A non-asymptotic model for the stability analysis of thin biperiodic cylindrical shells

The object of considerations is a thin linear-elastic cylindrical shell with arbitrary cross-section having a periodic structure in both directions tangent to the shell midsurface. The aim of this paper is to propose a new averaged non-asymptotic model of dynamical stability problems for such shells. As a tool of modeling we shall apply the tolerance averaging technique, given for periodic structures in Woźniak and Wierzbicki [Averaging techniques in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, 2000]. In contrast with models obtained by means of asymptotic homogenization methods, the proposed one makes it possible to describe the effect of the period lengths on the global shell stability, called a length-scale effect.