Jędrysiak Jarosław
Department of Structural Mechanics, Łódź University of Technology, al. Politechniki 6, 90-924 Łódź, Poland.
Materials (Basel). 2022 Aug 16;15(16):5623. doi: 10.3390/ma15165623.
Thin elastic periodic plates are considered in this paper. Since the plates have a microstructure, the effect of its size on behaviour of the plates can play a crucial role. To take into account this effect, the tolerance modelling method is applied. This method allows us to obtain model equations with constant coefficients, which involve terms dependent of the microstructure size. Using the model equations, not only can formulas of fundamental lower-order vibration frequencies be obtained, but also formulas of higher-order vibration frequencies related to the microstructure. In this paper, the effect of the material periodic microstructure on free vibration frequencies for various boundary conditions of the plates was analysed. To obtain proper formulas of frequencies, the Ritz method is applied. Moreover, some results are compared to the results calculated using the FEM.
本文研究了薄弹性周期板。由于这些板具有微观结构，其尺寸对板行为的影响可能起着关键作用。为了考虑这种影响，应用了容差建模方法。该方法使我们能够获得具有常系数的模型方程，其中包含与微观结构尺寸相关的项。利用这些模型方程，不仅可以得到基本低阶振动频率的公式，还可以得到与微观结构相关的高阶振动频率的公式。本文分析了材料周期微观结构对板在各种边界条件下自由振动频率的影响。为了得到合适的频率公式，应用了瑞利方法。此外，还将一些结果与使用有限元法计算的结果进行了比较。
