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本文研究了补片《矩形》电极尺寸和质量对镀膜矩形晶体片的振动和能陷的影响。文中采用晶体片振动的Mindlin二维近似方程来保留厚度切变、厚度扭转和弯曲的耦合膜。通过采用位移公式以有限元法获得数值解,此解满足晶体片的边缘静止条件和在晶体片镀膜与非镀膜交界处的应力和位移的连续条件。文內对位置对称的补片电极矩形AT切石英片进行了数值计算,获得了晶体片和电极不同尺寸和不同质量时的谐振频率及其相应的二维振动膜。Mindlin和Lee,Lee和Spencer及Tiersten把计算结果同现有的分析结果做了比较,而Curran和Koneval把计算结果与实验数据进行了比较。所得二维Bechmann数基本上取决于三个参数:电极长度与晶体片厚度之比;电极宽度与晶体片厚度之比;以及电极质量与晶体单位面积质量之比。
In this paper, we study the influence of patch “rectangular” electrode size and mass on the vibration and energy sink of coated rectangular crystal sheets. In this paper, the Mindlin two-dimensional approximation equation of crystal vibration is used to keep the coupling film with thickness shear, thickness torsion and bending. The numerical solution is obtained by the finite element method using a displacement formula that satisfies the continuous condition of the edge static condition of the crystal piece and the stress and displacement at the interface between the crystal piece coating and the uncoated piece. In this paper, the position-symmetric rectangular AT-cut patch of patch electrode was numerically calculated, and the resonant frequency and its corresponding two-dimensional vibrating membrane with different size and different mass of the wafer and electrode were obtained. Mindlin and Lee, Lee and Spencer, and Tiersten compared the calculated results with the existing ones, while Curran and Koneval compared the results with the experimental data. The resulting two-dimensional Bechmann number basically depends on three parameters: the ratio of electrode length to the thickness of the wafer; the ratio of the electrode width to the thickness of the wafer; and the ratio of the mass of the electrode to the mass per unit area of the crystal.