用明林板理论分析各向同性圆板的自由振动

Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications Pub Date : 2014-12-29 DOI:10.1109/SPAWDA.2014.6998608

Hui Chen, Ji Wang, T. Ma, Jianke Du

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引用次数: 5

摘要

我们研究了具有自由边缘的各向同性圆形板的非轴对称振动。通过对直角坐标系下的Mindlin板方程的推导，得到圆柱坐标系下圆板的厚度-剪切、弯曲和厚度-扭转耦合模式的Mindlin一阶方程。用贝塞尔函数成功地求解了方程。作为验证和求解过程的一部分，获得了色散关系、频谱和模态振型的数值结果。频谱计算结果与Mindlin早期的研究结果吻合较好。系统地分析圆形板的高频振动是我们在圆形石英晶体谐振器中应用的第一步。

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An analysis of free vibrations of isotropic, circular plates with the Mindlin plate theory

We study non-axially symmetric vibrations of isotropic, circular plates with free edges. Mindlin's first-order equations governing the coupled thickness-shear, flexural, and thickness-twist modes are obtained for circular plates in cylindrical coordinates by following the derivation of Mindlin plate equations in Cartesian coordinates. The equations are successfully solved by Bessel functions. Numerical results for dispersion relations, frequency spectra, and mode shapes are obtained as parts of the validation and solution procedure. The calculated results of frequency spectra are in good agreement with Mindlin's earlier studies. It is our first step to analyze high frequency vibrations of circular plates in a systematic manner for applications in circular quartz crystal resonators.

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Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications

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