Thickness-shear vibration of an AT-cut quartz resonator with a hyperbolic contour

Li P.

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Thickness-shear vibration of an AT-cut quartz resonator with a hyperbolic contour

机译：具有双曲线轮廓的AT切割石英谐振器的厚度剪切振动

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A theoretical analysis is performed on thicknessshear vibrations of a contoured AT-cut quartz resonator with a hyperbolic thickness variation using the Legendre equation and hypergeometric function. Based on the solution, resonant frequencies and modes are calculated. Strong energy trapping of the modes is observed. The effects of the parameters of the hyperbolic contour on resonant frequencies and modes are examined. A comparison with the conventional contoured resonator in the literature with a quadratic thickness variation is made. The behaviors of the two types of resonators are qualitatively similar, with small but significant quantitative differences.

机译：使用勒让德方程和超几何函数，对具有双曲线厚度变化的轮廓AT切割石英谐振器的厚度剪切振动进行了理论分析。基于该解决方案，可以计算出谐振频率和模态。观察到模式的强能量陷阱。研究了双曲轮廓参数对共振频率和模态的影响。进行了与传统的轮廓谐振器的比较，其具有二次厚度变化。两种类型的谐振器的行为在质量上相似，但数量差异很小，但差异很大。

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《Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on》 |2012年第5期|p.1006-1012|共7页
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Li P.;
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1. Thickness-Shear and Thickness-Twist Vibrations of an AT-Cut Quartz Mesa Resonator [J] . He H., Liu J., Yang J. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on . 2011,第10期

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2. Frequency Shift of Thickness-Shear Vibrations of AT-Cut Quartz Resonators Due to a Liquid Layer with the Electrode Stiffness Considered [J] . Yun Jing, Jin Chen, Xiao Chen, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control . 2007,第7期

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3. Trapped thickness-shear modes in a contoured, partially electroded AT-cut quartz resonator [J] . Shi Junjie, Fan Cuiying, Zhao Minghao, The European physical journal. Applied physics . 2015,第1期

机译：轮廓化，部分电极化的AT切割石英谐振器中的陷波厚度剪切模式
4. Frequency-temperature relations of thickness-shear and flexural vibrations of contoured quartz resonators [C] . Lee, P.C.Y., Wang, Frequency Control Symposium, 1996. 50th., Proceedings of the 1996 IEEE International. . 1996

机译：仿形石英谐振器的厚度剪切和弯曲振动的频率-温度关系
5. Numerical analysis of the third overtone of thickness shear vibrations in silicon carbide-cut quartz resonators [D] . Zhang, Zhen 1994

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6. A Semi-Analytical Solution for the Thickness-Vibration of Centrally Partially-Electroded Circular AT-Cut Quartz Resonators [O] . Bin Wang, Xiaoyun Dai, Xintao Zhao, 2017

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7. Thickness-shear and thickness-twist vibrations of circular AT-cut quartz resonators [O] . He, Huijing, Yang, Jiashi, Jiang, Qing 2013

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8. Coupled Thickness-Shear and Thickness-Twist Vibrations of Unelectroded AT-Cut Quartz Plates [R] . Tiersten, H. F., Smythe, R. C. 1985

机译：耦合厚度 - 剪切和厚度 - 扭曲振动的未电子aT切割石英板

Thickness-shear vibration of an AT-cut quartz resonator with a hyperbolic contour

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