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双稳态压电悬臂梁发电系统的动力学建模及分析

孙舒 曹树谦

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双稳态压电悬臂梁发电系统的动力学建模及分析

孙舒, 曹树谦

Dynamic modeling and analysis of a bistable piezoelectric cantilever power generation system

Sun Shu, Cao Shu-Qian
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  • 针对双稳态压电悬臂梁发电系统进行了动力学建模与分析. 首先建立了能引发系统双稳态现象的磁力模型, 给出了两磁铁之间磁力的数学表达式; 其次建立了压电悬臂梁发电系统的集中参数模型, 得到了系统发生双稳态现象时磁铁之间的距离范围; 通过数值计算分析了系统的响应特性, 发现双稳态运动大大提高了系统的频率响应范围, 并且系统在低激励频率和低激励幅值下能发生大幅运动, 而激励幅值越大, 系统具有越高的能量逃离势阱产生大幅运动; 最后通过实验对数值计算结果进行了验证. 研究结果为双稳态压电悬臂梁发电系统的设计与应用提供了理论依据.
    Dynamic modeling and analysis of a bistable piezoelectric cantilever power generation system are presented. Firstly, a magnetic force model is established which could induce bistability, and the force mathematical expression between the two magnets is given. Secondly, a lumped parameter model of piezoelectric cantilever power generation system is built, and the range of distance between the two magnets is analyzed while the bistable phenomenon occurs. Thirdly, the response characteristics of the system are studied numerically. The results show that the beam undergoes large-amplitude motion at low frequency and low amplitude, and that the voltage response has a broadband. The system has high energy escaped from potential well when excitation amplitude imereases. Finally, the result is verified experimentally. This study provides a theoretical basis for the design and application of bistable piezoelectric cantilever power generation system.
    • 基金项目: 国家自然科学基金(批准号: 11172199)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11172199).
    [1]

    Wu X M, Fang H J, Lin J H, Ren T L, Liu L T 2008 Journal of Functional Materials and Devices 14 467 (in Chinese) [伍晓明, 方华军, 林建辉, 任天令, 刘理天 2008 功能材料与器件学报 14 467]

    [2]

    Arrieta A F, Hagedorn P, Erturk A, Inman D J 2010 Appl. Phys. Lett. 97 104102

    [3]

    Gammaitoni L, Neri I, Vocca H 2010 Chem. Phys. 375 435

    [4]

    Ferrari M, Ferrari V, Guizzetti M Andó B, Baglio S, Trigona C 2010 Sens. Actuators A: Phys. 162 425

    [5]

    Erturk A, Inman D J 2011 J. Sound Vib. 330 2339

    [6]

    Moon F C, Holmes P J 1979 J. Sound Vib. 65 275

    [7]

    Mann B P, Owens B A 2010 J. Sound Vib. 329 1215

    [8]

    S Stanton S C, McGehee C C, Mann B P 2010 Physica D 239 640

    [9]

    Han Q W, Li K, Yan L, Zhou J L, Wang Y, Chen W L H 2011 Piezoelectrics & Acoustooptics 33 85 (in Chinese) [韩权威, 李坤, 严玲, 周金龙, 王雨, 陈王丽华 2011 压电与声光 33 85]

    [10]

    Ma H A, Liu J Q, Tang G, Yang C S, Li Y G 2011 Transducer and Microsystem Technology 30 66 (in Chinese) [马华安, 刘景全, 唐刚, 杨春生, 李以贵 2011 传感器与微系统 30 66]

    [11]

    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]

    [12]

    Yung K W, Landecker P B, Villani D D 1998 Magnetic and Electrical Separation 9 39

    [13]

    Guckenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (New York: Springer-Verlag)

    [14]

    Lin M, Meng Y 2010 Acta Phys. Sin. 59 3627 (in Chinese) [林敏, 孟莹 2010 物理学报 59 3627]

    [15]

    Gottwald J A, Virgin L N, Dowell E H 1995 J. Sound Vib. 187 133

  • [1]

    Wu X M, Fang H J, Lin J H, Ren T L, Liu L T 2008 Journal of Functional Materials and Devices 14 467 (in Chinese) [伍晓明, 方华军, 林建辉, 任天令, 刘理天 2008 功能材料与器件学报 14 467]

    [2]

    Arrieta A F, Hagedorn P, Erturk A, Inman D J 2010 Appl. Phys. Lett. 97 104102

    [3]

    Gammaitoni L, Neri I, Vocca H 2010 Chem. Phys. 375 435

    [4]

    Ferrari M, Ferrari V, Guizzetti M Andó B, Baglio S, Trigona C 2010 Sens. Actuators A: Phys. 162 425

    [5]

    Erturk A, Inman D J 2011 J. Sound Vib. 330 2339

    [6]

    Moon F C, Holmes P J 1979 J. Sound Vib. 65 275

    [7]

    Mann B P, Owens B A 2010 J. Sound Vib. 329 1215

    [8]

    S Stanton S C, McGehee C C, Mann B P 2010 Physica D 239 640

    [9]

    Han Q W, Li K, Yan L, Zhou J L, Wang Y, Chen W L H 2011 Piezoelectrics & Acoustooptics 33 85 (in Chinese) [韩权威, 李坤, 严玲, 周金龙, 王雨, 陈王丽华 2011 压电与声光 33 85]

    [10]

    Ma H A, Liu J Q, Tang G, Yang C S, Li Y G 2011 Transducer and Microsystem Technology 30 66 (in Chinese) [马华安, 刘景全, 唐刚, 杨春生, 李以贵 2011 传感器与微系统 30 66]

    [11]

    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]

    [12]

    Yung K W, Landecker P B, Villani D D 1998 Magnetic and Electrical Separation 9 39

    [13]

    Guckenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (New York: Springer-Verlag)

    [14]

    Lin M, Meng Y 2010 Acta Phys. Sin. 59 3627 (in Chinese) [林敏, 孟莹 2010 物理学报 59 3627]

    [15]

    Gottwald J A, Virgin L N, Dowell E H 1995 J. Sound Vib. 187 133

计量
  • 文章访问数:  7095
  • PDF下载量:  1212
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-03-21
  • 修回日期:  2012-05-23
  • 刊出日期:  2012-11-05

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