Thickness-shear mode shapes and mass-frequency influence surface of a circular and electroded AT-cut quartz resonator

Finite-element solutions for the fundamental thickness shear mode and the second anharmonic overtone of a circular, 1.87-MHz AT-cut quartz plate with no electrodes are presented and compared with previous results for a rectangular plate of similar properties. The edge flexural mode in circular plates, a vibration mode not seen in the rectangular plate, is also presented. A 5-MHz circular and electroded AT-cut quartz plates is studied. A portion of the frequency spectrum is constructed in the neighborhood of the fundamental thickness-shear mode. A convergence study is presented for the electroded 5-MHz plate. A two-dimensional technique for visualizing the vibration mode solutions is presented. A contour plot of the mass-frequency influence surface for the plated 5-MHz resonator is presented. The mass-frequency influence surface is defined as a surface giving the frequency change due to a small localized mass applied to the resonator surface