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Thickness-Shear and Thickness-Twist Vibrations of Circular AT-Cut Quartz Resonators

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Abstract

Exact solutions for free vibration frequencies and modes are obtained for thickness-shear and thickness-twist vibrations of unelectroded circular AT-cut quartz plates governed by the two-dimensional scalar differential equation derived by Tiersten and Smythe. Comparisons are made with experimental results and the widely-used perturbation solution by Tiersten and Smythe under the assumption of weak in-plane anisotropy. Our solution is found to be much closer to the experimental results than the perturbation solution. For the frequency of the fundamental thickness-shear mode, the error of the perturbation method is 0.4549%, significant in resonator applications.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, 68588-0526, Lincoln, NE, USA

    Huijing He & Jiashi Yang

  2. School of Engineering, Sun Yat-Sen University, 510275, Guangzhou, China

    Qing Jiang

  3. Guangzhou Ande Biotechnology Co. Ltd., 510663, Guangzhou, China

    Qing Jiang

Authors
  1. Huijing He
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  2. Jiashi Yang
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  3. Qing Jiang
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Corresponding author

Correspondence to Jiashi Yang.

Additional information

The work was supported by the Phase III Construction of the ‘985’ Project of Sun Yat-Sen University. We acknowledge the support of the Introduction of Innovative R&D Team Project of Guangdong Province. We also acknowledge the support of the Science and Technology Planning Project of Guangdong Province (No. 2011A060901013) and the Science and Technology Planning Project of Guangzhou (No. 2011Y1-00029). And this work was also supported by the Industry-Universities-Research Cooperation Project of Guangdong Province and Ministry of Education of China (No. 2011A090200123). Additional support from the US Army Research Laboratory/US Army Research Office under agreement number W911NF-10-1-0293 is also acknowledged.

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He, H., Yang, J. & Jiang, Q. Thickness-Shear and Thickness-Twist Vibrations of Circular AT-Cut Quartz Resonators. Acta Mech. Solida Sin. 26, 245–254 (2013). https://doi.org/10.1016/S0894-9166(13)60023-3

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  • DOI: https://doi.org/10.1016/S0894-9166(13)60023-3

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