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

  • Received : 2020.03.10
  • Accepted : 2020.10.13
  • Published : 2021.01.25
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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.

Keywords

Acknowledgement

This research was supported by the Algerian Ministry of Higher Education and Scientific Research (MESRS) as part of the grant for the PRFU research project No. A01L02UN140120200002 and by the University of Tiaret, in Algeria.

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