This study presents the free vibration and buckling behavior of two directional (2D) functionally graded beams (FGBs) under arbitrary boundary conditions (BCs) for the first time. A fourknown shear and normal deformation (Quasi3D) theory where the axial and transverse displacements are assumed to be cubic and parabolic variation through the beam depth is employed based on the framework of the Ritz formulation. The equations of motion are derived from Lagrange’s equations. The developed formulation is validated by solving a homogeneous beam problem and considering different aspect ratios and boundary conditions. The obtained numerical results in terms of dimensionless fundamental frequencies and dimensionless first critical buckling loads are compared with the results from previous studies for convergence studies. The material properties of the studied problems are assumed to vary along both longitudinal and thickness directions according to the powerlaw distribution. The axial, bending, shear and normal displacements are expressed in polynomial forms with the auxiliary functions which are necessary to satisfy the boundary conditions. The effects of shear deformation, thickness stretching, material distribution, aspect ratios and boundary conditions on the free vibration frequencies and critical buckling loads of the 2DFGBs are investigated.
Birincil Dil  en 

Konular  Mühendislik ve Temel Bilimler 
Dergi Bölümü  Araştırma Makalesi 
Yazarlar 

Bibtex  @araştırma makalesi { aubtda361095,
journal = {Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik},
issn = {13023160},
eissn = {21460205},
address = {Anadolu Üniversitesi},
year = {2018},
volume = {19},
pages = {375  406},
doi = {10.18038/aubtda.361095},
title = {Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory},
key = {cite},
author = {Karamanlı, Armağan}
} 
APA  Karamanlı, A . (2018). Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik, 19 (2), 375406. DOI: 10.18038/aubtda.361095 
MLA  Karamanlı, A . "Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory". Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik 19 (2018): 375406 <http://dergipark.gov.tr/aubtda/issue/33078/361095> 
Chicago  Karamanlı, A . "Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory". Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik 19 (2018): 375406 
RIS  TY  JOUR T1  Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory AU  Armağan Karamanlı Y1  2018 PY  2018 N1  doi: 10.18038/aubtda.361095 DO  10.18038/aubtda.361095 T2  Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik JF  Journal JO  JOR SP  375 EP  406 VL  19 IS  2 SN  1302316021460205 M3  doi: 10.18038/aubtda.361095 UR  http://dx.doi.org/10.18038/aubtda.361095 Y2  2018 ER  
EndNote  %0 Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory %A Armağan Karamanlı %T Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory %D 2018 %J Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik %P 1302316021460205 %V 19 %N 2 %R doi: 10.18038/aubtda.361095 %U 10.18038/aubtda.361095 
ISNAD  Karamanlı, Armağan . "Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a FourUnknown Shear and Normal Deformable Beam Theory". Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi A  Uygulamalı Bilimler ve Mühendislik 19 / 2 (Haziran 2018): 375406. http://dx.doi.org/10.18038/aubtda.361095 