Free Vibration Analysis of Porous FGM Plates on Elastic Foundations with Temperature-Dependent Material Properties

Aleksandar Radaković (), Dragan Čukanović, Aleksandar Nešović, Petar Knežević, Milan T. Djordjević and Gordana Bogdanović
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Aleksandar Radaković: Institute for Information Technologies Kragujevac, University of Kragujevac, Jovana Cvijića bb, 34000 Kragujevac, Serbia
Dragan Čukanović: Faculty of Technical Sciences, University of Priština in Kosovska Mitrovica, Knjaza Miloša 7, 38220 Kosovska Mitrovica, Serbia
Aleksandar Nešović: Institute for Information Technologies Kragujevac, University of Kragujevac, Jovana Cvijića bb, 34000 Kragujevac, Serbia
Petar Knežević: Faculty of Technical Sciences, University of Priština in Kosovska Mitrovica, Knjaza Miloša 7, 38220 Kosovska Mitrovica, Serbia
Milan T. Djordjević: Faculty of Technical Sciences, University of Priština in Kosovska Mitrovica, Knjaza Miloša 7, 38220 Kosovska Mitrovica, Serbia
Gordana Bogdanović: Faculty of Engineering, University of Kragujevac, Sestre Janjić 6, 34000 Kragujevac, Serbia

Mathematics, 2025, vol. 13, issue 18, 1-32

Abstract: This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel shape functions are introduced to accurately model transverse shear deformation across the plate thickness without employing shear correction factors. These functions are constructed to satisfy shear stress boundary conditions and capture nonlinear effects induced by material gradation and porosity. A variational formulation is developed to describe the dynamic response of FGM plates in a thermo-mechanical environment, incorporating temperature-dependent material properties and three porosity distributions: uniform, linear, and trigonometric. Numerical solutions are obtained using in-house MATLAB codes, allowing complete control over the formulation and interpretation of the results. The model is validated through detailed comparisons with existing literature, demonstrating high accuracy. The findings reveal that the porosity distribution pattern and gradient intensity significantly influence natural frequencies and mode shapes. The trigonometric porosity distribution exhibits favorable dynamic performance due to preserved stiffness in the surface regions. Additionally, the Kerr-type elastic foundation enables fine tuning of the dynamic response, depending on its specific parameters. The proposed approach provides a reliable and efficient tool for analyzing FGM structures under complex loading conditions and lays the groundwork for future extensions involving nonlinear, time-dependent, and multiphysics analyses.

Keywords: functionally graded materials; porous plates; free vibrations; elastic foundation; thermo-mechanical loading (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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