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- 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.
AtıfScopus21WoS22OpenAlex18
İncele - MakaleYalnız künye2022Scopus SJRQ2Bending analysis of two-directional functionally graded beams using trigonometric series functions
Turan, Muhittin
In the present paper, Navier’s method based on the first-order shear deformation theory for bending analysis of two-directional functionally graded beams subjected to various sets of boundary conditions is presented. In Navier's method, different trigonometric series functions are proposed for each boundary condition. The accuracy of these proposed functions was investigated and compared with the literature. It is also presented in a parametric study. The governing equations are derived according to Lagrange’s principle. The variation of the components of the beam material in the volume is defined by a power-law rule. The normalized maximum transverse deflections, the normalized axial and transverse shear stresses are obtained for various boundary conditions, gradation exponents (px, pz) in the x- and z-directions, and the slenderness (L/h). The trigonometric series functions used in this study give results that are quite compatible with the literature. In addition, the parametric study contributes to the literature.
AtıfScopus31WoS31OpenAlex27İncele - MakaleYalnız künye2018Scopus SJRQ1Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element
Kahya, Volkan; Turan, Muhittin
This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling analyses of functionally graded (FG) sandwich beams. The present element has 3 N + 7 degrees-of-freedom for an N-layer beam. Lagrange's equations are employed for derivation of the equations of motion. Two types of FG sandwich beams are considered: (a) Type A with FG faces and homogeneous ceramic core, and (b) Type B with homogeneous ceramic and metal faces and FG core. Natural frequencies and buckling loads are calculated numerically for different boundary conditions, power-law indices, and span-to-height ratios. Accuracy of the present element is demonstrated by comparisons with the results available, and discussions are made on the results given in graphs and tables for the sandwich beams considered.
AtıfScopus89WoS81OpenAlex81İncele