On the Effect of Period Lengths on Dynamic Stability of Thin Biperiodic Cylindrical Shells

The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure (i.e. a periodically varying thickness and/or periodically varying elastic and inertial properties) in both directions tangent to the shell midsurface. Such shells are called biperiodic. The aim of this paper is to propose a new averaged non-asymptotic model of biperiodic shells, which makes it possible to investigate parametric vibrations and dynamical stability of the shells under consideration. As a tool of modeling we shall apply the tolerance averaging technique. The resulting equations have constant coefficients. Moreover, in contrast with models obtained by the known asymptotic homogenization technique, the proposed one takes into account the effect of the period lengths on the overall dynamic shell behavior, called a length-scale effect. It will be shown that this effect plays an important role in the dynamical stability analysis of the shells considered in this paper.