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分析了微型抗磁悬浮振动能量采集器中悬浮磁体的受力特性，发现了能量采集器的单稳态和双稳态现象，研究了能量采集器在不同工作状态下该两种稳态类型时的动力学响应特性.当能量采集器处于非工作的单稳态状态时，其动力学响应是在线性系统的基础上加入非线性扰动、幅频响应曲线向右偏转；热解石墨板间距越大，非线性扰动越强烈，右偏现象则越显著.当能量采集器处于非工作的双稳态状态时，其动力学响应比较复杂，出现倍周期、4倍周期以及混沌等非线性系统特有的现象.当能量采集器处于工作状态的双稳态状态时，其振动频率和外界激励频率保持一致，进行周期振动.该研究对抗磁悬浮振动能量采集器的结构设计具有重要的参考价值，为提高能量采集器的响应特性和输出性能提供了理论指导.Based on diamagnetic levitation, the micro-vibration energy harvester is proposed, which has advantages such as low friction, low mechanical damping, low-frequency response and free of maintenance. The floating magnet is one of the most important parts in the vibration energy harvester. The dynamic properties of the floating magnet directly determine the output characteristics of the energy harvester. In order to study the vibration properties of the floating magnet, the force characteristics of the floating magnet are investigated in the vibration energy harvester. The magnetic and diamagnetic forces exerted on the floating magnet are simulated using finite element analysis software COMSOL Multiphysics. Then the dynamic characteristics of the floating magnet are further analyzed by MATLAB. In the case of the present study, when the gap between the two pyrolytic graphite plates is smaller than 7.7 mm, the floating magnet works in a monostable state. At the same time the floating magnet runs in a bistable state when the gap between the two pyrolytic graphite plates is larger than 7.7 mm. The two working states are in accordance with the experimental results. The results prove that the theoretical analysis and experimental results are in good agreement. Furthermore, the dynamic response of the energy harvester is studied in the two working states. When the coils are open-circuited and the energy harvester is in a monostable state, it is found that the dynamic response can be equivalent to that of a linear system with a nonlinear disturbance. So, the amplitude-frequency curve is right-skewed. We also analyze the influence of the gap between the two pyrolytic graphite plates on the amplitude-frequency curve. It is found that with the increase of the gap between the two pyrolytic graphite plates, the nonlinear disturbance becomes stronger, leading to a stronger right-skewed phenomenon in the amplitude-frequency curve. When the coils are open-circuited and the energy harvester is in a bistabtle state, the dynamic response is very complex, which includes double period, 4-time period and chaos. It is because the change of the amplitude of external excitation affects relative strength between the linear and nonlinear parts in the energy harvester system, resulting in the change of vibration characteristic of the floating magnet. When the coils are linked to load and the energy harvester is in a bistabtle state, the frequency of the energy harvester is consistent with that of the external excitation. This study can serve as a reference for designing the structure of the vibration energy harvester with using diamagnetic levitation. And it provides a theoretical guidance for improving the performance of the energy harvester and expanding the working bandwidth of the harvester. The energy harvester has vast application potential in wireless sensor networks and portable electronic devices.
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Keywords:
- diamagnetic levitation /
- energy harvester /
- dynamic response /
- nonlinearity
[1] Ma X C, Ye R F, Zhang T L, Zhang X Q 2016 Acta Phys. Sin. 65 177701(in Chinese) [马星晨, 叶瑞丰, 张添乐, 张晓青 2016 物理学报 65 177701]
[2] Liu L, Yuan F G 2013 J. Sound. Vib. 332 455
