Analysis of the electrically forced vibrations of piezoelectric mesa resonators

doi:10.1088/1674-1056/22/8/087704

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 87704-087704.doi: 10.1088/1674-1056/22/8/087704

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

Analysis of the electrically forced vibrations of piezoelectric mesa resonators

何慧晶^{a b}, 聂国权^a, 刘金喜^a, 杨嘉实^b

a Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
b Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA

收稿日期:2013-01-13 修回日期:2013-01-25 出版日期:2013-06-27 发布日期:2013-06-27
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11272222) and the National Key Basic Research Program of China (Grant No. 2012CB723300).

Analysis of the electrically forced vibrations of piezoelectric mesa resonators

He Hui-Jing (何慧晶)^{a b}, Nie Guo-Quan (聂国权)^a, Liu Jin-Xi (刘金喜)^a, Yang Jia-Shi (杨嘉实)^b

a Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
b Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA

Received:2013-01-13 Revised:2013-01-25 Online:2013-06-27 Published:2013-06-27
Contact: Yang Jia-Shi E-mail:jyang1@unl.edu
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11272222) and the National Key Basic Research Program of China (Grant No. 2012CB723300).

摘要/Abstract

摘要： We study the electrically forced thickness-shear and thickness-twist vibrations of stepped thickness piezoelectric plate mesa resonators made of polarized ceramics or 6-mm class crystals. A theoretical analysis based on the theory of piezoelectricity is performed, and an analytical solution is obtained using the trigonometric series. The electrical admittance, resonant frequencies, and mode shapes are calculated, and strong energy trapping of the modes is observed. Their dependence on the geometric parameters of the resonator is also examined.

关键词: crystal, plate, resonance, resonator

Abstract: We study the electrically forced thickness-shear and thickness-twist vibrations of stepped thickness piezoelectric plate mesa resonators made of polarized ceramics or 6-mm class crystals. A theoretical analysis based on the theory of piezoelectricity is performed, and an analytical solution is obtained using the trigonometric series. The electrical admittance, resonant frequencies, and mode shapes are calculated, and strong energy trapping of the modes is observed. Their dependence on the geometric parameters of the resonator is also examined.

Key words: crystal, plate, resonance, resonator

中图分类号: (Electromechanical resonance; quartz resonators)

77.65.Fs

77.65.-j (Piezoelectricity and electromechanical effects)

何慧晶, 聂国权, 刘金喜, 杨嘉实. Analysis of the electrically forced vibrations of piezoelectric mesa resonators[J]. 中国物理B, 2013, 22(8): 87704-087704.

He Hui-Jing (何慧晶), Nie Guo-Quan (聂国权), Liu Jin-Xi (刘金喜), Yang Jia-Shi (杨嘉实). Analysis of the electrically forced vibrations of piezoelectric mesa resonators[J]. Chin. Phys. B, 2013, 22(8): 87704-087704.

参考文献 33

[1]	Koga I 1932 Phys. 3 70
[2]	Tiersten H F 1963 J. Acoust. Soc. Am. 35 53
[3]	Tiersten H F 2003 IEEE Trans. Ultrason. Ferroelect. Freq. Control 50 1436
[4]	Mindlin R D 1965 Int. J. Solids Struct. 1 141
[5]	Yang Z T, Hu Y T and Yang J S 2009 Ultrason. 49 401
[6]	Mindlin R D and Lee P C Y 1966 Int. J. Solids Struct. 2 125
[7]	Yang J S and Kosinski J A 2004 IEEE Trans. Ultrason. Ferroelect. Freq. Control 51 1047
[8]	Tiersten H F and Smyth R C 1979 J Acoust. Soc. Am. 65 1455
[9]	Tiersten H F and Stevens D S 1986 J. Acoust. Soc. Am. 80 1122
[10]	Onoe M and Okada K 1969 Proc. 23rd Annual Frequency Control Symp. (Atlantic City: Institute of Electrical and Electronics Engineers)
[11]	Sinha B K 2001 IEEE Trans. Ultrason, Ferroelec. Freq. Control 48 1162
[12]	Shen F, O'Shea S J, Lee K H, Lu P and Ng T Y 2003 IEEE Trans. Ultrason. Ferroelect. Freq. Control 50 668
[13]	Ishizaki A, Sekimoto H, Tajima D and Watanabe Y 1995 Proc. IEEE Ultrasonics Symp. (USA: Institute of Electrical and Electronics Engineers)
[14]	Goka S, Sekimoto H and Watanabe Y 1999 Proc. IEEE Int. Frequency Control Symp. (France: Institute of Electrical and Electronics Engineers)
[15]	Goka S, Sekimoto H and Watanabe Y 2000 Proc. IEEE Int. Frequency Control Symp. (USA: Institute of Electrical and Electronics Engineers)
[16]	Sekimoto H, Goka S and Watanabe Y 2001 IEEE Trans. Ultrason. Ferroelect. Freq. Control 48 1302
[17]	Goka S, Tamura K, Sekimoto H, Watanabe Y and Sato T 2003 Proc. IEEE Int. Frequency Control Symp. (Tampa: Institute of Electrical and Electronics Engineers)
[18]	Watanabe Y, Goka S, Sato T and Sekimoto H 2003 Proc. IEEE Int. Frequency Control Symp. (Tampa: Institute of Electrical and Electronics Engineers)
[19]	Goka S, Mase Y, Sekimoto H, Watanabe Y and Sato T 2004 Proc. IEEE Int. Frequency Control Symp. (Montreal: Institute of Electrical and Electronics Engineers)
[20]	Goka S, Mase Y, Sekimoto H and Watanabe Y 2006 Proc. IEEE Int. Frequency Control Symp. (Miami: Institute of Electrical and Electronics Engineers)
[21]	He H J, Liu J X and Yang J S 2011 IEEE Trans. Ultrason. Ferroelect. Freq. Control 58 2050
[22]	Zhang H, Wang Z Q and Zhang S Y 2006 Acta Acustica 31 8
[23]	Mo S M, Zhao J Z, Wu G M and Chen J M 2008 Technical Acoustics 27 167
[24]	Du J K, Xian K, Wang J and Yang J S 2009 Ultrasonics 49 149
[25]	Qin L F, Chen Q M, Cheng H B and Wang Q M 2010 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 1840
[26]	Cao X S, Jin F and Yang J S 2012 IEEE Trans. Ultrason. Ferroelect. Freq. Control 59 2522
[27]	Wang W Y, Zhang C, Zhang Z T, Liu Y and Feng G P 2009 Chin. Phys. B 18 795
[28]	Ma T F, Zhang C, Feng G P and Jiang X N 2010 Chin. Phys. B 19 087701
[29]	Ma T F, Zhang C, Jiang X N and Feng G P 2011 Chin. Phys. B 20 057701
[30]	Yang J S 2010 Antiplane Motions of Piezoceramics and Acoustic Wave Devices (Singapore: World Scientific)
[31]	Bleustein J L 1969 J. Acoust. Soc. Am. 45 614
[32]	Tiersten H F 1969 Linear Piezoelectric Plate Vibrations (New York: Plenum)
[33]	Auld B A 1973 Acoustic Fields and Waves in Solids, Vol. 1 (New York: John Willey and Sons) pp. 357-382

Analysis of the electrically forced vibrations of piezoelectric mesa resonators

Analysis of the electrically forced vibrations of piezoelectric mesa resonators

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