Stress-induced frequency shifts in langasite thickness-mode resonators

In this paper, we report on our study of stress-induced effects on thickness vibrations of a langasite plate. The plate is assumed to be doubly-rotated, specified by angles /spl phi/ and /spl theta/. The stresses are assumed to be uniform and planar. The first-order perturbation integral as developed by Tiersten for frequency shifts in resonators is used. The dependence of frequency shifts on /spl phi/ and /spl theta/ is calculated and examined, and loci of stress-compensation are determined. The analysis makes use of the third-order material constants that are available for langasite but not for its isomorphs.