Several extensions of Mindlin-Gazis’s analysis of rotated Y-cut of quartz (invited)

Rectangular AT-cut of quartz plate vibrating in the fundamental thickness shear mode is widely used in frequency control and selection. There are numerous spurious responses due to finite dimensions of contour besides of the main desired shear mode. Hence it is important to choose dimensions yielding a good separation between the main mode and spurious modes. Mindlin derived approximate two dimensional equations of motion of crystal plates, which take into account the coupling of flexural, extensional and face shear deformations with each other and with the main shear modes [1]. Its numerical solutions by Mindlin and Gazis [2] showed a beautiful agreement with experimental data by Koga and Fukuyo [3]–[5]. This paper explores a wealth of both the analysis and the data, which has not been discussed.