Wave propagation of bi-directional porous FG beams using Touratier's higher-order shear deformation beam theory

Slimane Debbaghi, Mouloud Dahmane, Mourad Benadouda, Hassen Ait Atmane, Nourddine Bendenia and Lazreg Hadji

Abstract

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature. The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.

Key Words

bi-directional FG beam; frequencies; porosity types; Touratier's higher-order shear deformation; wave propagation

Address

Slimane Debbaghi: LDDI, Hydrocarbons and Renewable Energies, UAD-Adrar, B. P281, Adrar 01000, Algeria Mouloud Dahmane: Department of Planning and Hydraulic Engineering, Higher National School of Hydraulics, Blida 9000, Algeria Mourad Benadouda: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Hassen Ait Atmane: Civil Engineering Department, University of Hassiba Ben Bouali, Algeria Nourddine Bendenia: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Lazreg Hadji: Laboratory of Geomatics and Sustainable Development, University of Tiaret, Tiaret, 14000, Algeria

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