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.
Application of photoelastic method to measurement of dynamic stress distribution for NS-GT cut quartz crystal resonator
A dynamic photoelastic method is a very effective measuring technique for the stress distribution of the vibrating quartz resonators because the stress distribution is measured directly. When this method was applied to observe stress distributions of BT cut quartz resonators, many interesting results were obtained. In the present paper, stress distributions of the NS-GT cut quartz crystal resonators are measured experimentally by this method when the resonators are vibrating in the resonant frequency. Vibration modes of the NS-GT cut resonators are estimated with experimental data of stress distributions. This experiment for the NS-GT cut quartz crystal resonators has exposed existence of an asymmetrical mode of vibration at the resonant frequency and magnitude of asymmetrical modes are in proportion to a thickness of the resonator. This asymmetrical mode of resonant vibration has been analyzed by the finite element simulation, but we could not give convincing proofs until this experiment. The finite element simulation and the result of this experiment go to show that asymmetry modes at the resonant vibration are caused by elastic stiffness constant C/sub 16/ of the NS-GT cut quartz crystal resonator. This constant c/sub 16/ is dependent upon thickness of the resonator.
Vibration modes of AT-cut convex quartz resonators
The thickness shear mode forms and frequency spectrum of AT-cut plano-convex and biconvex quartz crystal resonators are obtained by an approximate analytic method. The results show good agreement with the mode forms observed by x-ray topography and the measured frequencies.