Modes of vibration, motion inductance, and resonance interval of circular, convex AT-cut bevelled design trapped energy quartz resonators
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The approximate solution of the Tiersten equation for coupled TS-TT vibrations in circular, convex AT-cut bevelled design (double contoured) trapped energy resonators is considered. The analysis is carried out for every harmonics of the thickness mode and the corresponding anharmonic overtones. The dependence of the frequency and the frequency factor on the geometry of the piezoelement is given. A characteristic length of the mode form is introduced. The relationship between this characteristic length and the mechanical active region is given. This relationship determines the condition of application of the approximate solution for the case of vibrations in trapped-energy resonators. The possibility of calculating the motion inductance, the capacitance relationship and the resonance interval is pointed out. The analysis accounts for the relation between these parameters and the geometry of the piezoelement and the size of the electrodes. A reasonable agreement between the theoretical results and the experimental data obtained is also shown.
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