Journal article 698 views
Role of Roots of Orthogonal Polynomials in the Dynamic Response of Stochastic Systems
Journal of Engineering Mechanics, Volume: 142, Issue: 8, Start page: 06016004
Swansea University Author: Sondipon Adhikari
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DOI (Published version): 10.1061/(ASCE)EM.1943-7889.0001102
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...
Published in: | Journal of Engineering Mechanics |
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ISSN: | 0733-9399 1943-7889 |
Published: |
2016
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Online Access: |
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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 |
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College: |
Faculty of Science and Engineering |
Issue: |
8 |
Start Page: |
06016004 |