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In this paper, we investigate the coherence resonance of a piezoelectric energy harvester of beam subjected to an axial force. The fractional damping is considered. First, a nonlinear model of the energy harvesting system with fractional damping and random excitation is set up. The coupling equations of dynamics and electrics are derived. Euler- Maruyama-Leipnik method is used to solve the fractional order differential equations. The signal-to-noise ratios, mean responses, and other statistical quantities under the damping forces with different orders are computed. The results obviously show the appearance of coherence resonance. It can be seen that the reduction of fractional order not only reduces the critical value of noise level, thus leading to coherence resonance, but also increases the amplitude on the occurrence of coherence resonance. So it is possible to maximize harvest power for a given density or variance of random excitation by varying system parameters.
[1] Harne R L, Wang K W 2013 Smart. Mater. Struct. 22 023001
[2] Masana R, Daqaq M F 2011 J. Vib. Acoust. 133 011007
[3] Masana R, Daqaq M F 2011 J. Sound. Vib. 330 6036
[4] Masana R, Daqaq M F 2012 J. Appl. Phys. 111 044501
[5] Sun S, Cao S Q 2012 Acta Phys. Sin. 61 210505 (in Chinese) [孙舒, 曹树谦 2012 物理学报 61 210505]
[6] Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Litak G 2012 J. Intellig. Mater. Syst. Struct. 23 1505
[7] McInnes C R, Gorman D G, Cartmell M P 2008 J. Sound Vib. 318 655
[8] 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]
[9] Cao Z J, Li P F, Hu G 2007 Chin. Phys. Lett. 24 882
[10] Litak G, Friswell M I, Adhikari S 2010 Appl. Phys. Lett. 96 214103
[11] Kumar G S Prasad G 1993 J. Mater. Sci. 28 2545
[12] Shen Y J, Yang S P, Xing H J, Gao G S 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3092
[13] Shen Y J, Yang S P, Xing H J, Ma H X 2012 Int. J. Nonlin. Mech. 47 975
[14] Cao J Y, Zhou S X, Inman D J, Chen Y Q 2014 Nonlinear Dyn. 1320 6
[15] Litak G, Borowiec M 2014 Nonlinear Dyn. 77 681
[16] Cao Q, Wiercigroch M, Pavlovskaia E E, Grebogi C, Thompson J M T 2008 Phil. Trans. R. Soc. A 366 635
[17] Tian R L, Cao Q J, Yang S P 2010 Nonlinear Dyn. 59 19
[18] Tian R L, Yang X W, Cao Q J, Wu Q L 2012 Chin. Phys. B 21 020503
[19] Vinogradov A M, Schmidt V H, Tuthill G F 2004 Mech. Mater. 36 1007
[20] Guyomar D, Sebald G 2012 Sensor Actuat A: Phys. 189 74
[21] Petras I 2011 Fractional-Order Nonlinear System: Modeling, Analysis and Simulation (Berlin: Springer Publications) p19
[22] Hanggi P, Talkner P, Borkovec M 1990 Rev. Mod. Phys. 62 251
[23] Leng Y G, Lai Z H 2014 Acta Phys. Sin. 63 020502 (in Chinese) [冷永刚, 赖志慧 2014 物理学报 63 020502]
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[1] Harne R L, Wang K W 2013 Smart. Mater. Struct. 22 023001
[2] Masana R, Daqaq M F 2011 J. Vib. Acoust. 133 011007
[3] Masana R, Daqaq M F 2011 J. Sound. Vib. 330 6036
[4] Masana R, Daqaq M F 2012 J. Appl. Phys. 111 044501
[5] Sun S, Cao S Q 2012 Acta Phys. Sin. 61 210505 (in Chinese) [孙舒, 曹树谦 2012 物理学报 61 210505]
[6] Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Litak G 2012 J. Intellig. Mater. Syst. Struct. 23 1505
[7] McInnes C R, Gorman D G, Cartmell M P 2008 J. Sound Vib. 318 655
[8] 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]
[9] Cao Z J, Li P F, Hu G 2007 Chin. Phys. Lett. 24 882
[10] Litak G, Friswell M I, Adhikari S 2010 Appl. Phys. Lett. 96 214103
[11] Kumar G S Prasad G 1993 J. Mater. Sci. 28 2545
[12] Shen Y J, Yang S P, Xing H J, Gao G S 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3092
[13] Shen Y J, Yang S P, Xing H J, Ma H X 2012 Int. J. Nonlin. Mech. 47 975
[14] Cao J Y, Zhou S X, Inman D J, Chen Y Q 2014 Nonlinear Dyn. 1320 6
[15] Litak G, Borowiec M 2014 Nonlinear Dyn. 77 681
[16] Cao Q, Wiercigroch M, Pavlovskaia E E, Grebogi C, Thompson J M T 2008 Phil. Trans. R. Soc. A 366 635
[17] Tian R L, Cao Q J, Yang S P 2010 Nonlinear Dyn. 59 19
[18] Tian R L, Yang X W, Cao Q J, Wu Q L 2012 Chin. Phys. B 21 020503
[19] Vinogradov A M, Schmidt V H, Tuthill G F 2004 Mech. Mater. 36 1007
[20] Guyomar D, Sebald G 2012 Sensor Actuat A: Phys. 189 74
[21] Petras I 2011 Fractional-Order Nonlinear System: Modeling, Analysis and Simulation (Berlin: Springer Publications) p19
[22] Hanggi P, Talkner P, Borkovec M 1990 Rev. Mod. Phys. 62 251
[23] Leng Y G, Lai Z H 2014 Acta Phys. Sin. 63 020502 (in Chinese) [冷永刚, 赖志慧 2014 物理学报 63 020502]
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