Natural vibrations of prestressed thin functionally graded plates with dense system of ribs in two directions

The subject of this paper are thin functionally graded plates with dense system of ribs. The plates are subjected to the normal forces acting in the midplane of the plates. Considered plates are made of two families of homogeneous materials, respectively for ribs and matrix. The main feature of considered plates is that a distance between the ribs is comparable to the thickness of the plate. The width of the ribs can vary slowly in the midplane of the plate. This allows 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. The effect of initial stress, geometry and materials properties of the functionally graded plate on free vibration frequencies is examined.