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

作者：Tomczyk Barbara^*; Szczerba Pawel

来源：Composite Structures, 2017, 162: 365-373.

DOI：10.1016/j.compstruct.2016.11.083

• Thin transversally graded shells
• Tolerance-periodic microstructure
• Tolerance modelling
• Asymptotic modelling
• Dynamic problems

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.

• 出版日期2017-2-15