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Chin. Phys. B, 2013, Vol. 22(4): 047702    DOI: 10.1088/1674-1056/22/4/047702
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator

He Hui-Jinga, Yang Jia-Shia, Zhang Wei-Pingb, Wang Jic
a Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA;
b 1785 Pebblewood Lane, Hoffman Estates, IL 60195, USA;
c Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China
Abstract  We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin's two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases: pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.
Keywords:  quartz      plate      resonance      resonator     
Received:  23 June 2012      Published:  01 March 2013
PACS:  77.65.Fs (Electromechanical resonance; quartz resonators)  
  77.65.-j (Piezoelectricity and electromechanical effects)  
Fund: Project supported in part by the National Natural Science Foundation of China (Grant Nos. 10932004, 11072116, and 10772087) and the Doctoral Program Fund of Ministry of Education of China (Grant No. 20093305110003/JW). Additional Funds were from the Sir Y. K. Pao Chair Professorship, the K. C. Wong Magna Fund through Ningbo University, and the K. C. Wong Education Foundation in Hong Kong. The project also supported in part by the US Army Research Laboratory/US Army Research Office (Grant No. W911NF-10-1-0293).
Corresponding Authors:  Yang Jia-Shi     E-mail:  jyang1@unl.edu

Cite this article: 

He Hui-Jing, Yang Jia-Shi, Zhang Wei-Ping, Wang Ji Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator 2013 Chin. Phys. B 22 047702

[1] Mindlin R D 1951 J. Appl. Phys. 22 316
[2] Mindlin R D and Lee P C Y 1966 Int. J. Solids Structures 2 125
[3] Mindlin R D and Spencer W J 1967 J. Acoust. Soc. Am. 42 1268
[4] Tiersten H F 1985 J. Acoust. Soc. Am. 78 1684
[5] Yong Y K and Stewart J T 1991 IEEE Trans. Ultrason., Ferroelect., Freq. Control 38 67
[6] Wang J and Zhao W H 2005 IEEE Trans. Ultrason., Ferroelect., Freq. Control 52 2023
[7] Wang J N, Hu Y T and Yang J S 2010 IEEE Trans. Ultrason., Ferroelect., Freq. Control 57 1146
[8] Chen G J, Wu R X, Wang J, Du J K and Yang J S 2012 IEEE Trans. Ultrason., Ferroelect., Freq. Control 59 811
[9] Wang J and Yang J S 2000 Appl. Mech. Rev. 53 87
[10] Mindlin R D 1952 J. Appl. Phys. 23 83
[11] Tiersten H F and Mindlin R D 1962 Quart. Appl. Math. 20 107
[12] Bleustein J L and Tiersten H F 1968 J. Acoust. Soc. Am. 43 1311
[13] Mindlin R D 1974 Int. J. Solids Structures 10 453
[14] Zhang W P 1998 Proc. 1998 IEEE Int. Freq. Control Sym. 981
[15] Zhang W P and Doyle M 2000 Mechanics of Electromagnetic Materials and Structures, eds.Yang J S, Maugin G A (Amsterdam: IOS) p. 147
[16] Lee P C Y and Wang J 1996 J. Appl. Phys. 79 3411
[17] Lee P C Y and Lin W S 1998 J. Appl. Phys. 83 7822
[18] Wang J, Yu J D, Yong Y K and Imai T 2000 Int. J. Solids Structures 37 5653
[19] Wang J, Zhao W H and Du J K 2006 Ultrasonics. 44 869
[20] Zhang C L, Chen W Q and Yang J S 2009 Int. J. Appl. Elect. Mech. 31 207
[21] Yong Y K, Patel M S and Tanaka M 2010 IEEE Trans. Ultrason., Ferroelect., Freq. Control 57 1831
[22] Mindlin R D 1961 Quart. Appl. Math. 19 51
[23] Mindlin R D 1972 Int. J. Solids Structures 8 895
[24] Lee P C Y, Syngellakis S and Hou J P 1987 J. Appl. Phys. 61 1249
[25] Yang J S 2006 The Mechanics of Piezoelectric Structures (Singapore: World Scientific) Chap. 2 and Chap. 4
[26] Wang W Y, Zhang C, Zhang Z T, Liu Y and Feng G P 2009 Chin. Phys. B 18 795
[27] Ma T F, Zhang C, Feng G P and Jiang X N 2010 Chin. Phys. B 19 087701
[28] Ma T F, Zhang C, Jiang X N and Feng G P 2011 Chin. Phys. B 20 057701
[29] Tiersten H F 1969 Linear Piezoelectric Plate Vibrations (New York: Plenum) p. 186
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