Frequency–Temperature Analysis of Thickness-Shear Vibrations of SC-Cut Quartz Crystal Plates with the First-Order Mindlin Plate Equations

With the incremental thermal field theory by Lee and Yong, the Mindlin plate equations for the analysis of thickness-shear vibrations of SC-cut quartz crystal with the consideration of thermal effect have been obtained. By assuming straight-crested waves in a rectangular plate, the dispersion relations, frequency spectra, mode shapes, and frequency–temperature relations of the thickness-shear mode of SC-cut quartz crystal plates are calculated with plate configurations. The computational results from SC-cut quartz crystal plates are compared with those from AT-cut, which shows that SC-cut resonators have better frequency–temperature relation as a validation. For practical applications, such results will be useful in the precision design and improvement of SC-cut quartz crystal resonator structures.