Exact thickness-shear resonance frequency of electroded piezoelectric crystal plates

The determination of the precise thickness-shear frequency of electroded crystal plates has practical importance in quartz crystal resonator design and fabrication, especially when the high fundamental thickness-shear frequency has reduced the crystal plate thickness to such a degree that proper consideration of the effect of electrodes is very important. The electrodes effect as mass loading in the estimation of the resonance frequency has to be modified to consider the stiffness of electrodes, as the relative strength is increasingly noticeable. By following a known procedure in the determination of the thickness-shear frequency of an infinite AT-cut crystal plate, frequency equations of crystal plate without and with piezoelectric effect are obtained in terms of elastic constants and the electrode material density. After solving these equations for the usual design parameters of crystal resonators, the design process can be optimized to pinpoint the precise configuration to avoid time-consuming trial and reduction steps. Since these equations and solutions are presented for widely used materials and parameters, they can be easily integrated into the existing crystal resonator design and manufacturing processes.

石英晶体板高频振动的三维有限元分析

通过建立石英晶体板的三维模型,运用有限元分析软件ANSYS获得了石英晶体板厚度剪切振动的振动频率和位移云图。验证了数值计算结果的收敛性并提出了避免振动模态强烈耦合的石英晶体板最佳长厚比的选取方法。模型分析过程中发现,六面体网格比四面体网格易观察到石英晶体板的厚度剪切振动。

带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正、逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比,外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力,从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究,应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用状态空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层极采用高阶和一阶剪切变形理论进行计算,结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言,由于激励器主要是引起板的剪切变形,而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能,因此高阶剪切变形理论可以提供板变形的更为精确的解。因此,对于厚度剪切型激励器,剪切变形理论的选取对于板变形结果的好坏有重要的作用。