Abstract
This paper describes an analysis of anisotropic torsional resonators with the Ritz method and its application to quartz crystal tuning fork-type resonators which are easily formed by a chemical etching process. In this paper, resonant frequency and frequency temperature behavior of the resonators are clarified using the frequency equation which is given as a function of torsional rigidity derived from the Ritz method, and miniaturized torsional resonators with a small series resistance R1 and a high quality factor are obtained. A torsional rigidity is first derived theoretically; then, a series of analytical results are compared with the measured data, Both results show good agreement, and a miniaturized resonator is successfully obtained with a small series resistance R1 and a high quality factor particularly in the vicinity of 500 kHz.
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