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Approximate Analysis of Response Variability of Uncertain Linear Systems

Papadimitriou, C. and Katafygiotis, L. S. and Beck, J. L. (1995) Approximate Analysis of Response Variability of Uncertain Linear Systems. Probabilistic Engineering Mechanics, 10 (4). pp. 251-264. ISSN 0266-8920 .

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A probabilistic methodology is presented for obtaining the variability and statistics of the dynamic response of multi-degree-of-freedom linear structures with uncertain properties. Complex mode analysis is employed and the variability of each contributing mode is analyzed separately. Low-order polynomial approximations are first used to express modal frequencies, damping ratios and participation factors with respect to the uncertain structural parameters. Each modal response is then expanded in a series of orthogonal polynomials in these parameters. Using the weighted residual method, a system of linear ordinary differential equations for the coefficients of each series expansion is derived. A procedure is then presented to calculate the variability and statistics of the uncertain response. The technique is extended to the stochastic excitation case for obtaining the variability of the response moments due to the variability of the system parameters. The methodology can treat a variety of probability distributions assumed for the structural parameters. Compared to existing analytical techniques, the proposed method drastically reduces the computational effort and computer storage required to solve for the response variability and statistics. The performance and accuracy of the method are illustrated by examples.

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Additional Information:Copyright © 1995 Elsevier Science Limited. The partial support of this work from the grant BCS- 9309149 from the National Science Foundation is gratefully acknowledged by the first author.
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Record Number:CaltechAUTHORS:20120829-153939460
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33693
Deposited By: Carmen Nemer-Sirois
Deposited On:30 Aug 2012 17:41
Last Modified:30 Aug 2012 17:41

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