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Length-scale effect in dynamic problems for thin biperiodically stiffened cylindrical shells

机译：动力问题中的长度尺度效应对薄的双周期加劲圆柱壳

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摘要

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss a new mathematical averaged model for the analysis of selected dynamic problems for these shells. This, so-called, general combined asymptotic-tolerance model is derived by applying a certain extended version of the known tolerance (non-asymptotic) modelling procedure. This version is based on a new notion of weakly slowly-varying functions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the proposed combined model have constant coefficients depending also on a cell size. Hence, this model can be applied to study the effect of a microstructure size on dynamic behaviour of the shells (the length-scale effect). An important advantage of this model is that it makes it possible to analyse micro-dynamics of biperiodic shells independently of their macro-dynamics. The differences between the proposed general combined model and the corresponding known less accurate standard combined model derived by means of the more restrictive concept of slowly-varying functions are discussed. As an example there are determined and analysed cell-depending micro-vibrations of the biperiodic shells under consideration.
机译：考虑的对象是在周向和轴向具有周期性微异质结构的薄线性弹性基尔霍夫-洛夫型圆柱壳（双周期壳）。这项贡献的目的是为了制定和讨论一种新的数学平均模型，用于分析这些壳体的选定动态问题。通过应用已知公差（非渐近）建模过程的某个扩展版本，可以得出这种所谓的一般组合渐近公差模型。该版本基于微弱变化函数的新概念。与具有高振荡，不连续和周期系数的起始精确壳方程相反，所提出的组合模型的控制方程具有恒定的系数，这也取决于像元大小。因此，该模型可用于研究微观结构尺寸对壳体动力学行为的影响（长度尺度效应）。该模型的一个重要优点是可以独立于宏观动力学来分析双周期壳的微观动力学。讨论了提出的一般组合模型与相应的已知精度较差的标准组合模型之间的差异，这些模型是通过函数的限制性更强的概念导出的。作为示例，确定并分析了所考虑的双周期壳的取决于细胞的微振动。

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