磁振子压电能量采集器的多尺度分析

赵健; 张国策; 陈立群

doi:10.3879/j.issn.1000-0887.2015.08.002

磁振子压电能量采集器的多尺度分析

doi: 10.3879/j.issn.1000-0887.2015.08.002

赵健¹,
张国策²,
陈立群^1,2,3

¹上海大学上海市应用数学和力学研究所,上海 200072;²上海大学理学院力学系,上海 200444;³上海市力学在能源工程中的应用重点实验室(上海大学),上海 200072

基金项目: 国家自然科学基金（重点项目）（11232009）；上海市重点学科项目（S30106）

详细信息

作者简介:
赵健(1989—)，女，山东日照人，硕士（E-mail: zhaojianwenhao@163.com）；陈立群(1963—)，男，上海人，博士，博士生导师（通讯作者. E-mail: lqchen@staff.shu.edu.cn）.

中图分类号: O322
计量
- 文章访问数: 1282
- HTML全文浏览量: 96
- PDF下载量: 968
- 被引次数: 0
出版历程
- 收稿日期: 2015-04-10
- 修回日期: 2015-06-30
- 刊出日期: 2015-08-15

Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

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)

摘要

摘要: 根据磁振子压电能量采集器实验系统的数学模型，基于系统静平衡位形，引入坐标变换，建立相对位移的标准控制方程.利用Taylor级数展开法处理磁力非线性项，运用多尺度法近似解析分析，通过消除长期项获得可解性条件，并由此推导出稳态响应时的幅频关系.四阶Runge-Kutta方法用于数值计算受迫振动时间历程，数值算例给出了系统前两阶主共振下的稳态幅频响应关系及其失稳区域.结果表明多尺度方法所得到的一致有效解具有较高精度，可以为优化设计磁振子压电能量采集器提供理论依据.
- 受迫振动 /
- 非线性 /
- 多尺度方法 /
- 能量采集
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

HTML全文

参考文献(15)

[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.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1282
HTML全文浏览量: 96
PDF下载量: 968
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

磁振子压电能量采集器的多尺度分析

doi: 10.3879/j.issn.1000-0887.2015.08.002

作者简介:
赵健(1989—)，女，山东日照人，硕士（E-mail: zhaojianwenhao@163.com）；陈立群(1963—)，男，上海人，博士，博士生导师（通讯作者. E-mail: lqchen@staff.shu.edu.cn）.

计量

Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

计量

目录

留言板

磁振子压电能量采集器的多尺度分析

doi: 10.3879/j.issn.1000-0887.2015.08.002

作者简介: 赵健(1989—)，女，山东日照人，硕士（E-mail: zhaojianwenhao@163.com）；陈立群(1963—)，男，上海人，博士，博士生导师（通讯作者. E-mail: lqchen@staff.shu.edu.cn）.

计量

出版历程

Multi-Scale Analysis of Piezoelectric Energy Harvesters With Magnetic Oscillators

计量

出版历程

目录

作者简介:
赵健(1989—)，女，山东日照人，硕士（E-mail: zhaojianwenhao@163.com）；陈立群(1963—)，男，上海人，博士，博士生导师（通讯作者. E-mail: lqchen@staff.shu.edu.cn）.