Non-Linear Vibrations of Graphene Nanoplatelet-Reinforced Composite Beams using Non-Local Strain Gradient Theory

With the growing integration of nanotechnology into everyday life and the importance of nanoelectromechanical systems, this article examines the nonlinear free vibrations of an Euler-Bernoulli (EB) composite beam reinforced with graphene nanoplatelets (GN), considering the Non-Local Strain Gradient Theory (NLSGT). First, the elastic properties of the nanocomposite reinforced with GN were calculated using the rules of mixtures and the Halpin-Tsai (HT) model. Then, the Equations describing the motion for the EB beam were obtained through the virtual work law, the NLSGT, and the von Kármán (VK) strain field, and were analyzed through the homotopy technique. After solving the Equations, the obtained results were compared with those available in other sources, showing a very good agreement. Finally, the outcomes of varying the graphene plates (GPLs) weight fraction, the GPLs distribution, and the proportional ratio of length to thickness of the beam regarding the non-linear natural frequency (NF) were investigated where one of the important results of this paper is that the highest non-linear NF occurs first in the X-GPLRC distribution, then in the A-GPLRC distribution, and finally in the O-GPLRC distribution.