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弯曲振动薄圆盘的共振频率和等效电路参数研究

张小丽 林书玉 付志强 王勇

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弯曲振动薄圆盘的共振频率和等效电路参数研究

张小丽, 林书玉, 付志强, 王勇

Study on resonance frequency and equivalent circuit parameters of a thin disk in flexural vibration

Zhang Xiao-Li, Lin Shu-Yu, Fu Zhi-Qiang, Wang Yong
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  • 机电等效电路是分析复合换能器常用的一种解析方法, 但对薄圆盘而言, 由于弯曲振动的复杂性, 其等效集中参数很难获得, 该方法很少被应用. 本文从分布参数系统与集中参数系统等效角度, 根据动能相等原则和势能相等原则, 给出了弯曲振动薄圆盘的集中参数: 等效质量和等效弹性系数, 得到了共振频率方程, 并用ATILA软件模拟了其振动分布情况, 可以看出解析结果与数值结果趋于一致. 最后给出了分析复合振动系统时薄圆盘集中参数模型的等效电路. 本文的结果对弯曲振动复合换能器的设计提供了理论参考.
    The electro-mechanical equivalent circuit is the most common method of analyzing and designing composite transducers. However, for the thin disk, because of the complexity of flexural vibration, equivalent lumped parameters are difficult to obtain, and so this method is rarely used. From the point of equivalent view of the distributed parameter system and lumped parameter system, according to the kinetic energy equal principle and the potential energy equal principle in this paper, we give the lumped parameter equivalent mass and equivalent elasticity coefficient of the flexural vibration, and the resonance frequency equations as well. The results from the analytical method are in good agreement with those from the finite element method. Finally, the equivalent circuit of lumped parameter model of the thin disk in analyzing the composite vibration system is given. These results can serve as a reference for designing flexural vibration composite transducers.
    • 基金项目: 国家自然科学基金(批准号:11174192)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11174192).
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    Gallego-Juarez J A, Rodriguez-Corral G, Sarabia E R, Vazquez-Martinez F, Campos-Pozuelo C, Acosta-Aparicio V M 2002 Ultrasonics 40 889

    [2]

    Yuan Y L, Ma Y P, Wang D S 2004 Mechanical Engineer 10 46 (in Chinese) [袁艳玲, 马玉平, 王得胜 2004 机械工程师 10 46]

    [3]

    Lin S Y 2006 Ultrasonics 44 545

    [4]

    Watanabe Y, Mori E 1996 Ultrasonics 34 235

    [5]

    Pan X J, He X P 2010 Acta Phys. Sin. 59 7911 (in Chinese) [潘晓娟, 贺西平 2010 物理学报 59 7911]

    [6]

    He X P 2010 Acta Phys. Sin. 59 3290 (in Chinese) [贺西平 2010 物理学报 59 3290]

    [7]

    Mason W P 1964 Physical Acoustics Principles and Methods (Vol. 1) (New York: Academic Press) p72

    [8]

    Paganelli R P, Romani A, Golfarelli A, Magi M, Sangiorgi E, Tartagni M 2010 Sens. Actuators A 160 9

    [9]

    Lin S Y 2004 Principle and Design of Ultrasonic Transducer (Beijing: Science Press) p162 (in Chinese) [林书玉 2004 超声换能器的原理及设计(北京: 科学出版社)第162页]

    [10]

    Lin S Y 2012 IEEE Trans Ultrason. Ferroelectr. Freq. Control 59 139

    [11]

    Wang Q S 2001 Journal of Anqing Teachers College (Natural Science Edition) 7 1 (in Chinese) [王其申 2001 安庆师范学院学报(自然科学版) 7 1]

    [12]

    Xu Z L 1982 Elastic Mechanics (Vol. 2) (Beijing: People's Education Press) p263 (in Chinese) [徐芝纶 1982 弹性力学(下册) (北京: 人民教育出版社)第263页]

    [13]

