An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory

This paper presents a Ritz-type analytical solution for buckling and free vibration analysis of functionally graded (FG) sandwich beams with various boundary conditions using a quasi-3D beam theory. It accounts a hyperbolic distribution of both axial and transverse displacements. Equations of motion are derived from Lagrange's equations. Two types of FG sandwich beams namely FG-faces ceramic-core (type A) and FG-core homogeneous-faces (type B) are considered. Numerical results are compared with earlier works and investigated effects of the power-law index, thickness ratio of layers, span-to-depth ratio and boundary conditions on the critical buckling loads and natural frequencies.