Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: An analytical approach

• Published in: Thin-walled structures Vol. 120; pp. 366 - 377
• Main Authors: Rezaei, A.S., Saidi, A.R., Abrishamdari, M., Mohammadi, M.H. Pour
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2017
• Subjects: Analytical solution; Free vibration; Functionally graded; Plate theory; Porous; Plate theory; Functionally graded; Free vibration; Analytical solution; Porous
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2017.08.003

In this paper, the free vibration analysis of rectangular plates composed of functionally graded materials with porosities is investigated based on a simple first-order shear deformation plate theory. The network of pores in assumed to be empty or filled by low pressure air and the material properties of the plate varies through the thickness. Using Hamilton's principle and utilizing the variational method, the governing equations of motion of FG plates with porosities are derived. Considering two boundary layer functions, the governing equations of the system are rewritten and decoupled. Finally, two decoupled equations are solved analytically for Lévy-type boundary conditions so as to obtain the eigenfrequencies of the plate. The effects of porosity parameter, power law index, thickness-side ratio, aspect ratio, porosity distribution and boundary conditions on natural frequencies of the plate are investigated in detail. •An analytical solution for free vibration analysis of porous FG plates is presented.•The variation of natural frequency with respect to e depends upon the value of n.•Opposite trends for variation of ϖ against, is seen as gets larger.•The variation of natural frequency is more sensitive to n for FGM-I plates.