The frequency temperature dependence of coupled extensional, flexural, and width-shear vibrations of rotated X-cut quartz plates

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Abstract
The frequency temperature dependence of rotated X-cut quartz plates is studied in the case where the presence and coupling of the extensional, flexural, and width-shear modes are taken into account by using a set of one-dimensional approximate equations previously derived. The dependence of the turnover-point temperature as a function of width-to-length ratio for different values of orientation angle, and as a function of orientation angle for various values of the width-to-length ratio, is studied. The predicted results are presented and compared with measured values.

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