This paper is the first to explore the coupled dynamics of geometrically and material-wise imperfect axially functionally graded (AFG) graphene nanoplatelets-reinforced viscoelastic third-order shear deformable beams. Four AFG graphene nanoplatelets distribution patterns are considered. Porosity, as the material imperfection, is modelled using a Gaussian Random Field model. Four thickness-wise functionally graded porosity distribution patterns are modelled. Effects of geometric imperfection are included by assigning an initial curvature to the beam. To consider the influences associated with energy dissipation caused by internal friction, the Kelvin-Voigt model for viscosity is used. External dissipative energy is modelled using a transverse damper. The effective material properties of the AFG beams are calculated using a modified Halpin-Tsai micromechanics model, together with a rule of mixture. Coupled axial, transverse, and rotational motion equations are obtained by employing a Hamiltonian approach and third-order shear deformation. The natural frequencies are obtained using a modal decomposition method. A simplified version of the graphene nanoplatelets-reinforced AFG structure is verified by a computer code-based finite element method. This novel study on the effects of geometrical imperfection on the sensitivity of beams towards porosity imperfections demonstrates the significance of scrutinising the effects of one imperfection on another.