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

This paper presents the three-dimensional analysis of spurious vibrations in rectangular AT-cut quartz plates, based on exact equations of motion. According to the classical concept, three-dimensional displacements are described with linear combination of the eigenmodes guided along the X crystal axis. Guided eigenmodes are determined by applying the one-dimensional finite element method to the two-dimensional problem, and their amplitudes are determined using the variational technique for the three-dimensional problem. By means of the present method, we can perform the three-dimensional analysis of spurious vibrations with a high degree of accuracy within a reasonable computation time. As numerical examples, frequency spectra for rectangular AT-cut quartz plates are computed and compared with Koga's experimental data. A convergence study is carried out for the mode for which the frequency spectra are not satisfactory, and corresponding vibrational patterns are also shown.