On modelling of periodic plates with inhomogeneity period of an order of the plate thickness

In this contribution, a new averaged non-asymptotic model of Reissner-type plates with a periodic non-homogeneous structure is proposed. This model is obtained by the tolerance averaging technique (TAT) and makes it possible to investigate the effect of the period length parameter on the overall plate behaviuor (the length-scale effect). A new element is applying TAT directly to the equation of 3D-theory of elasticity of solids with periodic structures. Then, taking into account the Hencky-Bolle kinematic assumption, a non-asymptotic 2D-model of plates with periods of an order of the plate thickness is derived. The proposed model is applied to the analysis of some vibration problems.