Some remarks on dynamic results for averaged and exact models of thin periodic plates

The aim of the paper is to show certain justification of the new non-asymptotic model of thin periodic plates, derived using the tolerance averaging (Woźniak and Wierzbicki, 2000). The model describes the effect of periodicity cell size on overall plate behaviour, on the contrary to known homogenised models. Results obtained from those models will be compared to solution to and from the "exact" discrete model. It is shown that for long-wave propagation problems, results obtained for a special case of a periodic plate strip (weightless but covered by a periodically distributed system of two concentrated masses) within the non-asymptotic model are close results calculated from the known "exact" solutions based on the method used to analyse longitudinal vibrations of one-dimensional diatomic lattice (Brillouin, 1953). Similar conformity, taking place in special cases of short waves, is also presented.