An analysis of vibration and buckling behaviors of nano-composite beams reinforced with agglomerated carbon nanotubes via differential quadrature finite element method

This article aims to investigate the buckling and free vibration behaviors of nanocomposite beams reinforced with functionally graded (FG) agglomerated carbon nanotubes (CNTs) in polymeric beams matrix. In order to estimate the material properties of the FG CNTs reinforced beam, the Eshelby-Mori-Tanaka rule on the basis of equivalent fiber is employed. Moreover, the Lagrange's principle is used to achieve the governing equations under supposition of the refined higher order beam theory without need of any shear correction factor. The differential quadrature finite element method (DQFEM) as a robust and precise numerical procedure is utilized to achieve the natural frequencies and buckling loads with various boundary supports. Then, the assessment of the effects of different factors such as of CNTs agglomeration parameters, different patterns of CNTs distribution, length to thickness quotients, and mixed boundary conditions on the vibrational and buckling responses of agglomerated CNTs reinforced beam are explored. It is concluded that the current numerical solution based DQFEM is efficient and accurate for predicting the mechanical behavior of the nanocomposite structures. Moreover, the stability and vibration responses of the NC beams can be significantly affected by tailoring the agglomeration parameters.