Optimal electrode shape and size of a few singly rotated quartz and langasite resonators

Based on Mindlin's early work, we calculate and plot optimal electrode shape and size of Y-cut quartz, At-cut quartz, and Y-cut langasite plate thickness-shear resonators. The electrodes obtained are optimal in that they satisfy Bechmann's number in every direction. The results are useful in the design optimization of these resonators.