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Free vibration characteristics of a functionally graded beam by finite element method
Faculty
Science
Year:
2011
Type of Publication:
Article
Pages:
412-425
Authors:
Eltaher, M. A, Mahmoud, F. F, Alshorbagy, Amal E
DOI:
10.1016/j.apm.2010.07.006
Journal:
APPLIED MATHEMATICAL MODELLING ELSEVIER SCIENCE INC
Volume:
35
Research Area:
Engineering; Mathematics; Mechanics
ISSN
ISI:000282241200032
Keywords :
FG beam, Euler-Bernoulli beam, Free vibration, Finite element
Abstract:
This paper presents the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law. The present model is more effective for replacing the non-uniform geometrical beam with axially or transversally uniform geometrical graded beam. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler-Bernoulli beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Numerical results are presented in both tabular and graphical forms to figure out the effects of different material distribution, slenderness ratios, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of the beam. (C) 2010 Elsevier Inc. All rights reserved.
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