论文部分内容阅读
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.
Thickness shear vibration is the working mode of quartz crystal resonator, and it is very important for the design of resonator to know accurately the distribution of thickness-shear vibration mode.Nowadays, the frequency and mode calculated by straight wave assumption are not Which is in full compliance with the actual precise vibration mode of quartz crystal plate and can not exactly meet the needs of engineering design.Based on Mindlin high-order plate theory, the finite element method is used to analyze the high-frequency vibration mode of quartz crystal plate, To solve the problem of eigenvalue calculation of large-scale linear equations.Through calculating the frequency spectrum of the vibration frequency with the ratio of length to thickness, the result is in good agreement with the results in the known literature, and the finite The results show that the displacement distribution of the thickness-shear vibration in the midline of the plate is also given. The influence of the different mass ratios of the metal electrode on the thickness-shear vibration mode is analyzed. The complex vibration in the quartz crystal plate Mode.The results of this paper are instructive for the design of quartz crystal resonators.