Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories

This paper presents an analytical solution for vibration and buckling of functionally graded (FG) sandwich beams using various quasi-3D theories, which consider effects of both shear and normal deformation. Sandwich beams with FG skins-homogeneous core and homogeneous skins-FG core are considered. By using the Hamilton's principle, governing equations of motion are derived. An analytical solution is presented, and the obtained results by various quasi-3D theories are compared with each other and with the available solutions in the literature. The effects of normal strain, power-law indexes, skin-core-skin thickness and slenderness ratios on vibration and buckling behaviour of sandwich beams are investigated.