Application of the photo-elastic method to measurement of dynamic stress distribution for NS-GT cut quartz crystal resonators
NS-GT cut quartz crystal resonators are widely used as a frequency standard element in consumer products and communication equipment. The vibration mode of the resonators was analyzed by the finite element method (FEM) because they have a complicated shape. As a result, an asymmetrical vibration mode at the main resonant frequency has been obtained by the FEM simulation. But, it is necessary to confirm the asymmetrical vibration mode experimentally because it is just a simulation. In this paper, stress distributions of the NS-GT cut quartz crystal resonators are measured experimentally by using a dynamic photo-elastic method when the resonators are vibrating in the resonant frequency; thereafter, vibration modes of the NS-GT cut resonators are estimated with the experimental data of the stress distributions. This experiment for the NS-GT cut quartz crystal resonators exposes the existence of a twisted asymmetrical vibration mode at the main resonant frequency, with the magnitude of the twisted vibration in proportion to thickness of the resonators.
Measurement of thickness-shear-stress distribution of the oscillating plano-convex AT-cut quartz-crystal resonator
The paper compares measured and calculated thickness-shear-stress distributions of a plano-convex AT-cut quartz-crystal resonator oscillating at its fundamental, 3rd overtone and 5th overtone thickness-shear resonant vibration frequencies. The calculated resonant frequencies and the vibration-stress distribution calculated numerically using a finite-element method show good agreement with those obtained experimentally.
A New Quartz-Crystal Plate, Designated the GT, Which Produces a Very Constant Frequency over a Wide Temperature Range
In this paper, a new quartz-crystal plate, designated the GT, is described which produces a very constant frequency over a wide temperature range. This crystal does not change by more than one part in a million over a 100-degree centigrade range of temperature. This crystal obtains its great temperature stability from the fact that both the first and second derivatives of the frequency by the temperature are zero. Both the frequency and temperature coefficient can be independently adjusted. This crystal has been applied in frequency standards, in very precise oscillators, and in filters subject to large temperature variations. It has given a constancy of frequency considerably in excess of that obtained by any other crystal. A crystal chronometer, using this type of crystal, was recently lent to the Geophysical Union for measurements on the variation of gravity and the chronometer is reported to have kept time within several parts in 10 million, although no temperature control was used.