ABSTRACT In the previous paper, we reported that the dynamic photo-elastic method was a very effective measuring technique for the stress distribution of vibrating quartz crystal resonators. The existence of a twisted asymmetrical vibration mode has been verified experimentally when the NS-GT cut quartz crystal resonator was vibrating in the main resonant frequency (MRF) [1]. A MRF and a sub-resonant frequency (SRF) of the NS-GT cut quartz resonator were defined as follows. If a mechanical standing wave was in the x′ or y′ direction of the resonator, the former was MRF vibration and the latter was SRF vibration, respectively.
In this paper, stress distributions of two samples of the NS-GT cut quartz crystal resonator, one of which had a thickness of 80 μ m and the other 150 μ m, were measured by the dynamic photo-elastic method when the resonators were vibrating in each SRF. Thereafter, vibration modes of those resonators were estimated by the experimental data of stress distributions.
We can find that the vibration mode of the 80-μm resonator had a simple mechanical standing wave on the y′ direction and the vibration mode of the 150-μm resonator was combined with a shearing mode in the SRF vibration. From the experiment, we decided that vibration modes of the NS-GT cut quartz crystal resonator were composed of the longitudinal stress T3′ belonging to the z′ direction of the plate and of the shearing stress T5′ when the plate thickness was thickened and the resonator was oscillating in the SRF.
1999 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control Vol. 46, pp. 1175-1182, 1999
© 1999, by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.