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Thickness-Shear And Thickness-Twist Vibrations Of Circular At-Cut Quartz Resonators, Huijing He, Jiashi Yang, Qing Jiang

Department of Mechanical and Materials Engineering: Faculty Publications

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.