考虑电极效应的Mindlin板方程的修正系数
orrection Factors of the Mindlin Plate Equations with the Consideration of Electrodes
Mindlin板理论在石英晶体谐振器厚度剪切的高频率振动中分析起着至关重要的作用。为了简化分析,众多的耦合振动模态被缩减成最基本的强耦合方程,为了确保能够在截止频率得到精确解,引进了修正系数来确保结果的准确性,得到了从简单板理论到考虑电极质量效应的修正系数。高阶修正系数能够保证在考虑电极质量效应时AT切石英晶体板的厚度振动的精确性。在系统研究中发现修正系数可以通过选取特定的强耦合模态进行分析得到,得到的修正系数方程可以方便的应用到基于Mindlin板理论的有限元分析中。
he Mindlin plate theory has been playing a role vital in the analysis of high frequency vibrations of quartz crystal resonators at the thickness-shear mode. The coupled equations with infinite number of vibration modes have been truncated to retain essential ones with strong couplings for simplified analysis, and correction factors have been introduced to ensure exact solutions at cut-off frequencies as part of the validation procedure. Starting form plates without complications, correction factors have also been modified to include electrodes for their mass effect. Such results have been important to higher-order correction factors to ensure accurate consideration of electrodes in the AT-cut quartz crystal plates. The findings in factors systematic study are readily available for the analytical equations with selected modes with strong couplings, and equally convenient for the implementation of the finite element analysis with the Mindlin plate equations.
杜建科、王文军、王骥、吴荣兴、陈桂佳、马廷峰
力学物理学晶体学
Mindlin板振动剪切修正石英谐振器
Mindlinplatevibrationshearcorrectioncrystalresonator
杜建科,王文军,王骥,吴荣兴,陈桂佳,马廷峰.考虑电极效应的Mindlin板方程的修正系数[EB/OL].(2012-04-16)[2025-08-25].http://www.paper.edu.cn/releasepaper/content/201204-225.点此复制
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