Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity

Youcef Tlidji, Rabia Benferhat and Hassaine Daouadji Tahar

Abstract

The effect of distribution shape of porosity using a quasi-3D theory for free vibration analysis of FG microbeams is studied analytically in the present paper. The microbeams are simply-supported and nonhomogeneous, with power function variation of Young's modulus along their thickness. The modified coupled stress theory is utilized to consolidate size dependency of microbeam. Both even and uneven distribution shape of porosity are considered and the effective properties of porous FG microbeams are defined by theoretical formula with an additional term of porosity. The equation of motion is obtained through Hamilton's principle, however, Navier type solution method is used to obtain frequencies. The influences played by many parameters are also investigated.

Key Words

free vibration; FG microbeam; quasi 3D theory; distribution shape of porosity

Address

Youcef Tlidji: Department of Civil Engineering, University of Tiaret, Algeria; Laboratory of Matérials et Hydrology, University of Sidi Bel Abbés, Algeria Rabia Benferhat: Department of Civil Engineering, University of Tiaret, Algeria; Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria Hassaine Daouadji Tahar: Department of Civil Engineering, University of Tiaret, Algeria;Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria

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