Buckling and free flexural vibration of an asymmetric sandwich beam with a functionally graded core

This paper is devoted to an asymmetrical sandwich beam with a functionally graded core with three different variants of boundary conditions. An analytical model of this beam, considering individual nonlinear shear deformation theory, is developed. Based on Hamilton’s principle, two differential equations of motion for this beam are obtained. These equations are solved analytically, and as a consequence, the critical forces and basic natural frequencies for each beam support variant are determined. Detailed calculations are carried out for selected exemplary beam structures, and their results are compared with numerical FEM analysis.