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Chin. Phys. B, 2013, Vol. 22(4): 047702    DOI: 10.1088/1674-1056/22/4/047702

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

He Hui-Jing (何慧晶)a, Yang Jia-Shi (杨嘉实)a, Zhang Wei-Ping (张卫平)b, Wang Ji (王骥)c
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      Revised:  09 September 2012      Accepted manuscript online: 
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:

Cite this article: 

He Hui-Jing (何慧晶), Yang Jia-Shi (杨嘉实), Zhang Wei-Ping (张卫平), Wang Ji (王骥) Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator 2013 Chin. Phys. B 22 047702

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