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Chin. Phys. B, 2020, Vol. 29(10): 100503    DOI: 10.1088/1674-1056/aba5fd
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Broadband energy harvesting based on one-to-one internal resonance

Wen-An Jiang(姜文安)1, Xin-Dong Ma(马新东)1, Xiu-Jing Han(韩修静)1,†, Li-Qun Chen(陈立群)2,3, and Qin-Sheng Bi(毕勤胜)1
1 Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
2 School of Science, Harbin Institute of Technology, Shenzhen 518055, China
3 Department of Mechanics, Shanghai University, Shanghai 200072, China
Abstract  

We design an electromechanical transducer harvesting system with one-to-one internal resonance that can emerge a broader spectrum vibrations. The novel harvester is composed of a Duffing electrical circuit coupled to a mobile rod, and the coupling between both components is realized via the electromagnetic force. Approximate analytical solutions of the electromechanical system are carried out by introducing the multiple scales analysis, also the nonlinear modulation equation for one-to-one internal resonance is obtained. The character of broadband harvesting performance are analyzed, the two peaks and one jump phenomenon bending to the right for variation of control parameters are observed. It is shown that an advanced bandwidth over a corresponding linear model that does not possess a modal energy interchange.

Keywords:  energy harvesting      internal resonance      broadband      nonlinear modal interactions  
Received:  14 April 2020      Revised:  06 July 2020      Published:  05 October 2020
PACS:  05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)  
  77.65.-j (Piezoelectricity and electromechanical effects)  
Corresponding Authors:  Corresponding author. E-mail: xjhan@mail.ujs.edu.cn   
About author: 
†Corresponding author. E-mail: xjhan@mail.ujs.edu.cn
* Project supported by the National Natural Science Foundation of China (Grant Nos. 11632008 and 11702119), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170565), China Postdoctoral Science Foundation (Grant No. 2020M671353), and Jiangsu Planned Projects for Postdoctoral Research Funds, China (Grant No. 2020Z376).

Cite this article: 

Wen-An Jiang(姜文安), Xin-Dong Ma(马新东), Xiu-Jing Han(韩修静)†, Li-Qun Chen(陈立群), and Qin-Sheng Bi(毕勤胜) Broadband energy harvesting based on one-to-one internal resonance 2020 Chin. Phys. B 29 100503

Fig. 1.  

Schematic diagram of the electromechanical transducer vibratory energy harvesters.

Fig. 2.  

Model of nonlinear capacitor.[42]

Fig. 3.  

Frequency-resonance curves for different amplitudes of voltage source.

Fig. 4.  

Frequency-resonance curves for different cubic nonlinear coefficients.

Fig. 5.  

Frequency-resonance curves for different resistors R1.

Fig. 6.  

Frequency-resonance curves for different damping coefficients.

Fig. 7.  

Frequency-resonance curves for different magnetic strengths B1.

Fig. 8.  

Frequency-resonance curves for different magnetic strengths B2.

Fig. 9.  

Comparison of the internal resonance and the linear results.

Fig. 10.  

Comparison of the analytical and the numerical results.

