Fundamental Frequency Analysis of Hybrid Functionally Graded Graphene Platelets/Fiber Reinforced Rectangular Composite Plates

The fundamental frequency of graphene platelets and fiber-reinforced laminate plates was determined, adopting functionally graded (FG) distribution of the reinforcement along the thickness. Uniform and four nonuniform distributions of graphene nanoplatelets were studied. The problem was solved using first-order shear deformation theory within finite element analysis. The effective material properties of the three-phase laminate were determined using micromechanics equations, the Halpin-Tsai model, and the rule of mixtures. Various parameters were tested, including different FG distributions, boundary conditions, fiber orientations, and volume contents for graphene and fiber reinforcements. Results indicate that as the volume content of fibers increases, uniform graphene reinforcement leads to higher frequencies than non-uniform FG graphene distributions. For low fiber content, with values less than 5% (glass) and 7.8% (carbon), a non-uniform FG distribution of graphene (Type X) results in the highest frequencies. In addition, it is shown that for higher graphene content values, the graphene reinforced laminate with zero fiber reinforcement leads to higher fundamental frequencies than the laminate with the hybrid graphene-fiber reinforcement. Those results can contribute to cost-effective design of nanocomposites.