Buckling and free vibrations of rectangular plates with symmetrically varying mechanical properties - Analytical and FEM studies

Abstract

Abstract The subject of the paper is a rectangular plate with symmetrically varying mechanical properties in the thickness direction. The nonlinear hypothesis of deformation of the straight line normal to the plate neutral surface is assumed. The field of displacements of the plate is formulated assuming this hypothesis. Based on the Hamilton’s principle three differential equations of motion are obtained. The system of equations is analytically solved. The critical loads and fundamental natural frequencies for exemplary plates are derived. Moreover, the FEM model of the plate in the ABAQUS system is developed, and analogical calculations for exemplary plates are carried out. The calculation results of these two methods are compared.