Journal
ENGINEERING STRUCTURES
Volume 33, Issue 12, Pages 3696-3701Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.engstruct.2011.08.006
Keywords
Functionally graded material; Non-uniform cross-section; Haar wavelets
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Funding
- Estonian Science Foundation [ETF 8830]
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Vibrations of non-uniform and functionally graded (FG) beams with various boundary conditions and varying cross-sections are investigated using the Euler-Bernoulli theory and Haar matrices. It is assumed that the cross-section and material properties vary along the beam in the axial direction. The system of the governing equations is transformed with the aid of a set of simplest wavelets. To validate the present results, the non-homogeneity of the beams is discussed in detail and the calculated frequencies are compared with those of the existing literature. The results show that the Haar wavelet approach is capable of calculating frequencies for the beams with different shapes, rigidity, mass density, small or large translational and rotational boundary coefficients. The advantage of the novel approach consists in its simplicity, accuracy and swiftness. (C) 2011 Elsevier Ltd. All rights reserved.
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