Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

ZHAO Jian; ZHANG Guo-ce; CHEN Li-qun

doi:10.3879/j.issn.1000-0887.2015.08.002

Volume 36 Issue 8

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ZHAO Jian, ZHANG Guo-ce, CHEN Li-qun. Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators[J]. Applied Mathematics and Mechanics, 2015, 36(8): 805-813. doi: 10.3879/j.issn.1000-0887.2015.08.002

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Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

doi: 10.3879/j.issn.1000-0887.2015.08.002

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;²Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, P.R.China;³Shanghai Key Laboratory of Mechanics in Energy Engineering(Shanghai University), Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China(Key Program)(11232009)

Received Date: 2015-04-10
Rev Recd Date: 2015-06-30
Publish Date: 2015-08-15

Abstract

Abstract

A piezoelectric energy harvester with a magnetic oscillator was studied. The dynamic equation was derived via introduction of coordinate transform based on the equilibrium configuration. The Taylor series expansion method was employed to deal with the nonlinear function of the magnetic force. The multi-scale method was applied to obtain the steady-state periodic solutions of the system. The solvability condition and the amplitude-frequency relationship were derived through elimination of the secular terms. Then the Runge-Kutta method was used to numerically calculate the system’s forced vibration time history and give the amplitude-frequency response characteristics and instability boundary of the 1st 2 primary resonance cases. The results show that the multi-scale analysis yields uniformly valid solutions of high accuracy, and provides a theoretic base for the optimal design of piezoelectric energy harvesters with magnetic oscillators.
- forced vibration,
- nonlinearity,
- multi-scale method,
- energy harvesting

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References(15)

References

[1]	杨志安, 贾尚帅. RLC串联电路与微梁耦合系统1∶2内共振分析[J]. 应用力学学报, 2010,27(1): 80-85.(YANG Zhi-an, JIA Shang-shuai. Analysis of the 1∶2 internal resonance of coupled RLC circuit and microbeam system[J].Chinese Journal of Applied Mechanics,2010,27(1): 80-85.(in Chinese))
[2]	李海涛, 秦卫阳. 双稳态压电能量获取系统的分岔混沌阈值[J]. 应用数学和力学, 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.(in Chinese))
[3]	郭抗抗, 曹树谦. 压电发电悬臂梁的非线性动力学建模及响应分析[J]. 动力学与控制学报, 2014,12(1): 18-23.(GUO Kang-kang, CAO Shu-qian. Nonlinear modeling and analysis of piezoelectric cantilever energy harvester[J].Journal of Dynamics and Control,2014,12(1): 18-23.(in Chinese))
[4]	杨德庆, 刘正兴. 自由端受集中力作用下压电悬臂梁弯曲问题解析解[J]. 力学季刊, 2003,24(3): 327-333.(YANG De-qing, LIU Zheng-xing. Analytical solution for bending of a piezoelectric cantilever beam under an end load[J].Chinese Quarterly of Mechanics,2003,24(3): 327-333.(in Chinese))
[5]	Williams C B, Yates R B. Analysis of a micro-electric generator for microsystems[J].Sensors and Actuators A: Physical,1996,52(1/3): 8-11.
[6]	Kim I H, Jung H J, Lee B M, Jang S J. Broadband energy-harvesting using a two degree-of-freedom vibrating body[J].Applied Physics Letters,2011,98(21): 214102.
[7]	Shahruz S M. Design of mechanical band-pass filters with large frequency bands for energy scavenging[J].Mechatronics,2006,16(9): 523-531.
[8]	Ferrari M, Ferrari V, Guizzetti M, Marioli D, Taroni A. Piezoelectric multifrequency energy converter for power harvesting in autonomous microsystems[J].Sensors and Actuators A: Physical,2008,142(1): 329-335.
[9]	YANG Zeng-tao, YANG Jia-shi. Connected vibrating piezoelectric bimorph beams as a wide-band piezoelectric power harvester[J].Journal of Intelligent Material Systems and Structures,2009,20(5): 569-574.
[10]	Daqaq M F, Masana R, Erturk A, Quinm D D. On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion[J].Applied Mechanics Reviews,2014,66(4): 040801.
[11]	Cottone F, Vocca H, Gammaitoni L. Nonlinear energy harvesting[J].Physical Review Letters,2009,102(8): 080601.
[12]	WU Hao, TANG Li-hua, YANG Yao-wen, SOH Chee-kiong. A novel two-degrees-of-freedom piezoelectric energy harvester[J].Journal of Intelligent Material Systems and Structures,2013,24(3): 357-368. doi: 10.1177/1045389X12457254.
[13]	WU Hao, TANG Li-hua, YANG Yao-wen, SOH Chee-kiong. Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester[J].Journal of Intelligent Material Systems and Structures,2014,25(14): 1875-1889. doi: 10.1177/1045389X14541494.
[14]	TANG Li-hua, YANG Yao-wen. A nonlinear piezoelectric energy harvester with magnetic oscillator[J].Applied Physics Letters,2012,101(9): 094102.
[15]	Daqaq M F, Stabler C, Qaroush Y, Seuaciuc-Osório T. Investigation of power harvesting via parametric excitations[J].Journal of Intelligent Material Systems and Structures,2009,20(5): 545-557.