Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates

A procedure based on approximate solutions of three-dimensional equations of wave propagation is utilized for calculating Bechmann’s number for the harmonic overtones of thickness-shear modes in the rotated Y-cut quartz crystal plates. Bechmann’s number is used for the optimization and improvement o...

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Main Authors:	Han Zhang, Yumei Chen, Ji Wang
Format:	Article
Language:	English
Published:	MDPI AG 2020-07-01
Series:	Coatings
Subjects:	resonator vibration frequency electrode optimization
Online Access:	https://www.mdpi.com/2079-6412/10/7/667

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spelling	doaj-2fa2829120824a75ac50bdd625b27c0b2020-11-25T03:42:54ZengMDPI AGCoatings2079-64122020-07-011066766710.3390/coatings10070667Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal PlatesHan Zhang0Yumei Chen1Ji Wang2Key Laboratory of Noise and Vibration, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, ChinaPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo 315211, ChinaSchool of Electrical and Mould Engineering, Taizhou Vocational College of Science and Technology, Taizhou 318020, ChinaA procedure based on approximate solutions of three-dimensional equations of wave propagation is utilized for calculating Bechmann’s number for the harmonic overtones of thickness-shear modes in the rotated Y-cut quartz crystal plates. Bechmann’s number is used for the optimization and improvement of electrodes to yield superior performance in the design of quartz crystal resonators. Originally, Bechmann’s number is found through practical experiences, and analytical results were provided afterward to enable optimal design of novel resonator structures. The outcomes in this study are from a simplified theoretical prediction and they are consistent with known empirical results, making it is possible to design optimal quartz crystal resonators for cases without adequate experimental data for a higher frequency and smaller size.https://www.mdpi.com/2079-6412/10/7/667resonatorvibrationfrequencyelectrodeoptimization
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Han Zhang Yumei Chen Ji Wang
spellingShingle	Han Zhang Yumei Chen Ji Wang Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates Coatings resonator vibration frequency electrode optimization
author_facet	Han Zhang Yumei Chen Ji Wang
author_sort	Han Zhang
title	Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates
title_short	Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates
title_full	Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates
title_fullStr	Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates
title_full_unstemmed	Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates
title_sort	bechmann’s number for harmonic overtones of thickness-shear vibrations of rotated y-cut quartz crystal plates
publisher	MDPI AG
series	Coatings
issn	2079-6412
publishDate	2020-07-01
description	A procedure based on approximate solutions of three-dimensional equations of wave propagation is utilized for calculating Bechmann’s number for the harmonic overtones of thickness-shear modes in the rotated Y-cut quartz crystal plates. Bechmann’s number is used for the optimization and improvement of electrodes to yield superior performance in the design of quartz crystal resonators. Originally, Bechmann’s number is found through practical experiences, and analytical results were provided afterward to enable optimal design of novel resonator structures. The outcomes in this study are from a simplified theoretical prediction and they are consistent with known empirical results, making it is possible to design optimal quartz crystal resonators for cases without adequate experimental data for a higher frequency and smaller size.
topic	resonator vibration frequency electrode optimization
url	https://www.mdpi.com/2079-6412/10/7/667
work_keys_str_mv	AT hanzhang bechmannsnumberforharmonicovertonesofthicknessshearvibrationsofrotatedycutquartzcrystalplates AT yumeichen bechmannsnumberforharmonicovertonesofthicknessshearvibrationsofrotatedycutquartzcrystalplates AT jiwang bechmannsnumberforharmonicovertonesofthicknessshearvibrationsofrotatedycutquartzcrystalplates
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Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates

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