Details
| Original language | English |
|---|---|
| Article number | 111056 |
| Journal | Reliability Engineering and System Safety |
| Volume | 261 |
| Early online date | 5 Apr 2025 |
| Publication status | E-pub ahead of print - 5 Apr 2025 |
Abstract
This paper focuses on linear systems/structures endowed with fractional derivative subject to nonstationary excitations with non-separable evolutionary power spectral density. Two efficient approximate analytical solutions of the time-varying response statistics are proposed based on the stochastic averaging technique. Specifically, a convenient approximation of fractional derivatives is employed in the stochastic averaging treatment. This leads to an equivalent natural frequency and damping ratio in the obtained governing equation of response amplitude. The equivalent parameters, which also correspond to an equivalent integer-order linear system, can be determined by solving a quite simple one-dimensional algebraic equation. Further, an approximate analytical determination of time-variant response statistics can be made via two approaches. The first follows the standard stochastic averaging treatment, yielding a concise expression and a corresponding eigenfunction expansion. The second solves directly the equivalent integer-order system subject to the same excitation as the original system, yielding Sconsistently accuracy in general. The accuracy of the two approximate analytical solutions is numerically assessed under various system parameters and excitations, by comparing with pertinent Monte Carlo simulation results.
Keywords
- Approximate analytical solution, Equivalent system, Fractional derivative, Nonstationary excitation, Stochastic averaging
ASJC Scopus subject areas
- Engineering(all)
- Safety, Risk, Reliability and Quality
- Engineering(all)
- Industrial and Manufacturing Engineering
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Reliability Engineering and System Safety, Vol. 261, 111056, 09.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-stationary response determination of linear systems/structures with fractional derivative elements
AU - Luo, Yi
AU - Spanos, Pol D.
N1 - Publisher Copyright: © 2025
PY - 2025/4/5
Y1 - 2025/4/5
N2 - This paper focuses on linear systems/structures endowed with fractional derivative subject to nonstationary excitations with non-separable evolutionary power spectral density. Two efficient approximate analytical solutions of the time-varying response statistics are proposed based on the stochastic averaging technique. Specifically, a convenient approximation of fractional derivatives is employed in the stochastic averaging treatment. This leads to an equivalent natural frequency and damping ratio in the obtained governing equation of response amplitude. The equivalent parameters, which also correspond to an equivalent integer-order linear system, can be determined by solving a quite simple one-dimensional algebraic equation. Further, an approximate analytical determination of time-variant response statistics can be made via two approaches. The first follows the standard stochastic averaging treatment, yielding a concise expression and a corresponding eigenfunction expansion. The second solves directly the equivalent integer-order system subject to the same excitation as the original system, yielding Sconsistently accuracy in general. The accuracy of the two approximate analytical solutions is numerically assessed under various system parameters and excitations, by comparing with pertinent Monte Carlo simulation results.
AB - This paper focuses on linear systems/structures endowed with fractional derivative subject to nonstationary excitations with non-separable evolutionary power spectral density. Two efficient approximate analytical solutions of the time-varying response statistics are proposed based on the stochastic averaging technique. Specifically, a convenient approximation of fractional derivatives is employed in the stochastic averaging treatment. This leads to an equivalent natural frequency and damping ratio in the obtained governing equation of response amplitude. The equivalent parameters, which also correspond to an equivalent integer-order linear system, can be determined by solving a quite simple one-dimensional algebraic equation. Further, an approximate analytical determination of time-variant response statistics can be made via two approaches. The first follows the standard stochastic averaging treatment, yielding a concise expression and a corresponding eigenfunction expansion. The second solves directly the equivalent integer-order system subject to the same excitation as the original system, yielding Sconsistently accuracy in general. The accuracy of the two approximate analytical solutions is numerically assessed under various system parameters and excitations, by comparing with pertinent Monte Carlo simulation results.
KW - Approximate analytical solution
KW - Equivalent system
KW - Fractional derivative
KW - Nonstationary excitation
KW - Stochastic averaging
UR - http://www.scopus.com/inward/record.url?scp=105002809361&partnerID=8YFLogxK
U2 - 10.1016/j.ress.2025.111056
DO - 10.1016/j.ress.2025.111056
M3 - Article
AN - SCOPUS:105002809361
VL - 261
JO - Reliability Engineering and System Safety
JF - Reliability Engineering and System Safety
SN - 0951-8320
M1 - 111056
ER -