Investigating the influence of porosity distribution rates on free vibration of FG beams utilizing state space method

Youcef Tlidji, Rabia Benferhat and Hassaine Daouadji Tahar

Abstract

The paper focuses on the free vibration analysis of Functionally Graded (FG) beams under various boundary conditions, accounting for the presence of porosity. The effect of different porosity distribution rates is also investigated by employing a newly modified power law formulation to adjust the material properties in the thickness direction of porous FG beams. The displacement model used in this formulation is based on the higher-order shear deformation theory (HDT). Utilizing Hamilton's principle, the governing equation for the free vibration analysis of FG beams is derived. A comprehensive comparative study is conducted, comparing the results obtained with other existing theories. The findings from this comparative analysis, using the state space approach, provide valuable insights into the vibration behavior of FG beams. Analytical solutions are presented to explore the impact of porosity distribution rates, volume exponent, slenderness ratio, and boundary conditions on vibration characteristics. Numerical examples demonstrate that these key parameters significantly influence the vibration response of FG beams.

Key Words

FG beam; free vibration analysis; HDT; porosity distribution rate; state space approach

Address

Youcef Tlidji: Department of Civil Engineering, University of Tiaret, Algeria; Laboratory Materials and Structures Laboratory, University of Tiaret, 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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