Micro-dynamics of Thin Tolerance-Periodic Cylindrical Shells

Thin linearly elastic Kirchhoff-Love-type open circular cylindrical shells having a functionally (transversally) graded macrostructure and a tolerance-periodic microstructure in circumferential direction are objects of consideration. At the same time, the shells have constant structure in axial direction. On the microscopic level, the geometrical, elastic and inertial properties of these shells are determined by highly oscillating, non-continuous and tolerance-periodic functions in circumferential direction. On the other hand, on the macroscopic level, the averaged (effective) properties of the shells are described by functions being smooth and slowly varying along circumferential direction. The aim of this note is to study some problems of micro-dynamics of these shells, e.g. micro-vibrations depending on a cell size, The micro-dynamic problems will be analysed in the framework of the averaged asymptotic-tolerance model. Contrary to the exact shell equations with highly oscillating, non-continuous and tolerance-periodic coefficients, governing equations of the averaged model mentioned above have continuous and slowly varying coefficients depending also on a cell size. An important advantage of this model is that it makes it possible to investigate micro-dynamics of the tolerance-periodic shells independently of their macro-dynamics.