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...

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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
Descripción
Sumario: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.

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