Study on stability and free vibration behavior of porous FGM beams

Riadh Bennai, Redhwane Ait Atmane, Fabrice Bernard, Mokhtar Nebab, Noureddine Mahmoudi, Hassen Ait Atmane, Salem Mohammed Aldosariand Abdelouahed Tounsi

Abstract

In this paper, buckling and free vibration of imperfect, functionally graded beams, including porosities, are investigated, using a higher order shear strain theory. Due to defects during the manufacturing process, micro porosities may appear in the material, hence the appearance of this imperfection in the structure. The material properties of the beams are assumed to vary regularly, with power and sigmoid law, in the direction of thickness. A novel porosity distribution affecting the functionally graded volume fraction is presented. For the compact formulation used for cementite-based materials and already used in P-FGM, we have adapted it for the distribution of S-FGM. The equations of motion in the FG beam are derived using Hamilton's principle. The boundary conditions for beam FG are assumed to be simply supported. Navier's solution is used to obtain the closed form solutions of the FG beam. The numerical results of this work are compared with those of other published research to verify accuracy and reliability. The comparisons of different shear shape functions, the influence of porosity, thickness and inhomogeneity parameters on buckling and free vibration of the FG beam are all discussed. It is established that the present work is more precise than certain theories developed previously.

Key Words

buckling; free vibration; functionally graded beams; high order shear deformation theory; porosity coefficient; porosity

Address

Riadh Bennai:1)Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Algeria 2)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria Redhwane Ait Atmane:Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Fabrice Bernard:LGCGM, IINSA RENNES France Mokhtar Nebab:1)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria 2)Department of Civil Engineering, Faculty of Sciences, University of M'Hamed BOUGARA Boumerdes, Algeria Noureddine Mahmoudi:Department of mechanical engineering, university of Saida, Algeria Hassen Ait Atmane:1)Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Algeria 2)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria Salem Mohammed Aldosari:1)Enhanced Composite and Structures Centre, School of Aerospace, Transport, and Manufacturing, Cranfield University, Cranfield MK43 0AL, UK 2)National Center for Aviation Technology, King Abdulaziz City for Science and Technology (KACST), Riyadh 11442, Saudi Arabia Abdelouahed Tounsi:1)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2)YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea

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