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中心部分电极化圆形AT切石英谐振器厚度振动的半解析解

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

作者信息

Wang Bin, Dai Xiaoyun, Zhao Xintao, Qian Zhenghua

机构信息

State Key Laboratory of Mechanics and Control of Mechanical Structures/College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.

出版信息

Sensors (Basel). 2017 Aug 7;17(8):1820. doi: 10.3390/s17081820.

DOI:10.3390/s17081820
PMID:28783124
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5579582/
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.

摘要

通过求解由蒂尔斯滕（Tiersten）和斯迈思（Smythe）推导的二维（2D）标量微分方程，得到了无限大的部分电极化圆形AT切石英板厚度剪切振动的振动频率和模式。利用坐标变换从控制方程推导出马蒂厄（Mathieu）方程和修正马蒂厄方程，并采用配置法处理边界条件。通过COMSOL软件得到的结果验证了共振频率和陷波模式的解。当前的研究为解决圆形石英谐振器的振动分析提供了一种理论方法。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/8f4515b1895f/sensors-17-01820-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/5dcb5f40d448/sensors-17-01820-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/ea734be80593/sensors-17-01820-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/2872c223d88f/sensors-17-01820-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/eaa82a00c130/sensors-17-01820-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/2df9132e3de9/sensors-17-01820-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/5a747fdbc922/sensors-17-01820-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/8f4515b1895f/sensors-17-01820-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/5dcb5f40d448/sensors-17-01820-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/ea734be80593/sensors-17-01820-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/2872c223d88f/sensors-17-01820-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/eaa82a00c130/sensors-17-01820-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/2df9132e3de9/sensors-17-01820-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/5a747fdbc922/sensors-17-01820-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/be40/5579582/8f4515b1895f/sensors-17-01820-g007.jpg

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本文引用的文献

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Effects of mismatched electrodes on an AT-cut quartz resonator.不匹配电极对AT切石英谐振器的影响。
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Five-mode frequency spectra of x3-dependent modes in AT-cut quartz resonators.AT 切石英谐振器中 x3 相关模式的五模频率谱。
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Frequency spectra of AT-cut quartz plates with electrodes of unequal thickness.不等厚度电极 AT 切石英板的频谱。
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