摘要
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.
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.
基金
supported by the Phase Ⅲ Construction of the ‘985’ Project of Sun Yat-Sen University
support of the Introduction of Innovative R&D Team Project of Guangdong Province
support of the Science and Technology Planning Project of Guangdong Province (No. 2011A060901013)
the Science and Technology Planning Project of Guangzhou (No. 2011Y1-00029)
supported by theIndustry-Universities-Research Cooperation Project of Guangdong Province and Ministry of Education of China (No.2011A090200123)
support from the US Army Research Laboratory/US Army Research Office under agreement number W911NF-10-1-0293
