Overtone Modes in an At-Cut Quartz Trapped-Energy Resonator with Elliptical Electrodes

Abstract

We analyze thickness-shear vibrations of an at-cut quartz plate with elliptical electrodes. The electrodes are essentially optimal in the sense of Mindlin in that they approximately satisfy the criterion for the Bechmann number in every direction. The scalar differential equation derived by Tiersten and Smythe is used which allows us to obtain the overtone modes in addition to the fundamental modes.