Stress-Induced Frequency Shifts of Degenerate Thickness-Shear Modes in Rotated Y-Cut Quartz Resonators

We study stress-induced frequency shifts in a rotated Y-cut quartz resonator (θ = 23.7°) with degenerate fundamental thickness-shear modes when the biasing stress is not present. Using the recently derived perturbation procedure for degenerate frequencies in crystal resonators, we show that when a planar stress system is applied, the degenerate frequency splits into two. This phenomenon is expected to be typical for degenerate frequencies in crystal resonators and may be responsible in part for the jump discontinuities in frequency temperature curves and other frequency jump phenomena.