Measurement of vibration modes of the NS-GT out quartz crystal oscillating in the by-resonant frequency

Stress distributions of two samples of the NS-GT cut quartz crystal resonator, one of which had a thickness of 80 /spl mu/m and the other 150 /spl mu/m, were measured by the dynamic photo-elastic method as the resonators were vibrating in each by-resonant frequency. Thereafter, vibration modes of those resonators have been estimated by the experimental data of obtained stress distributions. The estimated vibration mode of the resonator of 80 /spl mu/m coincided with the result of the finite element method simulation (FEM). The vibration mode of NS-GT cut quartz crystal resonators was a simple extension mode within z'-direction at the by-resonant oscillation. The resonator of 150 /spl mu/m does not coincide with the result of the FEM. It has a very complicated twist asymmetrical vibration mode at the by resonant frequency. We can only estimate the vibration mode of the resonator of 150 /spl mu/m experimentally by using a dynamic photo-elastic method. The vibration mode of the NS-GT cut quartz crystal resonator, when its thickness were thick, and it vibrated in its by-resonant frequency, were composed of the longitudinal stress T3' belong to z'-direction of the plate and the shearing stress T5' caused by the elastic stiffness constant c55 of the plate.