Free Vibration Analysis of Bi-Dimensional Timoshen- ko Por Beam

This study presents a semi-analytical solution for free vibration analysis of bi-dimensional functionally graded (۲D-FG) porous Timoshenko beam. To achieve this goal, Equations of motion for the beam are derived by using Hamilton's principle and then the derived equations are solved in the framework of Galerkin’s well-known semi-analytical method for solution of equations. The material properties of the beam are variable along thickness and length ac-cording 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. De-tailed 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, slenderness ratios (L/h), on the non-dimensional frequency of the beam. The accuracy of the proposed model is validated based on a comparison of the results with the accepted studies.