Static Buckling and Free Vibration Analysis of Bi-Dimensional FG Metal Ceramic Porous Beam

This study presents an analytical solution for static buckling and free vibration analysis of bi-dimensional functionally graded (2D-FG) metal-ceramic porous beams. To achieve this goal, equations of motion for the beam are derived by using Hamilton's principle and then the derived equations were solved in the framework of Galerkin’s well-known analytical method for solution of equations. The material properties of the beam are variable along with thickness and length according to the power-law function. During the fabrication of functionally graded materials (FGMs), porosities may occur due to technical problems causing micro-voids to appear. Detailed mathematical derivations are presented and numerical investigations are performed, while emphasis is placed on investigating the effect of various parameters such as FG power indexes along both directions of thickness and length, porosity, and slenderness ratios (L/h), on the non-dimensional frequency and static buckling of the beam based on new higher deformation beam theory. The accuracy of the proposed model is validated based on comparisons of the results with the accepted studies. According to the result in both buckling and vibration analysis, the presented modified transverse shear stress along the thickness has shown closer consequences in comparison with TBT.