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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Effects of a liquid layer on thickness-shear vibrations of rectangular AT-cut quartz plates
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Effects of a liquid layer on thickness-shear vibrations of rectangular AT-cut quartz plates

机译：液层对矩形AT切割石英板厚度剪切振动的影响

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摘要

Thickness-shear vibrations of rectangular AT-cut quartz with one face in contact with a layer of Newtonian (linearly viscous and compressible) fluid are studied. The two-dimensional (2D) governing equations for vibrations of piezoelectric crystal plates given previously are used in the present study. The solutions for 1D shear wave and compressional wave in a liquid layer are obtained, and the stresses at the bottom of the liquid layer are used as approximations to the stresses exerted on the crystal surface in the plate equations. Closed form solutions are obtained for both free and piezoelectrically forced thickness-shear vibrations of a finite, rectangular AT-cut quartz plate in contact with a liquid layer of finite thickness. From the present solutions, a simple and explicit formula is deduced for the resonance frequency of the fundamental thickness-shear mode, which includes the effects of both shear and compressional waves in the liquid layer and the effect of the thickness-to-length ratio of the crystal plate. The formula reduces to the widely used frequency equation obtained by many previous investigators for infinite plates. The resonance frequency of a rectangular AT-cut quartz, computed as a function of the thickness of the adjacent liquid layer, agrees closely with the experimental data measured by Schneider and Martin (Anal. Chem., vol. 67, pp. 3324-3335, 1995).
机译：研究了矩形AT切割石英的厚度-剪切振动，该石英的一个面与一层牛顿流体（线性粘滞和可压缩）接触。本研究中使用了先前给出的压电晶体板振动的二维（2D）控制方程。获得了液层中一维剪切波和压缩波的解，并且液层底部的应力被用作板式方程中施加到晶体表面的应力的近似值。对于与有限厚度的液层接触的矩形矩形AT切割石英板的自由振动和压电强迫的厚度剪切振动，都获得了闭合形式的解。从目前的解决方案中，推导出了基本厚度-剪切模式的共振频率的一个简单明确的公式，其中包括液层中的剪切波和压缩波的影响以及厚度的长度-长度比的影响。水晶板。该公式简化为许多以前的研究人员针对无限板所获得的广泛使用的频率方程。矩形AT切割石英的共振频率根据相邻液层厚度的函数计算，与Schneider和Martin（Anal。Chem。，第67卷，第3324-3335页）测得的实验数据非常吻合。 （1995年）。

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