Ali Dabbagh - MSc Student, School of Mechanical Engineering, College of Engineering, University of Tehran, North Kargar St., ۱۱۱۵۵-۴۵۶۳, Tehran, Iran.
Abbas Rastgoo - Professor, School of Mechanical Engineering, College of Engineering, University of Teh-ran, North Kargar St., ۱۱۱۵۵-۴۵۶۳, Tehran, Iran.
Farzad Ebrahimi - Associate Professor, Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Noroozian Blvd., ۳۴۱۴۸-۹۶۸۱۸, Qazvin, Iran.

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 nanocompo-site 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 so-lution guarantees the efficiency of the presented formulation. One can realize that the fre-quency of the beam can be deeply influenced by tuning the porosity coefficient as well as the weight fraction of the graphene platelets.

Vibration; multi-scale hybrid nanocomposite; refined higher-order beam theory; Rayleigh-Ritz method.