APPLICATION OF LEES PLATE EQUATIONS TO ANALYSIS OF SPURIOUS VIBRATIONS OF RECTANGULAR AT-CUT QUARTZ PLATES

Strip AT-cut quartz resonators have recently been developed and are wi dely used in frequency applications because of their small size. Many spurious resonances can be supported in a rectangular AT-cut plate. Th erefore, analysis of the influence of both the X and Z' dimensions of the plate upon the spurious characteristics is necessary to design the strip resonators. However, it is very difficult to exactly solve thre e-dimensional Equations of elasticity. The practical analysis of spuri ous characteristics has been carried out on tile basis of approximate two-dimensional equations. In this paper, the applicability of Lee's t wo-dimensional equations to AT-cut. plates is examined. The resonant f requencies are calculated as a function of X-length, and are compared to Koga's experimental data. The result shows that new correction fact ors should be introduced in the equations in order to adjust the appro ximate values of wave numbers for the thickness-flexure waves propagat ing in X and Z' directions.