Finite element frequency analysis of GPL/carbon fiber/epoxy porous nanocomposite beams
1دانشکده مهندسی مکانیک، پردیس دانشکدههای فنی، دانشگاه تهران، تهران، ایران
2گروه مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه بینالمللی امام خمینی (ره)، قزوین، ایران
In this paper, a finite element (FE) based solution will be presented for the vibration problem of porous beams constructed from a multi-scale hybrid nanocomposite consisted of graphene platelet, carbon fiber, and epoxy matrix. The equivalent stiffness of the hybrid nanocomposite was obtained using a micromechanical homogenization procedure based on the well-known Halpin-Tsai method in association with the saturated porous model. Furthermore, the governing equations of the problem will be obtained mixing the concept of infinitesimal strains in a continuous system with the kinematic relations of refined shear deformable beams. The achieved equations will be solved via Rayleigh-Ritz numerical method to enrich the natural frequency of the nanocomposite structure. Comparison of the results achieved from the presented numerical method with those received from the Navier-type analytical solution guarantees the efficiency of the presented formulation. One can realize that the frequency of the beam can be deeply influenced by tuning the porosity coefficient as well as the weight fraction of the graphene platelets.