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

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Wang, Bin, Dai, Xiaoyun, Zhao, Xintao, Qian, Zhenghua
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5579582/
https://www.ncbi.nlm.nih.gov/pubmed/28783124
http://dx.doi.org/10.3390/s17081820
_version_ 1783260734691475456
author Wang, Bin
Dai, Xiaoyun
Zhao, Xintao
Qian, Zhenghua
author_facet Wang, Bin
Dai, Xiaoyun
Zhao, Xintao
Qian, Zhenghua
author_sort Wang, Bin
collection PubMed
description 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.
format Online
Article
Text
id pubmed-5579582
institution National Center for Biotechnology Information
language English
publishDate 2017
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-55795822017-09-06 A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators Wang, Bin Dai, Xiaoyun Zhao, Xintao Qian, Zhenghua Sensors (Basel) Article 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. MDPI 2017-08-07 /pmc/articles/PMC5579582/ /pubmed/28783124 http://dx.doi.org/10.3390/s17081820 Text en © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Bin
Dai, Xiaoyun
Zhao, Xintao
Qian, Zhenghua
A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators
title A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators
title_full A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators
title_fullStr A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators
title_full_unstemmed A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators
title_short A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators
title_sort semi-analytical solution for the thickness-vibration of centrally partially-electroded circular at-cut quartz resonators
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5579582/
https://www.ncbi.nlm.nih.gov/pubmed/28783124
http://dx.doi.org/10.3390/s17081820
work_keys_str_mv AT wangbin asemianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT daixiaoyun asemianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT zhaoxintao asemianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT qianzhenghua asemianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT wangbin semianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT daixiaoyun semianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT zhaoxintao semianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators
AT qianzhenghua semianalyticalsolutionforthethicknessvibrationofcentrallypartiallyelectrodedcircularatcutquartzresonators

Ejemplares similares