Abstract
We study transient effects in AT-cut quartz plate thickness-shear mode acoustic wave resonators. Mindlin's equations for thin crystal plates are employed. Based on the relatively slow evolution of the vibration amplitude compared to the high-frequency thickness-shear vibration, a first-order differential equation governing the amplitude evolution is obtained. The equation allows simple and accurate solutions for transient processes in quartz resonators. A few numerical examples of resonator startup and turning off are given. The equation can be applied to other transient processes in crystal resonators such as driving voltage fluctuations and generalized to resonator-based acoustic wave sensors.
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