Free vibration analysis of an O-pattern graphene reinforced axial functionally graded polymer matrix nano-composite non-uniform beam

Recently, the demand for nanocomposites in the form of functionally graded materials (FGM) has increased because of their improved weight-to-stiffness ratios, less delamination effects, and ability to have desired qualities at the right location. Additionally, compared to typical composites, static qualities like strength and elasticity are superior. In this research work, a model for an axially graphene-reinforced functionally graded polymer matrix nanocomposite non-uniform beam is prepared, to obtain the dynamic behavior of the beam in form of its Natural Frequencies. Along the length of the beam, the graphene Nano reinforcement is dispersed in an epoxy polymer matrix as “O” pattern using a function. Material modulus at each location of the beam is modelled using Halpin-Tsai micromechanics theory, the mass density and Poisson’s Ratio of the beam are determined using rule of mixture. The geometry non-uniformity of the beam is modelled using an exponential function. Using MATLAB software code, simulation and parametric analysis of the beam are performed for various slenderness ratios and varied boundary conditions. The non-uniform beam result is obtained after the result for a uniform beam is used to validate it. In result it is analyzed that for the particular geometric and reinforcement configuration of the beam, as the non-uniformity in the beam geometry is increases, the fundamental frequency decreases, and the slenderness ratio has also the same effect on its fundamental frequency.