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- Title
A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators.
- Authors
Bin Wang; Xiaoyun Dai; Xintao Zhao; Zhenghua Qian
- 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.
- Subjects
MATHIEU functions; BOUNDARY value problems; VIBRATION (Mechanics); CRYSTAL oscillators; CRYSTAL resonators
- Publication
Sensors (14248220), 2017, Vol 17, Issue 8, p1820
- ISSN
1424-8220
- Publication type
Article
- DOI
10.3390/s17081820