An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters

Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structure...

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Bibliographic Details
Published in:Computers & structures Vol. 87; no. 9; pp. 582 - 590
Main Authors: Chen, Su Huan, Ma, Liang, Meng, Guang Wei, Guo, Rui
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2009
Elsevier
Subjects:
Computational techniques
Efficient method
Epsilon-algorithm
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Natural frequencies
Physics
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Uncertain-but-bounded parameters
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Efficient method
Uncertain-but-bounded parameters
Epsilon-algorithm
Natural frequencies
Natural frequency
Uncertain system
Vibration
Taylor series
Eigenvalue problem
Modeling
Interval arithmetic
Neumann series
ISSN:0045-7949, 1879-2243
Online Access:Get full text
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Summary:Using interval theory and the second-order Taylor series, the eigenvalue problems of structures with multi-parameter can be transformed into those with single parameter. The epsilon-algorithm is used to accelerate the convergence of the Neumann series to obtain the bounds of eigenvalues of structures with single interval parameter, thus increasing the computing accuracy and reducing the computational effort. Finally, the effect of uncertain parameters on natural frequencies is evaluated. Two engineering examples show that the proposed method can give better results than those obtained by the first-order approximation, even if the uncertainties of parameters are fairly large.
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ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2009.02.009