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 C₁₆ of the NS-GT cut quartz crystal resonator. This constant c₁₆ is dependent upon thickness of the resonator