[1]
Challa V, Prasad M, Shi Y, Fisher F 2008 Smart Mater. Struct. 75 015035
[2]
Shahruz S M 2006 J. Sound Vib. 292 987 DOI: 10.1016/j.jsv.2005.08.018
[3]
Fan K Q, Xu C H, Wang W D, Fang Y 2014 Chin. Phys. B 23 084501 DOI: 10.1088/1674-1056/23/8/084501
[4]
Li H T, Qin W Y 2016 Chin. Phys. B 25 110503 DOI: 10.1088/1674-1056/25/11/110503
[5]
Zhang Y W, Wang C, Yuan B, Fang B 2017 Shock Vib. 1987456 1
[6]
Yan Z M, Hajj M 2017 J. Intel. Mat. Syst. Str. 28 254 DOI: 10.1177/1045389X16649450
[7]
Cao D X, Gao Y H, Hu W H 2019 Acta Mech. Sinica 35 894 DOI: 10.1007/s10409-019-00852-3
[8]
Tan T, Yan Z M, Zou Y J, Zhang W M 2019 Mech. Syst. Signal Pr. 123 513 DOI: 10.1016/j.ymssp.2019.01.004
[9]
Jiang W A, Sun P, Zhao G L, Chen L Q 2019 Appl. Math. Mech. -Engl. Ed. 40 579 DOI: 10.1007/s10483-019-2467-8
[10]
Guo X Y, Wang S B, Sun L, Cao D X 2020 Acta Mech. Sinica 36 234 DOI: 10.1007/s10409-019-00923-5
[11]
Cottone F, Vocca H, Gammaitoni L 2009 Phys. Rev. Lett. 102 080601 DOI: 10.1103/PhysRevLett.102.080601
[12]
Wang G Y, Tang L H 2017 Mech. Syst. Signal Pr. 86 29 DOI: 10.1016/j.ymssp.2016.10.001
[13]
Zou H X, Zhang W M, Wei K X, Li W B, Peng Z K, Meng G 2016 J. Appl. Mech. 83 121005 DOI: 10.1115/1.4034563
[14]
Lan C B, Qin W Y 2017 Mech. Syst. Signal Pr. 85 71 DOI: 10.1016/j.ymssp.2016.07.047
[15]
Zhou Z Y, Qin W Y, Du W F, Zhu P, Liu Q 2019 Mech. Syst. Signal Pr. 115 162 DOI: 10.1016/j.ymssp.2018.06.003
[16]
Cao J Y, Zhou S X, Wang W, Lin J 2015 Appl. Phys. Lett. 106 173903 DOI: 10.1063/1.4919532
[17]
Zhou Z Y, Qin W Y, Zhu P 2017 Mech. Syst. Signal Pr. 84 158 DOI: 10.1016/j.ymssp.2016.07.001
[18]
Wang B, Zhang Q C, Wang W, Feng J J 2018 Mech. Syst. Signal Pr. 112 305 DOI: 10.1016/j.ymssp.2018.04.027
[19]
Yang S, Cao Q J 2019 J. Stat. Mech.-Theory E 033405
[20]
Li H T, Qin W Y 2015 Nonlinear Dyn. 81 1751 DOI: 10.1007/s11071-015-2104-3
[21]
Li H T, Qin W Y, Lan C B, Deng W Z, Zhou Z Y 2016 Smart Mater. Struct. 25 015001 DOI: 10.1088/0964-1726/25/1/015001
[22]
Chen L Q, Jiang W A 2015 J. Appl. Mech. 82 031004 DOI: 10.1115/1.4029606
[23]
Cao D X, Leadenham S, Erturk A 2015 Eur. Phys. J. Special Topics 224 2867 DOI: 10.1140/epjst/e2015-02594-4
[24]
Jiang W A, Chen L Q, Ding H 2016 Nonlinear Dyn. 85 2507 DOI: 10.1007/s11071-016-2841-y
[25]
Chen L Q, Jiang W A, Panyam M, Daqaq M F 2016 J. Acoust Vib. 138 061007 DOI: 10.1115/1.4034253
[26]
Wu Y P, Ji H L, Qiu J H, Han L 2017 Sens. Actuators A-Phys. 264 1 DOI: 10.1016/j.sna.2017.06.029
[27]
Yang W, Towfighian S 2017 Smart Mater. Struct. 26 095008 DOI: 10.1088/1361-665X/aa791d
[28]
Yang W, Towfighian S 2017 Mech. Syst. Signal Pr. 90 317 DOI: 10.1016/j.ymssp.2016.12.032
[29]
Rocha R T, Balthazar J M, Tusset A M, Piccirillo V, Felix J L P 2017 Meccanica 52 2583 DOI: 10.1007/s11012-017-0633-1
[30]
Xiong L Y, Tang L T, Mace B R 2018 Nonlinear Dyn. 91 1817 DOI: 10.1007/s11071-017-3982-3
[31]
Liu H J, Gao X M 2019 Nonlinear Dyn. 96 1067 DOI: 10.1007/s11071-019-04839-4
[32]
Nie X C, Tan T, Yan Z M, Yan Z T, Hajj M R 2019 Int. J. Mech. Sci. 159 287 DOI: 10.1016/j.ijmecsci.2019.06.009
[33]
Pan J N, Qin W Y, Deng W Z, Zhou H L 2019 Chin. Phys. B 28 017701 DOI: 10.1088/1674-1056/28/1/017701
[34]
Tcheutchoua F D, Woafo P 2011 J. Vib. Acoust. 133 061018 DOI: 10.1115/1.4004938
[35]
Jerrelind J, Stensson A 2000 Chaos Solit. Fract. 11 2413 DOI: 10.1016/S0960-0779(00)00016-3
[36]
Wang Z, Chau K T 2008 Chaos Solit. Fract. 36 694 DOI: 10.1016/j.chaos.2006.06.105
[37]
Zhang H, Chen D, Xu B, Wang F 2015 Energy Convers. Manage. 90 128 DOI: 10.1016/j.enconman.2014.11.020
[38]
Yamapi R, Orou J B, Woafo P 2003 J. Sound Vib. 259 1253 DOI: 10.1006/jsvi.2002.5289
[39]
Mogo J B, Woafo P 2007 J. Comput. Nonlinear Dyn. 2 374
[40]
Kitio KC A, Nana B, Woafo P 2010 J. Sound Vib. 329 3137 DOI: 10.1016/j.jsv.2010.02.003
[41]
Domguia U S, Abobda L T, Woafo P 2016 J. Comput. Nonlin. Dyn. 11 051006
[42]
Simo H, Woafo P 2011 Mech. Res. Commun. 38 537 DOI: 10.1016/j.mechrescom.2011.07.007
[43]
Emam S A, Nayfeh A H 2013 Int. J. Nonlin. Mech. 52 12 DOI: 10.1016/j.ijnonlinmec.2013.01.018
[44]
Zhang W, Yang J H, Zhang Y F, Yang S W 2019 Eng. Struct. 198 109501 DOI: 10.1016/j.engstruct.2019.109501
[45]
Zhang W, Liu Y Z, Wu M Q 2019 Compos. Struct. 225 111140 DOI: 10.1016/j.compstruct.2019.111140
[46]
Zhang Y F, Zhang W, Yao Z G 2018 Eng. Struct. 173 89 DOI: 10.1016/j.engstruct.2018.04.100
[47]
Yao M H, Ma L, Zhang W 2018 Sci. Chin. E 61 1404 DOI: 10.1007/s11431-017-9179-0
[48]
Yao M H, Zhang W, Yao Z G 2015 J. Vib. Acoust. 137 011002 DOI: 10.1115/1.4028710
[49]
Zhang W, Zhang J H, Yao M H, Yao Z G 2010 Acta Mech. 211 23 DOI: 10.1007/s00707-009-0210-3
[50]
Zhang W, Yao Z G, Yao M H 2009 Sci. China Ser. E 52 731 DOI: 10.1007/s11431-009-0051-2
[51]
Zhang W, Zhao M H 2012 Nonlinear Dyn. 70 295 DOI: 10.1007/s11071-012-0455-6
[52]
Nathamgari S P, Dong S Y, Medina L 2019 Nano Lett. 19 4052 DOI: 10.1021/acs.nanolett.9b01442
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