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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Accuracy of crystal plate theories for high-frequency vibrations in the range of the fundamental thickness shear mode
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Accuracy of crystal plate theories for high-frequency vibrations in the range of the fundamental thickness shear mode

机译：基本厚度剪切模式范围内用于高频振动的晶体板理论的精度

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摘要

The first-order plate theories with correction factors are generally assumed to predict accurately the plate modes which have half wavelengths greater than the plate thickness, and at frequencies up to 20% higher than the fundamental thickness shear frequency. This assumption is assessed by comparing the straight crested wave solutions of the plate theories with those of the three-dimensional elastic equations of motion. The frequency spectra for bandwidths of resonant frequencies versus the aspect ratio of length to thickness of plate are compared for three sets of plate equations: the first-order Mindlin plate equations, the third-order Mindlin plate equations, and the third-order Lee and Nikodem plate equations. The finite element results for a quartz SC-cut strip with free edges show that Mindlin's first-order plate equations, and Lee and Nikodem's third-order plate equations yield less accurate frequency spectra of the modes in the vicinity of the fundamental thickness shear mode than the third-order Mindlin plate equations without correction factors. The degree of inaccuracy increases with the ratio of plate length to thickness, and the slope of the modal branches in the frequency spectra. For a plate length to thickness ratio of 31 to 33, the first-order plate theory is found to yield accurate frequency spectra for normalized frequencies less than 0.3, which is lower than previously assumed. At normalized frequencies greater than 0.3, deviations are seen in the frequency spectra, starting with the modal branches which are more steeply inclined.
机译：通常假定具有校正因子的一阶板理论可准确预测具有大于板厚度一半波长且在比基本厚度剪切频率高20％的频率下的板模式。通过将板理论的直波解与三维运动弹性方程的直波解进行比较，可以评估该假设。比较了三组板式方程的共振频率带宽与板长与板厚纵横比的频谱关系：一阶Mindlin板方程，三阶Mindlin板方程以及三阶Lee和Nikodem板方程。具有自由边缘的石英SC切割带的有限元结果表明，Mindlin的一阶板式方程以及Lee和Nikodem的三阶板式产生的频谱在基本厚度剪切模式附近的频谱不如没有校正因子的三阶Mindlin板方程。不精确度随板长与厚度之比以及频谱中模态分支的斜率而增加。对于板长与厚度之比为31到33的情况，发现一阶板理论可为小于0.3的归一化频率生成准确的频谱，该频谱低于先前的假设。在大于0.3的归一化频率处，频谱中会出现偏差，从更陡峭倾斜的模态分支开始。

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