This work focuses on the behavior of non-local shear deformation beam theory for the vibration of functionally graded (FG) nanobeams with porosities that may occur inside the functionally graded materials (FG) during their fabrication, using the nonlocal differential constitutive relations of Eringen. For this purpose, the developed theory accounts for the higher-order variation of transverse shear strain through the depth of the nanobeam. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is verified by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameters, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM beam are represented by numerical examples.
(1) Youcef Gafour — University Djillali Liabes- Faculty of Technology, Sidi-Bel-Abbès, BP 89, Sidi Bel Abbès 22000 Algeria
(2) Abdelillah Benahmed — Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science, University of Sidi Bel Abbes, Algeria
(3) Ahmed Hamidi — Civil Engineering and Hydraulic Department, Faculty Technology, University of Bechar, P.O. Box 417, Street of Independence 08000, Algeria
(4) Mohamed Zidour, Tayeb Bensattalah — University of Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algeria
(5) Mohamed Zidour, Tayeb Bensattalah — Laboratory of Geomatics and Sustainable Development, University of Ibn Khaldoun-Tiaret, Algeria.
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