Mechanical & Materials Engineering, Department of


Document Type


Date of this Version

Summer 6-2013


Huijing He, et al. "Thickness-shear and thickness-twist vibrations of circular AT-cut quartz resonators" Acta Mechanica Solida Sinica Vol. 26 Iss. 3 (2013) p. 245 - 253


Published by AMSS Press, Wuhan, China


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.