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Role of Roots of Orthogonal Polynomials in the Dynamic Response of Stochastic Systems

E. Jacquelin, S. Adhikari, M. I. Friswell, J. -J. Sinou, Sondipon Adhikari

Journal of Engineering Mechanics, Volume: 142, Issue: 8, Start page: 06016004

Swansea University Author: Sondipon Adhikari

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Abstract

This paper investigates the fundamental nature of the polynomial chaos (PC) response of dynamic systems with uncertain parameters in the frequency domain. The eigenfrequencies of the extended matrix arising from a PC formulation govern the convergence of the dynamic response. It is shown that, in th...

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Published in: Journal of Engineering Mechanics
ISSN: 0733-9399 1943-7889
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa32193
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Abstract: This paper investigates the fundamental nature of the polynomial chaos (PC) response of dynamic systems with uncertain parameters in the frequency domain. The eigenfrequencies of the extended matrix arising from a PC formulation govern the convergence of the dynamic response. It is shown that, in the particular case of uncertainties and with Hermite and Legendre polynomials, the PC eigenfrequencies are related to the roots of the underlying polynomials, which belong to the polynomial chaos set used to derive the polynomial chaos expansion. When Legendre polynomials are used, the PC eigenfrequencies remain in a bounded interval close to the deterministic eigenfrequencies because they are related to the roots of a Legendre polynomial. The higher the PC order, the higher the density of the PC eigenfrequencies close to the bounds of the interval, and this tends to smooth the frequency response quickly. In contrast, when Hermite polynomials are used, the PC eigenfrequencies spread from the deterministic eigenfrequencies (the highest roots of the Hermite polynomials tend to infinity when the order tends to infinity). Consequently, when the PC number increases, the smoothing effect becomes inefficient. - See more at: http://ascelibrary.org/doi/full/10.1061/%28ASCE%29EM.1943-7889.0001102#sthash.Z9eFocUj.dpuf
College: Faculty of Science and Engineering
Issue: 8
Start Page: 06016004