Length-scale effect in dynamic problems for thin biperiodically stiffened cylindrical shells

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss a new mathematical averaged model for the analysis of selected dynamic problems for these shells. This, so-called, general combined asymptotic-tolerance model is derived by applying a certain extended version of the known tolerance (non-asymptotic) modelling procedure. 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 proposed combined model have constant coefficients depending also on a cell size. Hence, this model can be applied to study the effect of a microstructure size on dynamic behaviour of the shells (the length-scale effect). An important advantage of this model is that it makes it possible to analyse micro-dynamics of biperiodic shells independently of their macro-dynamics. The differences between the proposed general combined model and the corresponding known less accurate standard combined model derived by means of the more restrictive concept of slowly-varying functions are discussed. As an example there are determined and analysed cell-depending micro-vibrations of the biperiodic shells under consideration.