Thickness-shear vibration of an AT-cut quartz plate with elliptical electrodes and implications in optimal blank geometry

We analyze thickness-shear vibration of an ATcut quartz plate with elliptical electrodes. The electrodes are essentially optimal in the sense of Mindlin in that they approximately satisfy the criterion for Bechmann´s number in every direction. The results of our analysis suggest that optimal crystal blank geometry is essentially elliptical. We also suggest a way of machining elliptical crystal blanks.