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Article

A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators

by
Bin Wang
,
Xiaoyun Dai
,
Xintao Zhao
and
Zhenghua Qian
*
State Key Laboratory of Mechanics and Control of Mechanical Structures/College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
Author to whom correspondence should be addressed.
Sensors 2017, 17(8), 1820; https://doi.org/10.3390/s17081820
Submission received: 28 June 2017 / Revised: 26 July 2017 / Accepted: 2 August 2017 / Published: 7 August 2017
(This article belongs to the Special Issue Acoustic Wave Resonator-Based Sensors)
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Abstract

Vibration frequencies and modes for the thickness-shear vibrations of infinite partially-electroded circular AT-cut quartz plates are obtained by solving the two-dimensional (2D) scalar differential equation derived by Tiersten and Smythe. The Mathieu and modified Mathieu equations are derived from the governing equation using the coordinate transform and the collocation method is used to deal with the boundary conditions. Solutions of the resonant frequencies and trapped modes are validated by those results obtained from COMSOL software. The current study provides a theoretical way for figuring out the vibration analysis of circular quartz resonators.
Keywords: circular quartz plate; thickness-vibration; Mathieu function; collocation method; resonator circular quartz plate; thickness-vibration; Mathieu function; collocation method; resonator

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MDPI and ACS Style

Wang, B.; Dai, X.; Zhao, X.; Qian, Z. A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators. Sensors 2017, 17, 1820. https://doi.org/10.3390/s17081820

AMA Style

Wang B, Dai X, Zhao X, Qian Z. A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators. Sensors. 2017; 17(8):1820. https://doi.org/10.3390/s17081820

Chicago/Turabian Style

Wang, Bin, Xiaoyun Dai, Xintao Zhao, and Zhenghua Qian. 2017. "A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators" Sensors 17, no. 8: 1820. https://doi.org/10.3390/s17081820

APA Style

Wang, B., Dai, X., Zhao, X., & Qian, Z. (2017). A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators. Sensors, 17(8), 1820. https://doi.org/10.3390/s17081820

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