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.