Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets

This paper investigates the free and forced vibration characteristics of functionally graded multilayer graphene nanoplatelet (GPL)/polymer composite plates within the framework of the first-order shear deformation plate theory. The weight fraction of GPL nanofillers shows a layer-wise variation along the thickness direction with GPLs uniformly dispersed in the polymer matrix in each individual layer. The effective Young's modulus is predicted by the modified Halpin-Tsai model while the effective Poisson's ratio and mass density are determined by the rule of mixture. Governing differential equations of motion are derived and Navier solution based technique is employed to obtain the natural frequencies and dynamic response of simply supported functionally graded GPL/polymer plates under a dynamic loading. A parametric study is conducted, with a particular focus on the effects of GPL distribution pattern, weight fraction, geometry and size as well as the total number of layers on the dynamic characteristics of the plates.