Experimental study of vibrations of mesa-shaped AT-cut quartz plates

This paper describes an experimental study on the vibrations of mesa-shaped plates. We prepared X-elongated AT-cut quartz plates of 0.2 mm thickness, on which a bi-mesa structure was fabricated by a chemical etching process. Among many resonances measured around 8 MHz, we could observe strong spurious modes which were identified as the anharmonic thickness-shear (TS) and thickness-flexural (TF) modes by a theoretical analysis of straight-crested (X-Y´) vibrations. The strength and the frequency of each mode changed with the height of mesa portion. As the height was increased, the strength of TF mode decreased rapidly and the frequency lowered a little while both the strength and the frequency of anharmonic TS mode increased greatly. These experimental results, in good agreement with the theoretical ones, justify our prediction of spatial mode-separation, in which the TS and TF modes are confined in the inner and outer regions of the mesa-shaped plate, respectively. We also discuss the plano-mesa vibrations