Effects of mismatched electrodes on an AT-cut quartz resonator.

We study thickness-shear and thickness-twist free vibrations of a finite AT-cut quartz resonator with mismatched electrodes. 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 resonant frequencies, mode shapes, and vibration confinement resulting from the electrode inertia are calculated and examined.