Abstract
Two methods are developed for finding probabilistic characteristics of the eigenvalues and eigenvectors of a stochastic matrix. They are based on the mean zero-crossings rate of the characteristic polynomial of this matrix and a perturbation approach. The methods are applied to characterize probabilistically the natural frequencies of an uncertain dynamic system and to find the first two moments of the displacement of a simple oscillator with random damping and stiffness that is subject to white noise.
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References
Bharucha-Reid, A.T. and Sambandham, M. Random Polynomials. Academic Press, Inc., New York, 1986.
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Grigoriu, M. A Solution of Random Eigenvalue Problem by Crossing Theory, Report 91-2, School of Civil and Environmental Engineering, Cornell University, Ithaca, New York.
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© 1991 Computational Mechanics Publications
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Grigoriu, M. (1991). Solution of Random Eigenvalue Problem by Crossing Theory and Perturbation. In: Spanos, P.D., Brebbia, C.A. (eds) Computational Stochastic Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3692-1_8
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DOI: https://doi.org/10.1007/978-94-011-3692-1_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-698-0
Online ISBN: 978-94-011-3692-1
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