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Computational procedure for a fast calculation of eigenvectors and eigenvalues of structures with random properties

✍ Scribed by G.S Székely; G.I Schuëller

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
961 KB
Volume
191
Category
Article
ISSN
0045-7825

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✦ Synopsis

The inherent uncertainties in geometry, material properties, etc. of engineering structures can be represented by stochastic models, where the parameters are described by probabilistic laws. Results from any analysis based on stochastic models inherit probabilistic information as well, which can be used, e.g., for reliability analysis. Particularly in linear dynamics of structures the calculation and analysis of random eigenvalues and eigenvectors is crucial. A very ¯exible, however computationally intensive way to analyze such systems is direct Monte Carlo simulation (MCS). In this paper procedures are shown, which allow a signi®cant reduction of computational eorts of the simulation using a subspace iteration scheme with ``optimally'' selected start-vectors. The procedures are not restricted to any kind of sampling technique.

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Iterative methods for the calculation of
Iterative methods for the calculation of a few of the lowest eigenvalues and corresponding eigenvectors of the AX = λBX equation with real symmetric matrices of large dimension
✍ Alexander V. Mitin 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 326 KB

New methods for the iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of a generalized eigenvalue problem are proposed. These methods use only multiplication of the A and B matrices on a vector. 0 1994 by John Wiley & Sons, Inc.