Application of Lee's Plate Equations to Analysis of Spurious Vibrations of Rectangular AT-Cut Quartz Plates

Abstract

Strip A T-cut quartz resonators have recently been developed and are widely used in frequency applications because of their small size. Many spurious resonances can be supported in a rectangular A T-cut plate. Therefore, 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 three-dimensional equations of elasticity. The practical analysis of spurious characteristics has been carried out on the basis of approximate two-dimensional equations. In this paper, the applicability of Lee's two-dimensional equations to A T-cut plates is examined. The resonant frequencies are calculated as a function of X-length, and are compared to Koga's experimental data. The result shows that new correction factors should be introduced in the equations in order to adjust the approximate values of wave numbers for the thickness-flexure waves propagating in X and Z ′ directions.

Gentle and fast atomic force microscopy with a piezoelectric scanning probe for nanorobotics applications

“…The oscillation mode of rectangular AT-cut quartz resonators has been studied in several works [31][32][33]. It is known with precision that the AT-cut quartz resonator fundamental oscillation mode is in the thickness shear mode, as depicted in figure 6.…”

Three-dimensional analysis of spurious vibrations in rectangular AT-cut quartz plates

“…3. Figure 4 shows the frequency spectra obtained using the corrected plate equations [3]. The deviation of the spectra calculated from the corrected plate equations is removed from the present results.…”

“…We showed that Lee et al's first order plate equations with two new correction factors predict well in all the spurious frequencies [3]. However, a few discrepancies still remain between calculat,ed and measured data [dl.…”

“…Comparison of calculated and measured represent results calculated from the 2c = 27.004 mm). The black curves present method, and the gray curves rep-represent results calculated from the resent, Koga's experimental data [4].corrected plate equations[3], and the gray curves represent.against N , for TF3T1-3,17 ( frequency=0.95867 MHz…”