Free Vibration Analysis of a Porous 2D Functionally Graded Beam Using a High-Order Shear Deformation Theory


Journal of Vibration Engineering and Technologies, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1007/s42417-023-00996-4
  • Journal Name: Journal of Vibration Engineering and Technologies
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Functionally graded, Higher order shear deformation theory, Finite element, Porous material, FINITE-ELEMENT MODEL, SANDWICH BEAMS, BENDING ANALYSIS, TIMOSHENKO, MICROBEAMS, BEHAVIOR
  • Karadeniz Technical University Affiliated: Yes


Purpose: This study considers the free vibration analysis of a porous bi-directional (2D) functionally graded (FG) beam using a higher order shear deformation theory (HSDT). Methods: The material properties are described by an exponential function, and the effect of porosity on these properties is expressed as a product, which is a pioneering application in the analysis of porous 2D FG beams. The approach used in this study allows for the calculation of natural frequencies even for high porosity parameters. The problem considers three porosity distribution functions, one for an even case and two for uneven cases, and Lagrange’s principle is used to derive the governing equations. A two-node finite element with eight degrees of freedom is used to solve the problem accurately and rapidly, even for short beams, without requiring any shear correction factors. Results: The normalized natural frequencies obtained in this study are validated by comparing them with those reported in two studies from the literature after convergence analysis. A parametric study is conducted to investigate the effects of material properties, porosity, and boundary conditions on the normalized natural frequencies and mode shapes. Conclusion: The results suggest that reducing porosity or increasing the rigidity at the center of the beam could increase natural frequencies and reduce vibrations.