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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 93
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Paper 285

A Theoretical Investigation on the Free Vibration of Functionally Graded Beams

N. Wattanasakulpong1, B.G. Prusty1, D.W. Kelly1 and M. Hoffman2

1School of Mechanical and Manufacturing Engineering, 2School of Material Science and Engineering,
University of New South Wales, Sydney, Australia

Full Bibliographic Reference for this paper
N. Wattanasakulpong, B.G. Prusty, D.W. Kelly, M. Hoffman, "A Theoretical Investigation on the Free Vibration of Functionally Graded Beams", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 285, 2010. doi:10.4203/ccp.93.285
Keywords: functionally graded beams, third order shear deformation theory, Ritz method.

Functionally graded materials (FGMs) have many advantages when used in engineering structural components. The methods of FGM fabrication and general information about FGMs including microstructure analysis of the graded materials was presented by Miyamoto et al. [1]. Unlike fiber-matrix laminated composites, FGMs do not have problems of de-bonding and delaminating that result from large inter-laminar stresses. A power law distribution is used to describe the variation of volume fraction of the material composition. With the power law index being not one or zero, the nonlinear compositional profile of material properties can be observed across the functionally graded (FG) beam thickness. Hence, it is expected that an improved third order shear deformation (TSDT) based on the more rigorous kinematics of displacements developed by Shi [2], which presents a cubic variation of displacement through the thickness, will be more suitable to predict free vibration results than the first order shear deformation (FSDT) and classical beam theory (CBT).

The theoretical formulation in the form of an eigenvalue problem derived from the improved theory is solved using the Ritz method with the polynomial displacements and rotation [3,4,5,6]. The numerical frequency results are compared with the published results based on the FSDT with a good agreement [7]. The new frequency results in relation to simply-clamped, simply-free and free-free boundary conditions are also presented in this paper. The significant effects of many aspects such as boundary conditions, material composition and slenderness ratio that cause the change in natural frequencies of FG beams are taken into consideration.

Y. Miyamoto, W.A. Kaysser, B.H. Rabin, A. Kawasaki, R.G. Ford, "Functionally graded materials: design, processing and application", Kluwer Academic Publishers, London, 1999.
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