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首页> 外文会议>Frequency Control Symposium, 1995. 49th., Proceedings of the 1995 IEEE International >On the accuracy of plate theories for the prediction of unwanted modes near the fundamental thickness shear mode
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On the accuracy of plate theories for the prediction of unwanted modes near the fundamental thickness shear mode

机译：关于板理论在基本厚度剪切模式附近预测有害模式的准确性

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The first order plate theories with correction factors are generally assumed to predict accurately the plate modes which have half wave lengths greater than the plate thickness, and at frequencies up to twenty percent 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 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 do not yield an accurate frequency spectra of the modes in the vicinity of the fundamental thickness shear mode, although the thickness shear mode itself is predicted accurately. The third order Mindlin plate equations without correction factors, on the other hand, predict well the frequency spectrum in the vicinity. The first order Mindlin plate theory is found to yield accurate frequency spectra for normalized frequencies less than 0.1, which is lower than previously assumed. At normalized frequencies greater than 0.1, deviations are seen in the frequency spectra, starting with the modal branches which are more steeply inclined.
机译：通常假设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的板模，并且其频率比基本厚度剪切频率高20％。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。比较了三组板方程的共振频率带宽与长度与厚度的长宽比的频谱关系：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切割带材的有限元结果表明，Mindlin的一阶板式方程以及Lee和Nikodem的三阶板式方程无法在基本厚度剪切模式附近产生模式的准确频谱，尽管厚度剪切模式本身可以准确预测。另一方面，没有校正因子的三阶Mindlin板方程很好地预测了附近的频谱。发现一阶Mindlin板理论可针对小于0.1的归一化频率产生准确的频谱，该频率低于先前的假设。在大于0.1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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