Analysis of the geometric non-uniformity effect on the free vibration characteristic of graphene reinforced axially functionally graded nano-composite beam

In this research work, an axially functionally graded (AFG) Nano-composite beam is modeled to observe the free vibration behavior beamfor non-uniform geometry. The beam is mathematically modeled as an Euler-Bernoulli beam using MATLAB code. Where the graphene Nanoplatelets (GPL) are axially reinforced with A and V type functions. The geometry nonuniformity in the beam is introduced with an exponential function, where the exponent of the equation governs the cross-section of the geometry. The material modulus and other properties at each section along the beam axis are modeled as particulate fiber randomly oriented composite with the help of Halpin Tsai theory and rule of mixture. The finite element method (FEM) is used for the solution and analysis of the model. The model is first validated for uniform geometry results then the non-dimensional fundamental frequency of the AFG beam is obtained for various parameter combinations. The results for various combinations are plotted and it is noted that the free vibration characteristic of the model is strongly dependent on non-uniformity in geometry, end-support constraints,and slenderness ratios (L/h 0 ) combination of the model. This research contributes significantly to the understanding of advanced composite structures and offers potential benefits for the design and optimization of these materials in various engineering applications. The study reveals significant variations in natural frequencies depending on the A type & V type GPL distribution pattern and geometric parameters, which are crucial for the structural integrity and performance of nano composite beams.