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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.
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Keywords:
- flexural vibration thin disk /
- resonance frequency /
- lumped parameters /
- equivalent circuit
[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]
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[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]
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