Polynomial chaos expansion in structural dynamics: accelerating the convergence of the first two statistical moment sequences

Jacquelin, E., Adhikari, S. , Sinou, J. -J. and Friswell, M. I. (2015) Polynomial chaos expansion in structural dynamics: accelerating the convergence of the first two statistical moment sequences. Journal of Sound and Vibration, 356, pp. 144-154. (doi: 10.1016/j.jsv.2015.06.039)

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Abstract

Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken׳s transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken׳s transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken׳s method are enough. This latter result is improved if a generalization of Aitken׳s method (recursive Aitken׳s transformation, Shank׳s transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Adhikari, Professor Sondipon
Authors: Jacquelin, E., Adhikari, S., Sinou, J. -J., and Friswell, M. I.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of Sound and Vibration
Publisher:Elsevier
ISSN:0022-460X
ISSN (Online):1095-8568
Published Online:17 July 2015

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