NONLINEAR FREE VIBRATION OF SHEAR DEFORMABLE FUNCTIONALLY GRADED POROUS BEAMS

This paper presents a nonlinear free vibration analysis of functionally graded (FG) porous beams with non-uniform porosity distributions. Timoshenko beam theory is employed to take into account the effect of transverse shear strains. The elastic moduli and mass density of porous beams vary continuously along the thickness direction based on symmetric and asymmetric porosity distributions. The typical mechanical property of an open-cell metal foam is used to obtain the relationship between coefficients of porosity and mass density. Based on von Karman type nonlinear strain-displacement relationships, the governing equation is derived with Ritz method and solved by a direct iterative algorithm. The effects of varying porosity distributions, porosity coefficients, boundary conditions and slenderness ratios are investigated through a detailed parametric study, indicating an effective way to improve the vibration behaviour of porous beams.