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While wireless sensors, data transmission devices and medical implant devices tend to miniaturization and low consumption, energy supply modes such as batteries, solar energy and wind energy are limited due to their defects. Instead, vibration energy harvesting can open up new possibilities for self-supplying the low-consumption devices. The narrow-band random vibration with center frequency is a typical vibration in the environment, and its characteristics are closely related to the environment.This paper takes the energy harvesting system with bi-stable piezoelectric cantilever beam as a research object, and the characteristics of system's equivalent linear natural frequency, linear and nonlinear stiffness under different intervals between magnets are analyzed. By using the narrow-band random excitation with a certain bandwidth output of the bandpass filter to simulate environment vibration and using Runge-Kutta method to solve the system equation numerically, the response of system and the characteristics of energy harvesting are studied.It is observed that the variation of the magnet spacings at peak output voltage, which possesses a central frequency, is related to the variation of the equivalent linear natural frequency of the system with the interval between magnets. When the variation of magnet spacing is triggered by the narrow-band random excitation with a certain bandwidth, there is always a constant interval between magnets, making the system produce a peak output, which is like a bi-stable system that produces the peak output at optimal spacing under broad-band excitation. On the other hand, there are also more than one or two different magnet spacings making the system produce peak outputs while excitation's center frequency changes in a certain range, and the peak outputs are formed by bi-stable or single-stable “resonance” of the system, induced at the equivalent linear natural frequency. And the demarcation point spacing of the single-stable and bi-stable vibration of the system are the magnet spacing when linear stiffness is zero.Therefore, for the narrow-band random excitation in the actual environment, the magnet spacing of the energy harvesting system can be reasonably arranged according to the specific working conditions to achieve better electromechanical energy conversion. The findings in this paper can provide some theoretical and technical support for the study of harvesting the vibration energy with characteristics of narrow-band random excitation.
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Keywords:
- narrow-band random excitation /
- bistable piezoelectric cantilever beam /
- equivalent linear natural frequency /
- energy harvesting
[1] Daqaq M F, Masana R, Erturk A, Quinn D D 2014 Appl. Mech. Rev. 66 040801
[2] Roundy S, Wright P K, Rabaey J 2003 Comput. Commun. 26 1131
[3] Wang H Y, Xie T, Shan X B, Yuan J B 2010 J. Xi'an Jiaotong Univ. 44 114 (in Chinese)[王红艳, 谢涛, 单小彪, 袁江波 2010 西安交通大学学报 44 114]
[4] Priya S, Inman D J (translated by Huang J Q, Huang Q A) 2011 Energy Harvesting Technologies (Nanjing: Dongnan University Press) pp34-62 (in Chinese)[(普利亚S, 茵曼D J 著 (黄见秋, 黄庆安 译) 2011 能量收集技术 (南京: 东南大学出版社) 第34–62页]
[5] Cottone F, Vocca H, Gammaitoni L 2009 Phys. Rev. Lett. 102 080601
[6] Gammaitoni L, Neri I, Vocca H 2009 Appl. Phys. Lett. 94 164102
[7] Ferrari M, Ferrari V, Guizzetti M, Andó B, Baglio S, Trigona C 2010 Sens. Actuat. A: Phys. 162 425
[8] Ferrari M, Baù M, Guizzetti M, Ferrari V 2011 Sens. Actuat. A: Phys. 172 287
[9] Chen Z S, Yang Y M 2011 Acta Phys. Sin. 60 074301 (in Chinese)[陈仲生, 杨拥民 2011 物理学报 60 074301]
[10] Gao Y J, Leng Y G, Fan S B, Lai Z H 2014 Smart Mater. Struct. 23 095003
[11] Beeby S P, Wang L, Zhu D, Weddell A S, Merrett G V 2013 Smart Mater. Struct. 22 075022
[12] Wischke M, Masur M, Kroner M, Woias P 2011 Smart Mater. Struct. 20 085014
[13] Harne R L, Wang K W 2013 J. Vib. Acoust. 136 021009
[14] Green P L, Papatheou E, Sims N D 2013 J. Intell. Mater. Syst. Struct. 24 1494
[15] Tan D, Leng Y G, Fan S B, Gao Y J 2015 Acta Phys. Sin. 64 060502 (in Chinese)[谭丹, 冷永刚, 范胜波, 高毓璣 2015 物理学报 64 060502]
[16] Guo K K 2015 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese)[郭抗抗 2015 博士学位论文 (天津: 天津大学)]
[17] He Q, Daqaq M F 2015 J. Vib. Acoust. 137 021009
[18] Daqaq M F 2010 J. Sound Vib. 329 3621
[19] Masana R, Daqaq M F 2013 J. Sound Vib. 332 6755
[20] Barton D A W, Burrow S G, Clare L R 2010 J. Vib. Acoust. 132 021009
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[1] Daqaq M F, Masana R, Erturk A, Quinn D D 2014 Appl. Mech. Rev. 66 040801
[2] Roundy S, Wright P K, Rabaey J 2003 Comput. Commun. 26 1131
[3] Wang H Y, Xie T, Shan X B, Yuan J B 2010 J. Xi'an Jiaotong Univ. 44 114 (in Chinese)[王红艳, 谢涛, 单小彪, 袁江波 2010 西安交通大学学报 44 114]
[4] Priya S, Inman D J (translated by Huang J Q, Huang Q A) 2011 Energy Harvesting Technologies (Nanjing: Dongnan University Press) pp34-62 (in Chinese)[(普利亚S, 茵曼D J 著 (黄见秋, 黄庆安 译) 2011 能量收集技术 (南京: 东南大学出版社) 第34–62页]
[5] Cottone F, Vocca H, Gammaitoni L 2009 Phys. Rev. Lett. 102 080601
[6] Gammaitoni L, Neri I, Vocca H 2009 Appl. Phys. Lett. 94 164102
[7] Ferrari M, Ferrari V, Guizzetti M, Andó B, Baglio S, Trigona C 2010 Sens. Actuat. A: Phys. 162 425
[8] Ferrari M, Baù M, Guizzetti M, Ferrari V 2011 Sens. Actuat. A: Phys. 172 287
[9] Chen Z S, Yang Y M 2011 Acta Phys. Sin. 60 074301 (in Chinese)[陈仲生, 杨拥民 2011 物理学报 60 074301]
[10] Gao Y J, Leng Y G, Fan S B, Lai Z H 2014 Smart Mater. Struct. 23 095003
[11] Beeby S P, Wang L, Zhu D, Weddell A S, Merrett G V 2013 Smart Mater. Struct. 22 075022
[12] Wischke M, Masur M, Kroner M, Woias P 2011 Smart Mater. Struct. 20 085014
[13] Harne R L, Wang K W 2013 J. Vib. Acoust. 136 021009
[14] Green P L, Papatheou E, Sims N D 2013 J. Intell. Mater. Syst. Struct. 24 1494
[15] Tan D, Leng Y G, Fan S B, Gao Y J 2015 Acta Phys. Sin. 64 060502 (in Chinese)[谭丹, 冷永刚, 范胜波, 高毓璣 2015 物理学报 64 060502]
[16] Guo K K 2015 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese)[郭抗抗 2015 博士学位论文 (天津: 天津大学)]
[17] He Q, Daqaq M F 2015 J. Vib. Acoust. 137 021009
[18] Daqaq M F 2010 J. Sound Vib. 329 3621
[19] Masana R, Daqaq M F 2013 J. Sound Vib. 332 6755
[20] Barton D A W, Burrow S G, Clare L R 2010 J. Vib. Acoust. 132 021009
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