
[3]	代显智, 文玉梅, 李平, 杨进, 江小芳. 采用磁电换能器的振动能量采集[J]. 物理学报, 2010,59(3): 2137-2146.(DAI Xian-zhi, WEN Yu-mei, LI Ping, YANG Jin, JIANG Xiao-fang. Vibration energy havester based on magnetoelectric transducer[J].Acta Physica Sinica, 2010,59(3): 2137-2146.(in Chinese))
[4]	陈仲生, 骆彦廷, 杨拥民. 非线性压电振动能量俘获行为建模及其不同参数影响机理研究[J]. 国防科技大学学报, 2013,35(2): 154-158.(CHEN Zhong-sheng, LUO Yan-ting, YANG Yong-min. Modeling of nonlinear piezoeletric vibration energy havesting behaviors and the effects of its different parameters[J]. Journal of National University of Defense Technology,2013,35(2): 154-158.(in Chinese))
[5]	Roundy S. On the effectiveness of vibration-based energy harvesting[J].Journal of Intelligent Material Systems and Structures,2005,16(10): 809-823.
[6]	孙舒, 曹树谦. 双稳态压电悬臂梁发电系统的动力学建模及分析[J]. 物理学报, 2012,61(21): 210505.(SUN Shu, CAO Shu-qian. Dynamical modeling and analysis of a bistable piezoeletric cantilever power generation system[J].Acta Physica Sinica,2012,61(21): 210505.(in Chinese))
[7]	Masana R, Daqaq M F. Electromechanical modeling and nonlinear analysis of axially loaded energy harvesters[J].Journal of Vibration and Acoustics, 2011,133(1): 011007.
[8]	Masana R, Daqaq M F. Relative performance of a vibratory energy harvester in mono-and bi-stable potentials[J].Journal of Sound and Vibration,2011,330(24): 6036-6052.
[9]	Masana R, Daqaq M F. Energy harvesting in the super-harmonic frequency region of a twin-well oscillator[J].Journal of Applied Physics,2012,111(4): 044501.
[10]	Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Litak G. Nonlinear piezoelectric vibration energy harvesting from an inverted cantilever beam with tip mass[J].Journal of Intelligent Material Systems and Structures,2012,23(3): 1505-1521.
[11]	Guckenheimer J, Holmes P.Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields [M]. New York: Springer-Verlag, 1983: 184-193.
[12]	Stanton S C, Mann B P, Owens B A M. Melnikov theoretic methods for characterizing the dynamics of a bistable piezoelectric inertial generator in complex spectral environments[J].Physica D,2012,241(6): 711-720.
[13]	Buckjohn C N D, Siewe M S, Fokou I S M, Tchawoua C, Kofane T C. Investigating bifurcations and chaos in magneto piezoelectric vibrating energy harvesters using Melnikov theory[J].Physica Scripta,2013,88(1): 015006.
[14]	Harne R L, Thota M, Wang K W. Concise and high-fidelity predictive criteria for maximizing performance and robustness of bistable energy harvester[J].Applied Physics Letters,2013,102(5): 053903.
[15]	Cottone F, Gammaitoni L, Vocca H, Ferrari M, Ferrari V. Piezoeletric buckled beam for random viration energy harvesting[J].Smart Materials and Structures,2012,21(3): 035021.
[16]	HUANG Xiu-chang, LIU Xing-tian, SUN Jing-ya, ZHANG Zhi-yi, HUA Hong-xing. Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: a theoretical and experimental study[J].Journal of Sound and Vibration,2014,333(4): 1132-1148.
[17]	Cao Q, Wiercigroch M, Pavlovskaia E E, Grebogi C, Thompson J M T. Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics[J]. Phil Trans R Soc A,2008,366(1865): 635-652.
[18]	TIAN Rui-lan, CAO Qing-jie, YANG Shao-pu. The codimension two bifurcation for the recent proposed SD oscillator[J].Nonlinear Dynamics,2010,59(1): 19-27.