Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory

Armağan Karamanlı

doi:10.18038/aubtda.361095

EN

Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory

Abstract

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 four-known shear and normal deformation (Quasi-3D) 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 power-law 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 2D-FGBs are investigated.

Keywords

2D Functionally Graded Beam,Ritz Method,Quasi-3D Theory,Vibration

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Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Armağan Karamanlı
0000-0003-3990-6515
Türkiye

Publication Date

June 30, 2018

Submission Date

December 4, 2017

Acceptance Date

March 15, 2018

Published in Issue

Year 2018 Volume: 19 Number: 2

DOI

https://doi.org/10.18038/aubtda.361095

IZ

https://izlik.org/JA62CW27DY

APA

Karamanlı, A. (2018). Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 19(2), 375-406. https://doi.org/10.18038/aubtda.361095

AMA

1.Karamanlı A. Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory. AUJST-A. 2018;19(2):375-406. doi:10.18038/aubtda.361095

Chicago

Karamanlı, Armağan. 2018. “Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19 (2): 375-406. https://doi.org/10.18038/aubtda.361095.

EndNote

Karamanlı A (June 1, 2018) Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19 2 375–406.

IEEE

[1]A. Karamanlı, “Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory”, AUJST-A, vol. 19, no. 2, pp. 375–406, June 2018, doi: 10.18038/aubtda.361095.

ISNAD

Karamanlı, Armağan. “Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 19/2 (June 1, 2018): 375-406. https://doi.org/10.18038/aubtda.361095.

JAMA

1.Karamanlı A. Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory. AUJST-A. 2018;19:375–406.

MLA

Karamanlı, Armağan. “Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 19, no. 2, June 2018, pp. 375-06, doi:10.18038/aubtda.361095.

Vancouver

1.Armağan Karamanlı. Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory. AUJST-A. 2018 Jun. 1;19(2):375-406. doi:10.18038/aubtda.361095