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

Year 2018, Volume: 19 Issue: 2, 375 - 406, 30.06.2018

Armağan Karamanlı

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

Cited By: 8

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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