Response statistics of nonlinear systems with fractional derivative elements subject to nonstationary excitations

In this paper nonlinear systems/structures endowed with fractional derivative elements are analyzed. The excitation considered can be either stationary or nonstationary, and either white or non-white. As an analysis tool, the stochastic averaging technique involving a widely-used approximation of fr...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics Vol. 113; no. 25; pp. 34371 - 34388
Main Authors: Luo, Yi, Spanos, Pol D.
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.12.2025
Subjects:
Approximation
Derivatives
Differential equations
Excitation
Galerkin method
Mathematical analysis
Monte Carlo simulation
Nonlinear systems
Power spectral density
Random vibration
ISSN:0924-090X, 1573-269X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper nonlinear systems/structures endowed with fractional derivative elements are analyzed. The excitation considered can be either stationary or nonstationary, and either white or non-white. As an analysis tool, the stochastic averaging technique involving a widely-used approximation of fractional derivatives is employed. This leads to a one-dimensional integer-order stochastic differential equation governing the evolution of the response amplitude. Further, the derived averaged Fokker–Planck-Kolmogorov equation is tackled by two techniques: the Galerkin technique and numerical path integration. Notably, significant modifications are needed to extend the Galerkin scheme to systems under nonstationary and nonwhite excitation with inseparable power spectral density. Numerical examples including a Van der Pol system, and a Duffing system are considered. The reliability and accuracy of the proposed scheme are demonstrated by juxtaposing the results derived by the proposed approaches with pertinent Monte Carlo simulation results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-025-11648-5