Effects of mismatched electrodes on an ATCut quartz resonator

We study thickness-shear and thickness-twist free vibrations of a finite AT-cut quartz resonator with mis- matched 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.