IEEE Trans Ultrason Ferroelectr Freq Control. 2013 Apr;60(4):858-63. doi: 10.1109/TUFFC.2013.2636.
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.
我们研究了仅在 AT 切石英板谐振器中沿 x3 方向具有空间变化的直线脊波和振动模式。使用各向异性弹性方程。绘制了无界板中面切和厚度扭转波的频散关系。对于边界条件耦合的有限板的面切和厚度扭转振动，获得了频率谱。重要的是，我们的分析产生了泛音模式的频率谱，这些模式似乎以前没有为 x3 相关模式获得过。给出了三阶和五阶泛音 AT 切石英谐振器的数值结果，表明高阶泛音模式与更多的模式耦合有关。
