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- MakaleAçık Erişim2024Scopus SJRQ2Free Vibration and Buckling Analysis of Porous Two-Directional Functionally Graded Beams Using a Higher-Order Finite Element Model
Turan, Muhittin; Adiyaman, Gokhan
A new type of functionally graded material (FGM) with material properties varying in two or three directions is needed to obtain materials with better mechanical properties and high-temperature resistance for use in the military, aerospace, automotive, and engineering structures. Considering the porosity that occurs during the production of these materials, it has become necessary to examine the free vibration and buckling behaviors. Therefore, this study investigated free vibration and buckling analysis of porous two-directional functionally graded (2D FG) beams subject to various boundary conditions. A high-order finite element based on parabolic shear deformation theory (PSDT) is proposed to solve this problem. Three types of porosity distributions were used in the study (FGP-1, FGP-2, and FGP-3). The governing equations are derived from Lagrange’s principle. The material change in the beam volume in both directions is defined by a power-law rule. The dimensionless fundamental frequencies and critical buckling loads are obtained for various boundary conditions, gradation exponents (px, pz), porosity coefficient (e), porosity distribution, and slenderness (L/h). The numerical results obtained with the proposed higher-order finite element are compatible with the literature.
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İncele - MakaleAçık Erişim2024Scopus SJRQ2Mixed series solution for vibration and stability of porous bi-directional functionally graded beams
Turan, Muhittin
A new analytical solution based on the Ritz method is presented in this paper for analyzing the free vibration and buckling behavior of porous bi-directional functionally graded (2D-FG) beams under various boundary conditions. The solution is based on first-order shear deformation theory (FSDT). The selection of solution functions used in Ritz methods distinguishes the methods from each other and determines the accuracy of the analytical solution. To accurately capture the system's behavior and achieve the desired results, these functions have been carefully selected as a combination of polynomial and trigonometric expressions tailored as mixed series functions for each boundary condition. The study considers three types of porosity, namely PFG-1, PFG-2, and PFG-3. The equations of motion are derived using Lagrange's principle, taking into account the power-law variation of the beam material components throughout the volume. The non-dimensional fundamental frequencies and critical buckling loads are calculated for different boundary conditions, gradation exponents in the x and z directions (px, pz), slenderness (L/h), porosity coefficient (e), and porosity types. Initially, the accuracy of the mixed series functions is investigated for non-porous bi-directional functionally graded beams, and the numerical results are compared with existing literature to validate the proposed solution. Subsequently, the paper focuses on analyzing the influence of porosity on the free vibration and buckling behavior of bi-directional functionally graded beams using the developed solution method.
AtıfScopus21WoS22OpenAlex18İncele