A NEW TOLERANCE MODEL OF VIBRATIONS OF THIN MICROPERIODIC CYLINDRICAL SHELLS

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a micro-periodic structure in circumferential direction (uniperiodic shells). At the same time the shells have constant structure in axial direction. The 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. This, so-called, general tolerance model is derived by means of a certain extended version of the known tolerance modelling of micro-heterogeneous media. 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 tolerance model have constant coefficients depending also on a period of inhomogeneity. Hence, the model makes it possible to investigate the effect of a cell size on the global shell dynamics (the length-scale effect). The differences between the general tolerance model proposed here and the corresponding known standard tolerance model derived by means of the more restrictive concept of slowly-varying functions are discussed.

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