Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets

This paper studies free vibration and elastic buckling of functionally graded porous nanocomposite beams where the internal pores and graphene platelets (GPLs) are layer-wise distributed in the matrix either uniformly or non-uniformly according to three different patterns. A multilayer beam model is proposed with material parameters varying across layers to achieve graded distributions in both porosity and nanofillers. Mechanical properties of closed-cell cellular solids under Gaussian Random Field scheme are used to determine the variation of Poisson's ratio and the relationship between porosity coefficients and mass density. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. Theoretical formulations are based on Timoshenko beam theory and Ritz method is employed to obtain the dimensionless fundamental natural frequency and critical buckling load of porous nanocomposite beams. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, geometry and size of GPL reinforcements on the free vibration and buckling behaviors of the nanocomposite beam with different metal matrixes and porosity coefficients. The results indicate that the effective stiffness of the porous nanocomposite beam can be best improved when both porosity distribution and GPL dispersion pattern are non-uniform but symmetric.