Tolerance and asymptotic modelling of dynamic problems for thin microstructured transversally graded shells

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• 作者：Barbara Tomczyk ; ^{barbara.tomczyk@p.lodz.pl} ; Paweł Szczerba
• 关键词：Thin transversally graded shells ; Tolerance-periodic microstructure ; Tolerance modelling ; Asymptotic modelling ; Dynamic problems
• 刊名：Composite Structures
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：162
• 期：Complete
• 页码：365-373
• 全文大小：521 K
• 卷排序：162

文摘

The objects of consideration are thin linearly elastic Kirchhoff-Love-type open circular cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. The first aim of this contribution is to formulate and discuss a new non-asymptotic averaged model for the analysis of selected dynamic problems for these shells. As a tool of modelling we shall apply the tolerance averaging technique. Contrary to the starting exact shell equations with highly oscillating, non-continuous and tolerance-periodic coefficients, governing equations of the proposed tolerance model have continuous and slowly varying coefficients depending also on a cell size. Hence, an important advantage of this model is that it makes it possible to study the effect of a microstructure size on the global shell dynamics (the length-scale effect). The second aim is to derive and discuss a certain asymptotic model being independent of a microstructure size. It will be shown that in the framework of the tolerance model not only the fundamental lower, but also the new additional higher-order free vibration frequencies can be derived and analysed.