Energy trapping of thickness-shear and thickness-twist modes in a partially electroded AT-cut quartz resonator

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