    Wei Y Y, Wang W X, Li H F 1999 Journal of University of Electronic Science and Technology 28 66 (in Chinese) [魏彦玉, 王文祥, 李宏福 1999 电子科技大学学报 28 66]

    [14]

    Xiong Z H, Liu Z Y 1988 Variational Principles in Elasticity (Changsha: Hunan University Press) p319 (in Chinese) [熊祝华, 刘子延 1988 弹性力学变分原理(长沙: 湖南大学出版社)第319页]

  • [1]

    Gallego-Juarez J A, Rodriguez-Corral G, Sarabia E R, Vazquez-Martinez F, Campos-Pozuelo C, Acosta-Aparicio V M 2002 Ultrasonics 40 889

    [2]

    Yuan Y L, Ma Y P, Wang D S 2004 Mechanical Engineer 10 46 (in Chinese) [袁艳玲, 马玉平, 王得胜 2004 机械工程师 10 46]

    [3]

    Lin S Y 2006 Ultrasonics 44 545

    [4]

    Watanabe Y, Mori E 1996 Ultrasonics 34 235

    [5]

    Pan X J, He X P 2010 Acta Phys. Sin. 59 7911 (in Chinese) [潘晓娟, 贺西平 2010 物理学报 59 7911]

    [6]

    He X P 2010 Acta Phys. Sin. 59 3290 (in Chinese) [贺西平 2010 物理学报 59 3290]

    [7]

    Mason W P 1964 Physical Acoustics Principles and Methods (Vol. 1) (New York: Academic Press) p72

    [8]

    Paganelli R P, Romani A, Golfarelli A, Magi M, Sangiorgi E, Tartagni M 2010 Sens. Actuators A 160 9

    [9]

    Lin S Y 2004 Principle and Design of Ultrasonic Transducer (Beijing: Science Press) p162 (in Chinese) [林书玉 2004 超声换能器的原理及设计(北京: 科学出版社)第162页]

    [10]

    Lin S Y 2012 IEEE Trans Ultrason. Ferroelectr. Freq. Control 59 139

    [11]

    Wang Q S 2001 Journal of Anqing Teachers College (Natural Science Edition) 7 1 (in Chinese) [王其申 2001 安庆师范学院学报(自然科学版) 7 1]

    [12]

    Xu Z L 1982 Elastic Mechanics (Vol. 2) (Beijing: People's Education Press) p263 (in Chinese) [徐芝纶 1982 弹性力学(下册) (北京: 人民教育出版社)第263页]

    [13]

    Wei Y Y, Wang W X, Li H F 1999 Journal of University of Electronic Science and Technology 28 66 (in Chinese) [魏彦玉, 王文祥, 李宏福 1999 电子科技大学学报 28 66]

    [14]

    Xiong Z H, Liu Z Y 1988 Variational Principles in Elasticity (Changsha: Hunan University Press) p319 (in Chinese) [熊祝华, 刘子延 1988 弹性力学变分原理(长沙: 湖南大学出版社)第319页]

计量
  • 文章访问数:  5000
  • PDF下载量:  1124
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-04-27
  • 修回日期:  2012-09-06
  • 刊出日期:  2013-02-05

弯曲振动薄圆盘的共振频率和等效电路参数研究

  • 1. 陕西师范大学应用声学研究所, 西安 710062
    基金项目: 国家自然科学基金(批准号:11174192)资助的课题.

摘要: 机电等效电路是分析复合换能器常用的一种解析方法, 但对薄圆盘而言, 由于弯曲振动的复杂性, 其等效集中参数很难获得, 该方法很少被应用. 本文从分布参数系统与集中参数系统等效角度, 根据动能相等原则和势能相等原则, 给出了弯曲振动薄圆盘的集中参数: 等效质量和等效弹性系数, 得到了共振频率方程, 并用ATILA软件模拟了其振动分布情况, 可以看出解析结果与数值结果趋于一致. 最后给出了分析复合振动系统时薄圆盘集中参数模型的等效电路. 本文的结果对弯曲振动复合换能器的设计提供了理论参考.

English Abstract

参考文献 (14)

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