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Structural Engineering and Mechanics
  Volume 64, Number 3, November10 2017, pages 381-390

Nonlinear free vibration of FG-CNT reinforced composite plates
Mostafa Mirzaei and Yaser Kiani

    Present paper deals with the large amplitude flexural vibration of carbon nanotube reinforced composite (CNTRC) plates. Distribution of CNTs as reinforcements may be uniform or functionally graded (FG). The equivalent material properties of the composite media are obtained according to a refined rule of mixtures which contains efficiency parameters. To account for the large deformations, von Kármán type of geometrical nonlinearity is included into the formulation. The matrix representation of the governing equations is obtained according to the Ritz method where the basic shape functions are written in terms of the Chebyshev polynomials. Time dependency of the problem is eliminated by means of the Galerkin method and the resulting nonlinear eigenvalue problem is solved employing a direct displacement control approach. Results are obtained for completely clamped and completely simply supported plates. Results are first validated for the especial cases of FG-CNTRC and cross-ply laminated plates. Afterwards, parametric studies are given for FG-CNTRC plates with different boundary conditions. It is shown that, nonlinear frequencies are highly dependent to the volume fraction and dispersion profiles of CNTs. Furthermore, mode redistribution is observed in both simply supported and clamped FG-CNTRC plates.
Key Words
    functionally graded; nonlinear free vibration; CNTRC; rectangular plate; Ritz method
Mostafa Mirzaei : Department of Mechanical Engineering, Faculty of Engineering, University of Qom, Qom, Iran
Yaser Kiani : Faculty of Engineering, Shahrekord University, Shahrekord, Iran

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