Free vibration and buckling analysis of functionally graded sandwich beams by Navier's method

Abstract

In this study, free vibration and buckling analyses of functionally graded (FGM) sandwich beams is investigated by Navier's method. Displacement field is defined according to the first order shear deformation theory, and the equations of motion are derived by the Lagrange's principle. Volumetric ceramic ratio is defined by a power-law rule. In the analytical solution, different trigonometric series functions are used for each end conditions considered. Two cases of functionally graded sandwich beams are considered: a) Homogeneous ceramic core and FGM faces (Type A), and b) FGM core and homogeneous faces (Type B). Natural frequencies and buckling loads are obtained for different boundary conditions, power-law indices and slenderness. Numerical results are compared with the available literature, and a good agreement are obtained between the results.