Overtone frequency spectra for ξ3-dependent modes in AT-cut quartz resonators [Correspondence]

We study straight-crested waves and vibration modes with spatial variations along the x₃ direction only in an AT-cut quartz plate resonator. The equations of anisotropic elasticity are used. Dispersion relations for face-shear and thickness-twist waves in unbounded plates are plotted. Frequency spectra are obtained for face-shear and thickness-twist vibrations of finite plates in which these modes are coupled by boundary conditions. Most importantly, our analysis produces the frequency spectra for overtone modes which do not seem to have been obtained before for x₃-dependent modes. Numerical results for third- and fifth-overtone AT-cut quartz resonators are presented, showing that higher-order overtone modes are associated with more mode couplings.