Journal article
Probability Distributions of Natural Frequencies of Uncertain Dynamic Systems
AIAA journal, Vol.47(6), pp.1579-1589
2009
DOI: 10.2514/1.42720
Abstract
This article presents a polynomial dimensional decomposition method for calculating the probability distributions of random eigenvalues commonly encountered in dynamic systems. The method involves a hierarchical decomposition of a multivariate function in terms of variables with increasing dimensions, a broad range of orthonormal polynomial bases consistent with the probability measure for a Fourier-polynomial expansion of component functions, and an innovative dimension-reduction integration for calculating the expansion coefficients. The new decomposition does not require sample points, yet it generates a convergent sequence of lower-variate estimates of the probability distributions of eigensolutions. Numerical results, including frequency distributions of a piezoelectric transducer, indicate that the decomposition method developed provides accurate, convergent, and computationally efficient estimates of the tail probabilistic characteristics of eigenvalues.
Details
- Title: Subtitle
- Probability Distributions of Natural Frequencies of Uncertain Dynamic Systems
- Creators
- Sharif RAHMAN - The University of Iowa, Iowa City, Iowa 52242, United States
- Resource Type
- Journal article
- Publication Details
- AIAA journal, Vol.47(6), pp.1579-1589
- Publisher
- American Institute of Aeronautics and Astronautics; Reston, VA
- DOI
- 10.2514/1.42720
- ISSN
- 0001-1452
- eISSN
- 1533-385X
- Language
- English
- Date published
- 2009
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064580202771
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