The frequency equation of thickness-shear vibrations of SC-cut quartz crystal plates

2016 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA) Pub Date : 2016-10-01 DOI:10.1109/SPAWDA.2016.7829994

Shao-yun Wang, R. Wu, Shih-Yung Pao, Liang-meng Zhang, T. Ma, Jianke Du, Ji Wang

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Abstract

The thickness-shear vibrations of a quartz crystal plate serve as the functioning mode of a resonator with strong couplings to many other modes of vibrations, which can affect the frequency and mode shape, consequently the resonator properties. For applications, it is always desired to have pure thickness-shear vibrations that only exist in an infinite plate. With the three-dimensional equations of elasticity in Cartesian coordinates, boundary conditions are approximated and the frequency equation of the thickness-shear mode is given in terms of materials constants and plate parameters. This relation shows that the thickness-shear frequency can be determined with known parameters of plates. The frequency equation then is compared with the frequency spectra from the Mindlin plate equations for the determination of some key coefficients. This is an extension of our earlier study on the frequency equation of AT-cut quartz crystal plates and it will be used in the design of SC-cut quartz crystal resonators of rectangular shape.

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SC 切割石英晶体板厚度剪切振动的频率方程

石英晶体板的厚度剪切振动是谐振器的功能模式，与许多其他振动模式具有很强的耦合性，会影响频率和模态振型，从而影响谐振器的特性。在应用中，人们总是希望获得只存在于无限板中的纯厚度剪切振动。利用直角坐标下的三维弹性方程，对边界条件进行了近似处理，并根据材料常数和板参数给出了厚度剪切模式的频率方程。这一关系表明，厚度剪切频率可以通过已知的板材参数确定。然后将频率方程与 Mindlin 板方程的频率谱进行比较，以确定一些关键系数。这是我们之前对 AT 切割石英晶体板频率方程研究的延伸，它将用于矩形 SC 切割石英晶体谐振器的设计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2016 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA)

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