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Transient Thermally Induced Frequency Excursions in AT- and SC-Cut Quartz Trapped Energy Resonators,
RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MECHANICAL ENGINEERING AERONAUTICAL ENGINEERING AND MECHANICS
In the AT- and SC- cuts of quartz the change in resonant frequency with temperature of a particular pure thickness mode the C-mode is essentially negligible in the absence of the electrodes, and the cut is said to be thermally compensated for that mode. Consequently, certain other effects, in particular the presence of the thin electrode films and the transverse trapping of energy, which is always present on account of the finite dimensions of the electrodes, have an important influence on the transient temperature dependence of the resonant frequencies of thermally compensated cuts. In this work the time-dependent frequency shifts due to rapid changes in the thermal environment at the surface of the crystal are calculated from the solution of the time-dependent heat conduction equation through the resulting thermally induced deformation state, the temperature derivatives of the fundamental elastic constants of quartz, the temperature dependence of the motional capacitive effect for the cuts considered and the now known trapped energy mode shapes with the aid of the equation for the perturbation in eigen-frequency of a piezoelectric solution due to a bias.
This article is from the Proceedings of the Annual Symposium on Frequency Control (37th), 1-3 Jun 83, Marriott Hotel, Philadelphia, Pennsylvania, AD-A136 673, p208-217.
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