Third-order Mindlin plate theory predictions for the frequency-temperature behavior of straight crested wave modes in AT- and SC-cut quartz plates

The frequency-temperature behavior of straight crested wave modes in AT- and SC-cut quartz plates are studied using Mindlin first- and third-order plate equations. The first order Mindlin plate theory with shear correction factors was previously found to yield an inaccurate frequency spectra of the modes in the vicinity of the fundamental thickness shear frequency. The third order Mindlin plate equations without correction factors, on the other hand, predict well the frequency spectrum in the same vicinity. In general, the frequency-temperature curves of the fundamental thickness-shear obtained from the first-order Mindlin plate theory are sufficiently different from those of the third-order Mindlin plate theory that they raise concerns. The least accurately predicted mode of vibration is the flexure mode which results in discrepancies in its frequency-temperature behavior. The accuracy of other modes of vibrations depends on the degree of couplings with the flexure mode. Mindlin first-order plate theory with only the shear correction factors is not sufficiently accurate for high frequency crystal vibrations at the fundamental thickness-shear frequency. Correction factors for the flexure and face-shear branches may be needed. Hence, a total of five correction factors may be needed for the first-order plate theory to yield accurate frequency spectra and frequency-temperature curves.