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 μm and the other 150 μm, 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 μm 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 μm 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 μm 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