Tolerance modeling of dynamic behavior of thin plates with dense system of ribs in two directions

The subject of this paper are thin composite rectangular plate. The plates are made of two families of ribs and homogeneous material of a matrix. The main feature of the considered plates is, that a distance between the ribs is comparable to the thickness of the plate. The widths of the ribs can vary slowly in the midplane of the plate. This allows you to get a desirable frequency of natural vibrations of the plate. The formulation of averaged model equations is based on the tolerance averaging approach (Wozniak et al. 2008, 2010). The general results of the contribution are illustrated using the analysis of natural vibrations of the plates under consideration. It will be carried out validation of the obtained mathematical model by comparison of results from obtained model equations with results from finite elements method (Abaqus program).