On the stability of thin periodic plates

In this paper a new modelling method of thin plates with a periodic structure along one direction and with a slowly-varying structure along the perpendicular direction in the planes parallel to the plate midplane is presented. The model is a certain generalisation of the length-scale model of periodic plates, which makes it possible to take into account the effect of periodicity cell size on the dynamics of plates with two-directional periodic structure (Jȩdrysiak and Woźniak, 1995; Jȩdrysiak, 1998). In order to describe this effect in stationary processes, e.g. a plate stability, for one-directional periodic plates the generalised model is applied in this paper. Applications to the stability problems and a comparison with effective stiffnesses models will be shown.