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带有分数阶阻尼的压电能量采集系统相干共振

李海涛 秦卫阳 周志勇 蓝春波

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带有分数阶阻尼的压电能量采集系统相干共振

李海涛, 秦卫阳, 周志勇, 蓝春波

Coherence resonance of piezoelectric energy harvester with fractional damping

Li Hai-Tao, Qin Wei-Yang, Zhou Zhi-Yong, Lan Chun-Bo
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  • 研究了含分数阶阻尼的双稳态能量采集系统的相干共振. 建立了带有分数阶阻尼的轴向受压梁压电能量采集系统动力学模型. 对于分数阶方程, 采用Euler-Maruyama-Leipnik方法进行求解, 计算了不同阻尼阶数下的能量采集系统的信噪比、响应均值、跃迁数目等统计物理量. 结果表明: 此压电能量采集系统在随机激励下可以实现相干共振, 阻尼阶数对相干共振的临界噪声强度和相干共振幅值有很大影响.
    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.
    • 基金项目: 国家自然科学基金(批准号:11172234)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11172234).
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    Masana R, Daqaq M F 2012 J. Appl. Phys. 111 044501

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    McInnes C R, Gorman D G, Cartmell M P 2008 J. Sound Vib. 318 655

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    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

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    Litak G, Friswell M I, Adhikari S 2010 Appl. Phys. Lett. 96 214103

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    Kumar G S Prasad G 1993 J. Mater. Sci. 28 2545

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    Shen Y J, Yang S P, Xing H J, Gao G S 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3092

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    Shen Y J, Yang S P, Xing H J, Ma H X 2012 Int. J. Nonlin. Mech. 47 975

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    Cao J Y, Zhou S X, Inman D J, Chen Y Q 2014 Nonlinear Dyn. 1320 6

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    Litak G, Borowiec M 2014 Nonlinear Dyn. 77 681

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    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]

  • [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]

计量
  • 文章访问数:  4546
  • PDF下载量:  999
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-05-23
  • 修回日期:  2014-06-30
  • 刊出日期:  2014-11-05

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