Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets

The thermal vibration of functionally graded (FG) porous nanocomposite beams reinforced by graphene platelets (GPLs) is studied. The beams are exposed to the thermal gradient with a multilayer structure. The temperature varies linearly across the thickness direction. Three different types of dispersion patterns of GPLs as well as porosity distributions are presented. The material properties vary along the thickness direction. By using the mechanical parameters of closed-cell cellular solid, the variation of Poisson's ratio and the relation between the porosity coefficient and the mass density under the Gaussian random field (GRF) model are obtained. By using the Halpin-Tsai micromechanics model, the elastic modulus of the nanocomposite is achieved. The equations of motion based on the Timoshenko beam theory are obtained by using Hamilton's principle. These equations are discretized and solved by using the generalized differential quadrature method (GDQM) to obtain the fundamental frequencies. The effects of the weight fraction, the dispersion model, the geometry, and the size of GPLs, as well as the porosity distribution, the porosity coefficient, the boundary condition, the metal matrix, the slenderness ratio, and the thermal gradient are presented.