Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs)

This paper studies the nonlinear free vibration of a multi-layer polymer nanocomposite beam reinforced by graphene platelets (GPLs) non-uniformly distributed along the thickness direction. Theoretical formulations are based on Hamilton's principle, Timoshenko beam theory, and von Kármán nonlinear strain-displacement relationship. The effective Young's modulus of the GPL/polymer composites is estimated by Halpin-Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies and amplitude of the beam are obtained numerically by employing Ritz method. The influences of the distribution pattern, weight fraction, geometry and size of GPL nanofillers, the total number of layers together with the vibration amplitude and boundary conditions on the nonlinear free vibration behavior are investigated. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements significantly increases the natural frequencies of the beam. Using larger sized GPLs with fewer single graphene layers and placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the linear and nonlinear natural frequencies.