Journal article 1144 views 263 downloads
Polynomial chaos-based extended Padé expansion in structural dynamics
E. Jacquelin,
O. Dessombz,
J.-J. Sinou,
S. Adhikari,
M. I. Friswell,
Michael Friswell,
Sondipon Adhikari
International Journal for Numerical Methods in Engineering
Swansea University Authors: Michael Friswell, Sondipon Adhikari
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DOI (Published version): 10.1002/nme.5497
Abstract
The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially...
| Published in: | International Journal for Numerical Methods in Engineering |
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| ISSN: | 0029-5981 |
| Published: |
2017
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa32201 |
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| Abstract: |
The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially around the eigenfrequencies of the dynamical system. In the present study, a new approach based on Padé approximants to obtain moments and pdf of the dynamic response in the frequency domain is proposed. A key difference between the direct polynomial chaos representation and the Padé representation is that the Padé approach has polynomials in both numerator and denominator. For frequency response functions, the denominator plays a vital role as it contains the information related to resonance frequencies, which are uncertain. A Galerkin approach in conjunction with polynomial chaos is proposed for the Padé approximation. Another physics-based approach, utilizing polynomial chaos expansions of the random eigenmodes, is proposed and compared with the proposed Padé approach. It is shown that both methods give accurate results even if a very low degree of the polynomial expansion is used. The methods are demonstrated for two degree-of-freedom system with one and two uncertain parameters. |
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| College: |
Faculty of Science and Engineering |