The problem of linear dynamic thermoelasticity in Kirchhoff–Love-type circular cylindrical shells having properties periodically varying in circumferential direction (uniperiodic shells) is considered. In order to describe thermoelastic behaviour of such shells, two mathematical averaged models are proposed— the non - asymptotic tolerance and the consistent asymptotic models. Considerations are based on the known Kirchhoff–Love theory of elasticity combined with Duhamel-Neumann thermoelastic constitutive relations and on Fourier’s theory of heat conduction. The non-asymptotic tolerance model equations depending on a cell size are derived applying the tolerance averaging technique and a certain extension of the known stationary action principle . The consistent asymptotic model equations being independent on a microstructure size are obtained by means of the consistent asymptotic approach . Governing equations of both the models have constant coefficients, contrary to starting shell equations with periodic, non-continuous and oscillating coefficients. As examples, two special length-scale problems will be analysed in the framework of the proposed models. The first of them deals with investigation of the effect of a cell size on the shape of initial distributions of temperature micro-fluctuations. The second one deals with study of the effect of a microstructure size on the distribution of total temperature field approximated by sum of an averaged temperature and temperature fluctuations.

中文翻译：

---

薄微周期圆柱壳动态热弹性问题的容差和渐近建模

考虑了具有沿圆周方向周期性变化的特性的 Kirchhoff-Love 型圆柱壳（单周期壳）中的线性动态热弹性问题。为了描述这种壳的热弹性行为，提出了两种数学平均模型——非渐近容差模型和一致渐近模型。考虑基于已知的 Kirchhoff-Love 弹性理论与 Duhamel-Neumann 热弹性本构关系和傅立叶热传导理论相结合。应用容差平均技术和已知静止作用原理的某种扩展，导出依赖于单元大小的非渐近容差模型方程。采用一致渐近方法得到了与微观结构尺寸无关的一致渐近模型方程。这两种模型的控制方程都具有常数系数，这与具有周期性、非连续和振荡系数的起始壳方程相反。作为例子，将在所提出的模型框架内分析两个特殊的长度尺度问题。其中第一个涉及研究单元尺寸对温度微波动初始分布形状的影响。第二个研究微观结构尺寸对由平均温度和温度波动之和近似的总温度场分布的影响。这两种模型的控制方程都具有常数系数，这与具有周期性、非连续和振荡系数的起始壳方程相反。作为例子，将在所提出的模型框架内分析两个特殊的长度尺度问题。其中第一个涉及研究单元尺寸对温度微波动初始分布形状的影响。第二个研究微观结构尺寸对由平均温度和温度波动之和近似的总温度场分布的影响。这两种模型的控制方程都具有常数系数，这与具有周期性、非连续和振荡系数的起始壳方程相反。作为例子，将在所提出的模型框架内分析两个特殊的长度尺度问题。其中第一个涉及研究单元尺寸对温度微波动初始分布形状的影响。第二个研究微观结构尺寸对由平均温度和温度波动之和近似的总温度场分布的影响。其中第一个涉及研究单元尺寸对温度微波动初始分布形状的影响。第二个研究微观结构尺寸对由平均温度和温度波动之和近似的总温度场分布的影响。其中第一个涉及研究单元尺寸对温度微波动初始分布形状的影响。第二个研究微观结构尺寸对由平均温度和温度波动之和近似的总温度场分布的影响。