Thickness-shear vibration characteristics of an AT-cut quartz resonator with rectangular ring electrodes

We studied thickness-shear vibration frequencies and modes in a rectangular AT-cut quartz plate resonator with ring electrodes. The electrodes are also rectangular, with their central parts missing and thus form rectangular ring electrodes. It was found that the vibration tends to be trapped in the electrode area and decays away from the electrode edges. By properly designing the electrode dimensions, the vibration can be made nearly uniform in the central part of the plate. This is particularly suitable for resonator-based sensor applications where the sensitivity is determined theoretically from the uniform vibration distribution of pure thickness-shear modes in an unbounded plate.