Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section

The purpose of this work is to investigate the effect of porosity on free vibration and buckling behaviours of non-uniform cross-section functionally graded porous beams. The material properties are considered varied along the thickness direction while the cross-section is non-uniform along the length of the beam. Three different patterns including symmetric, non-symmetric and uniform have been considered as the porosity distribution. The classical beam theory and Hamilton's principle are used to derive the governing equations of the problem and the derived formulations are solved using differential quadrature method. The obtained results were validated via both well-known and analytical reported solutions. The optimal discretization setting was determined via mesh independency study. Detailed parametric analyses are presented to get an insight into the effects of different mechanical parameters including porosity coefficient, slenderness ratio and varying cross-section on the fundamental frequency and critical buckling load. The results show that an increase in material porosity leads to a significant reduction in beam buckling capacity. However, the free vibration behaviour of beams completely depends on their porosity pattern. In addition, the symmetric distribution pattern has the best performance in the terms of beam buckling capacity and fundamental frequency.