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Advances in Nano Research
  Volume 14, Number 4, April 2023 , pages 375-389

The finite element method for dynamics of FG porous truncated conical panels reinforced with graphene platelets based on the 3-D elasticity
Lingqin Xia, Ruiquan Wang, Guang Chen, Kamran Asemi and Abdelouahed Tounsi

    In this study, free vibration analysis of functionally graded (FG) porous truncated conical shell panels reinforced by graphene platelets (GPLs) has been investigated for the first time. Additionally, the effect of three different types of porosity distribution and five different types of GPLs patterns on dynamic response of the shell are also studied. Halpin-Tsai micromechanical model and Voigt's rule are used to determine Young modulus, shear modulus and Poisson's ratio with mass densities of the shell, respectively. The main novelties of present study are: applying 3D elasticity theory and the finite element method in conjunction with Rayleigh-Ritz method to give more accurate results unlike other simplified shell theories, and also presenting a general 3D solution in cylindrical coordinate system that can be used for analyses of different structures such as circular, annular and annular sector plates, cylindrical shells and panels, and conical shells and panels. A convergence study is performed to justify the correctness of the obtained solution and numerical results. The impact of porosity and GPLs patterns, the volume of voids, the weight fraction of graphene nanofillers, semi vertex and span angles of the cone, and various boundary conditions on natural frequencies of the functionally graded panel have been comprehensively studied and discussed. The results show that the most important parameter on dynamic response of FG porous truncated conical panel is the weight fraction of nanofiller and adding 1% weight fraction of nanofiller could increase 57% approximately the amounts of natural frequencies of the shell. Moreover, the porosity distribution has great effect on the value of natural frequency of structure rather than the porosity coefficient.
Key Words
    FEM; graphene platelets; porosity; truncated conical shell panel; vibration; 3-D elasticity
Lingqin Xia: Department of Additive Manufacturing, Zhejiang Institute of Mechanical & Electrical Engineering, hangzhou,310053, China/ Zhejiang Huashuo Technology Co.,Ltd., Ningbo, 315825, China

Ruiquan Wang and Guang Chen: Department of Additive Manufacturing, Zhejiang Institute of Mechanical & Electrical Engineering, hangzhou,310053, China

Kamran Asemi: Department of Mechanical Engineering, Islamic Azad University, North Tehran Branch, Tehran, Iran

Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/ Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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