Abstract

We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower frequencies of the plate, the asymptotic results are compared with the results of analysis by finite elements.

中文翻译：

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参数可变的圆形薄板的自由振动频率

摘要

在这项工作中，我们研究了不均匀圆形薄板的横向振动。使用扰动方法，获得了板的自由振动频率的渐近公式，其厚度和杨氏模量线性地取决于半径。分析了边界条件对固定质量板的频率和频率行为的影响。对于较低频率的板，将渐近结果与有限元分析结果进行比较。