Finite element vibration analysis of multi-scale hybrid nanocomposite beams via a refined beam theory

Present manuscript is mainly arranged to take into consider the influences of nanofillers' aggregation, beam's shear deformation and various boundary conditions on the vibration frequency of multi-scale hybrid nanocomposites in the framework of finite element based Rayleigh-Ritz method. The constituent material is made from three phases, namely polymer matrix, macro-scale carbon fibers and nano-scale carbon nanotubes. Homogenization procedure is procured based on Eshelby-Mori-Tanaka approach incorporated with a micro-mechanical scheme to obtain the effective material properties via a two-step method. In addition, a new refined higher-order beam theory is introduced to govern shear stress and strain through the thickness direction. Furthermore, influences of different boundary conditions are included, too. The accuracy of the presented finite element formulations is examined by setting a comparison between the dimensionless frequency of multi-scale hybrid nanocomposite beams via both analytical and finite element solutions. Afterwards, parametric studies are adopted to put emphasize on the influence of various terms on the vibrational behaviors of nanocomposite beams. It is reported that influence of different parameters deeply depends on the magnitude of volume fraction of nanofillers inside the inclusions.