non-linear vibrations of graphene nanoplatelet-reinforced composite beams using non-local strain gradient theory

With the growing integration of nanotechnology into everyday life andthe importance of nanoelectromechanical systems, this article examines the nonlinearfree vibrations of an euler-bernoulli (eb) composite beam reinforced withgraphene nanoplatelets (gn), considering the non-local strain gradient theory(nlsgt). first, the elastic properties of the nanocomposite reinforced with gnwere 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 thevirtual work law, the nlsgt, and the von kármán (vk) strain field, and wereanalyzed through the homotopy technique. after solving the equations, the obtainedresults were compared with those available in other sources, showing a very goodagreement. finally, the outcomes of varying the graphene plates (gpls) weightfraction, the gpls distribution, and the proportional ratio of length to thickness ofthe beam regarding the non-linear natural frequency (nf) were investigated whereone of the important results of this paper is that the highest non-linear nf occursfirst in the x-gplrc distribution, then in the a-gplrc distribution, and finally inthe o-gplrc distribution.