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.

利用Lee和Yong的增量热场理论，获得了考虑热效应的SC切石英晶体厚度-剪切振动分析的Mindlin板方程。通过假定矩形板中的直波，用板的形状计算SC切割石英晶体板的厚度-剪切模式的色散关系，频谱，模式形状和频率-温度关系。将SC-cut石英晶体板的计算结果与AT-cut的计算结果进行了比较，这表明SC-cut谐振器具有更好的频率-温度关系作为验证。对于实际应用，这样的结果将对SC切割石英晶体谐振器结构的精确设计和改进有用。