[3] Dai X Z, Wen Y M, Li P, Yang J, Jiang X F 2010 Acta Phys. Sin. 59 2137(in Chinese) [代显智, 文玉梅, 李平, 杨进, 江小芳 2010 物理学报 59 2137]
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[5] de Pasquale G, Siyanbalapitiya C, Som A, Wang J 2009 International Conference on Electromagnetics in Advanced Applications Torino, Italy, September 14-18, 2009 p465
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[7] Sun Y L, Chen Z H, Chen X H, Yin C, Li D J, Ma X L, Zhao F, Zhang G, Shang P, Qian A R 2015 IEEE Trans. Bio-Med. Eng. 62 900
[8] Billot M, Piat E, Abadie J, Stempfl P 2016 Sensor. Actuat. A: Phys. 238 266
[9] Hiber W, Jakoby B 2013 IEEE Sens. J. 13 2786
[10] Liu W, Chen W Y, Zhang W P, Huang X G 2008 Electron. Lett. 44 681
[11] Su Y F, Zhang K, Ye Z T, Zhang K P 2016 Instrum. Tech. Sensor 10 28(in Chinese) [苏宇锋, 张坤, 叶志通, 张鲲鹏 2016 仪表技术与传感器 10 28]
[12] Ye Z T, Duan Z Y, Takahata K, Su Y F 2015 Appl. Phys.. 118 91
[13] Qin L Z, Su Y F, Liu W F 2016 J. Electron. Meas. Instrum. 30 1438(in Chinese) [秦立振, 苏宇锋, 刘武发 2016 电子测量与仪器学报 30 1438]
[14] Ravaud R, Lemarquand G, Babic S, Lemarquand V, Akyel C 2010 IEEE Trans. Magn. 46 3585
[15] Su Y F, Ye Z T, Xiao Z M, Takahata K 2015 IEEE 10th International Conference on NEMS Xi'an China, July 7-11, 2015 p116
[16] Liu K, Zhang W P, Liu W, Chen W Y, Li K, Cui F, Li S P 2010 Microsyst. Technol. 16 431
[17] Xu W 2001 Numerical Analysis Methods for Stochastic Dynamical System (Beijing: Science Press) p179 (in Chinese) [徐伟 2001 非线性随机动力学的若干数值方法和应用(北京:科学出版社) 第179页]
[18] Lai Z H 2014 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese) [赖志慧 2014 博士论文 (天津: 天津大学)]
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[1] Ma X C, Ye R F, Zhang T L, Zhang X Q 2016 Acta Phys. Sin. 65 177701(in Chinese) [马星晨, 叶瑞丰, 张添乐, 张晓青 2016 物理学报 65 177701]
[2] Liu L, Yuan F G 2013 J. Sound. Vib. 332 455
[3] Dai X Z, Wen Y M, Li P, Yang J, Jiang X F 2010 Acta Phys. Sin. 59 2137(in Chinese) [代显智, 文玉梅, 李平, 杨进, 江小芳 2010 物理学报 59 2137]
[4] Braunbek W 1939 Z. Phys. 112 764
[5] de Pasquale G, Siyanbalapitiya C, Som A, Wang J 2009 International Conference on Electromagnetics in Advanced Applications Torino, Italy, September 14-18, 2009 p465
[6] Cao J P, Yin D C, Qian A R, Tian Z C, Xu H Y, Huang Y P, Shang P 2011 Chin. J. Space Sci. 31 63(in Chinese) [曹建平, 尹大川, 骞爱荣, 田宗成, 续惠云, 黄勇平, 商澎 2011 空间科学学报 31 63]
[7] Sun Y L, Chen Z H, Chen X H, Yin C, Li D J, Ma X L, Zhao F, Zhang G, Shang P, Qian A R 2015 IEEE Trans. Bio-Med. Eng. 62 900
[8] Billot M, Piat E, Abadie J, Stempfl P 2016 Sensor. Actuat. A: Phys. 238 266
[9] Hiber W, Jakoby B 2013 IEEE Sens. J. 13 2786
[10] Liu W, Chen W Y, Zhang W P, Huang X G 2008 Electron. Lett. 44 681
[11] Su Y F, Zhang K, Ye Z T, Zhang K P 2016 Instrum. Tech. Sensor 10 28(in Chinese) [苏宇锋, 张坤, 叶志通, 张鲲鹏 2016 仪表技术与传感器 10 28]
[12] Ye Z T, Duan Z Y, Takahata K, Su Y F 2015 Appl. Phys.. 118 91
[13] Qin L Z, Su Y F, Liu W F 2016 J. Electron. Meas. Instrum. 30 1438(in Chinese) [秦立振, 苏宇锋, 刘武发 2016 电子测量与仪器学报 30 1438]
[14] Ravaud R, Lemarquand G, Babic S, Lemarquand V, Akyel C 2010 IEEE Trans. Magn. 46 3585
[15] Su Y F, Ye Z T, Xiao Z M, Takahata K 2015 IEEE 10th International Conference on NEMS Xi'an China, July 7-11, 2015 p116
[16] Liu K, Zhang W P, Liu W, Chen W Y, Li K, Cui F, Li S P 2010 Microsyst. Technol. 16 431
[17] Xu W 2001 Numerical Analysis Methods for Stochastic Dynamical System (Beijing: Science Press) p179 (in Chinese) [徐伟 2001 非线性随机动力学的若干数值方法和应用(北京:科学出版社) 第179页]
[18] Lai Z H 2014 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese) [赖志慧 2014 博士论文 (天津: 天津大学)]
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