The thickness-shear and thickness-twist vibrations of a finite and partially electroded AT-cut quartz resonator are investigated. The equations of anisotropic elasticity are used with the omission of the small elastic constant c56. An analytical solution is obtained using Fourier series from which the free vibration resonant frequencies, mode shapes, and energy trapping are calculated and examined.
Bibliographical noteFunding Information:
★ Corresponding author. E-mail: firstname.lastname@example.org ★★ Project supported by the National Nature Science Foundation of China (No. 10972147) and the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0971).
- quartz crystal
- thickness-shear vibration
- thickness-twist vibration