中文摘要：

厚度剪切振动是石英晶体谐振器的工作模态,精确了解厚度剪切振动模态的分布对于谐振器的设计有着十分重要的意义.目前,由直行波假设计算得到的频率和模态并不完全符合石英晶体板实际的精确振动模式,也不能精确满足工程设计的需要.本文基于Mindlin高阶板理论,采用有限元法来分析石英晶体板的高频振动模态,并在Linux并行集群上进行计算来解决大规模的线性方程组的特征值计算问题.通过计算得到了振动频率随长厚比变化的频谱图,其结果与已知文献中的结果比较,符合得较好,验证了有限元结果的可靠性.同时给出了厚度剪切振动在板中线处的位移分布,分析了金属电极的不同质量比对于厚度剪切振动模态的影响,解释了石英晶体板内的复杂的振动模式.本文的分析结果对石英晶体谐振器的设计具有指导意义.

英文摘要：

It is very important to understand the distribution of the thickness-shear modes accurately because the thickness-shear vibrations are the functioning mode of quartz crystal resonators. The frequencies and mode shapes calculated by straight-crested waves are not completely consistent with the exact vibration modes of quartz crystal plates. In this paper, high frequency vibration modes of a quartz crystal plate is analyzed by the finite element method which is based on high-order Mindlin plate theory. And the computation is performed on a Linux parallel cluster to solve the extremely large-scale eigenvalue systems and linear systems. Through the standard finite element procedure, the frequency spectra is obtained. The frequency spectra shows a good agreement with the known results in literature, which validated the numerical model. The displacement distribution of the thickness-shear vibration in the middle of the plate is also obtained and plotted. The influence of the mass ratio of the metal electrodes on the vibration modes is investigated, and the complex vibration modes of the quartz crystal plate are explained. The results of this paper are instructive to the design of quartz crystal resonators.