石英晶体板高频振动模态的有限元分析

发布时间：2018-07-01 07:57

本文选题：谐振器 + 石英晶体　；参考：《力学季刊》2017年02期

【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.
[Abstract]:Thickness shear vibration is the working mode of quartz crystal resonator. It is very important to accurately understand the distribution of thickness shear vibration mode for the design of resonator. At present, the frequencies and modes calculated by the assumption of straight traveling waves do not fully accord with the actual exact vibration modes of quartz crystal plates, nor can they meet the needs of engineering design. Based on Mindlin's high-order plate theory, the finite element method is used to analyze the high-frequency vibration modes of quartz crystal plate, and the calculation is carried out on Linux parallel cluster to solve the problem of eigenvalue calculation for large-scale linear equations. The frequency spectrum of the vibration frequency varying with the ratio of length to thickness is obtained. The results are in good agreement with the results in the known literature and verify the reliability of the finite element method. At the same time, the displacement distribution of thickness shear vibration at the line of plate is given, the influence of different mass ratio of metal electrode on thickness shear vibration mode is analyzed, and the complex vibration mode in quartz crystal plate is explained. The results obtained in this paper are helpful to the design of quartz crystal resonator.
【作者单位】：宁波大学机械工程与力学学院;宁波职业技术学院建筑工程系;
【基金】：国家自然科学基金(11372145)
【分类号】：TN752.2

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