Tolerance and asymptotic modelling of dynamic problems for thin microstructured transversally graded shells. (15th February 2017)

• Record Type: Journal Article
• Authors: Tomczyk, Barbara; Szczerba, Paweł
• Is Part Of: Composite structures. Volume 162(2017)
• Page Start: 365
• Page End: 373
• Publication Date: 2017-02-15
• Subjects: Thin transversally graded shells -- Tolerance-periodic microstructure -- Tolerance modelling -- Asymptotic modelling -- Dynamic problems; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2016.11.083
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: 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 .