Free vibration analysis of functionally graded graphene nanoplatelet-reinforced composite beams using mixed finite element method

The objective of this thesis is to investigate the free vibration behavior of transversely functionally graded straight beams reinforced with graphene nanoplatelets (GPLs). The matrix material is a polymer, forming a composite with GPLs, where the volume fraction of the reinforcement varies along the beam's thickness. The effective elasticity modulus is determined using the Halpin-Tsai micromechanical model, which accounts for the geometry and distribution of GNL reinforcements within the matrix material. A warping-included mixed finite element formulation has been developed for a two-node element based on Timoshenko beam theory. This formulation includes twelve degrees of freedom at each node, comprising three displacements, three section rotations, three forces, two bending moments, and one torsional moment. A comprehensive parametric study explores the effects of material distribution types, GPL weight fraction, and boundary conditions on the free vibration behavior in detail.