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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 66
COMPUTATIONAL MECHANICS: TECHNIQUES AND DEVELOPMENTS
Edited by: B.H.V. Topping
Paper VII.1

On the Random Eigenvalue Problem

H.J. Pradlwarter, G.S. Székély and G.I. Schüller

Institute of Engineering Mechanics, Leopold-Franzens University, Innsbruck, Austria

Full Bibliographic Reference for this paper
H.J. Pradlwarter, G.S. Székély, G.I. Schüller, "On the Random Eigenvalue Problem", in B.H.V. Topping, (Editor), "Computational Mechanics: Techniques and Developments", Civil-Comp Press, Edinburgh, UK, pp 173-180, 2000. doi:10.4203/ccp.66.7.1
Abstract
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 quite versatile, however computationally intensive way to analyze such systems is direct Monte Carlo Simulation. In this paper procedures are shown, which allow a significant reduction of computational efforts of the simulation using a subspace iteration scheme with "optimally" selected start-vectors. As the subspace iteration procedure, although quite accurate, requires a factorization of the stiffness matrix, as an alternative, a procedure based on component mode synthesis is suggested.

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