2D tolerance and asymptotic models in elastodynamics of a thin-walled structure with dense system of ribs

The object of analysis is a plane structure reinforced by a system of thin parallel-distributed ribs. It will be assumed that the number of the ribs is very large. The thickness of neighbouring ribs can smoothly change. The aim of contribution is to derive 2D-macroscopic mathematical models describing elastodynamic behaviour of the plate structure in plane-stress state. The consideration will be based on the tolerance averaging technique [9] and [10]. The general results of the contribution will be illustrated by the analysis of the free vibrations of a structure under consideration.