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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Mechanical effects of electrodes on the vibrations of quartz crystal plates
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Mechanical effects of electrodes on the vibrations of quartz crystal plates

机译：电极对石英晶体振动的机械影响

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摘要

A system of approximate first-order equations is extracted from an infinite system of 2D equations for piezoelectric crystal plates with thickness-graded material properties, which is deduced from the 3D equations of linear piezoelectricity. These equations are used to study mechanical effects on the thickness-shear (TS), flexural (F), and face-shear (FS) vibrations of an AT-cut quartz plated with two identical electrodes. Dispersion curves are calculated from the present 2D equations as well as the 3D equations. The comparison of these curves shows that the agreement is very close for all three frequency branches of TS, F, and FS modes in a range up to 1.5 times the fundamental TS frequency and for gold and aluminum electrodes with R, the ratio of the mass of the electrodes to that of the plate, equal to 0.05, without introducing any correction factors. In order to assess electrode effects, spectra of /spl Omega/ vs. a/b/sub q/ (length-to-thickness ratio of the quartz) are computed for plates with gold and aluminum electrodes and different R ratios. The spectrum of /spl Omega/ vs. R is computed for plates with aluminum electrodes and a given a/b/sub q/ ratio. For a plate with gold electrodes, the frequencies of predominant TS, F, and FS modes are decreasing as R increases, but the amount of frequency changes for the TS mode is much greater than those for the other two modes. However, for a plate with aluminum electrodes, the frequencies of the TS and FS modes are decreasing, but those of the F modes are increasing as R increases.
机译：从具有厚度梯度材料特性的压电晶体板的2D方程的无限系统中提取近似的一阶方程组，该系统由线性压电性的3D方程推导出来。这些方程式用于研究对镀有两个相同电极的AT切割石英的厚度剪切（TS），弯曲（F）和表面剪切（FS）振动的机械影响。从当前的2D方程以及3D方程计算色散曲线。这些曲线的比较表明，对于TS，F和FS模式的所有三个频率分支，在高达基本TS频率的1.5倍的范围内，对于具有R的金电极和铝电极，质量比电极的极板数与极板的极板数相等，等于0.05，而没有引入任何校正因子。为了评估电极效应，对于具有金和铝电极且具有不同R比率的板，计算了/ spl Omega / vs. a / b / sub q /的光谱（石英的长厚比）。对于具有铝电极且给定的a / b / sub q /比的板，计算/ spl Omega / vs. R的光谱。对于带有金电极的板，主要的TS，F和FS模式的频率随着R的增加而降低，但是TS模式的频率变化量远大于其他两种模式。然而，对于具有铝电极的板，TS和FS模式的频率降低，而F模式的频率随着R的增加而增加。

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