Two-dimensional charge patterns of spurious modes in rectangular AT-cut quartz plates

Many spurious resonances can be supported in a rectangular AT-cut quartz plate. Their vibrational shapes are complicated due to phase reversals along both X and Z´ axes. The surface charge patterns associated with spurious resonances are studied, to clarify their mode families. A novel system, based on the electric probe method, is developed to measure precisely the piezoelectric charges induced on the plate surface. The charge patterns of many spurious modes are measured on rectangular 1 MHz AT-cut plates, and examined with the calculated ones. The results show that almost all the charge patterns of spurious resonances are not straight-crested, but are two-dimensionally complex. A good agreement between the experiment and calculation clearly indicates that these modes belong to the thickness-flexure and the face-shear/flexure. It is also pointed out that Mindlin´s plate equations should be improved for applying to the full analysis of vibrational modes