Optimization of natural frequencies of bidirectional functionally graded beams

We propose a methodology to optimize the natural frequencies of functionally graded structures by tailoring their material distribution. The element-free Galerkin method is used to analyze the two-dimensional steady-state free and forced vibration of functionally graded beams. To optimize the materi...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2006-12, Vol.32 (6), p.473-484
Main Authors: Goupee, Andrew J, Vel, Senthil S
Format: Article
Language:English
Subjects:
Beams (structural)
Forced vibration
Frequencies
Functionally gradient materials
Galerkin method
Genetic algorithms
Interpolation
Optimization
Resonant frequencies
Spatial distribution
Two dimensional analysis
Vibration analysis
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Summary:We propose a methodology to optimize the natural frequencies of functionally graded structures by tailoring their material distribution. The element-free Galerkin method is used to analyze the two-dimensional steady-state free and forced vibration of functionally graded beams. To optimize the material composition, the spatial distribution of volume fractions of the material constituents is defined using piecewise bicubic interpolation of volume fraction values that are specified at a finite number of grid points. Subsequently, we use a real-coded genetic algorithm to optimize the volume fraction distribution for three model problems. In the first problem, we seek material distributions that maximize each of the first three natural frequencies of a functionally graded beam. The goal of the second model problem is to minimize the mass of a functionally graded beam while constraining its natural frequencies to lie outside certain prescribed frequency bands. The last problem aims to minimize the mass of a functionally graded beam by simultaneously optimizing its thickness and material distribution such that the fundamental frequency is greater than a prescribed value.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-006-0022-1