Details
Original language | English |
---|---|
Article number | 104247 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 147 |
Early online date | 23 Sept 2022 |
Publication status | Published - Dec 2022 |
Externally published | Yes |
Abstract
In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.
Keywords
- Fractional derivative, Globally-evolving-based generalized density evolution equation (GE-GDEE), Multi-dimensional, Nonlinear, Stochastic dynamic analysis
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Non-Linear Mechanics, Vol. 147, 104247, 12.2022.
Research output: Contribution to journal › Review article › Research › peer review
}
TY - JOUR
T1 - Stochastic response determination of multi-dimensional nonlinear systems endowed with fractional derivative elements by the GE-GDEE
AU - Luo, Yi
AU - Spanos, Pol D.
AU - Chen, Jianbing
N1 - Publisher Copyright: © 2022 Elsevier Ltd
PY - 2022/12
Y1 - 2022/12
N2 - In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.
AB - In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.
KW - Fractional derivative
KW - Globally-evolving-based generalized density evolution equation (GE-GDEE)
KW - Multi-dimensional
KW - Nonlinear
KW - Stochastic dynamic analysis
UR - http://www.scopus.com/inward/record.url?scp=85139826873&partnerID=8YFLogxK
U2 - 10.1016/j.ijnonlinmec.2022.104247
DO - 10.1016/j.ijnonlinmec.2022.104247
M3 - Review article
AN - SCOPUS:85139826873
VL - 147
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
SN - 0020-7462
M1 - 104247
ER -