Transient response analysis of nonlinear systems under combined nonstationary and stationary noise excitations: An improved complex fractional moment method

Jing Li, Yongchun Wang and Di Liu

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: This study presents a computational framework for modelling transient responses in nonlinear systems under combined nonstationary and stationary excitations, developing a solution strategy based on the improved complex fractional moment (CFM) method. The investigated single-degree-of-freedom nonlinear stochastic system incorporates nonstationary excitations exhibiting time-evolving statistical characteristics, where temporal variations in power spectral density (PSD) and frequency induce explicit time-dependence in system responses, leading to a nonautonomous Fokker-Planck-Kolmogorov (FPK) equation. The proposed methodology first transforms the original displacement-velocity response formulation into a reduced-order representation of the slow-varying amplitude process through equivalent linearization and stochastic averaging, establishing a nonautonomous amplitude FPK equation. Subsequently, an improved CFM method based on the fifth-order Gauss-Legendre quadrature is introduced to obtain the CFM of the system amplitude and reconstruct the transient probability density function (PDF) through the inverse Mellin transform. Finally, the displacement-velocity response domain of the original system is obtained using the Jacobian mapping, thereby achieving a complete characterization of the system's transient response characteristics. Numerical examples confirm the applicability of the method for various types of nonlinear systems with combined nonstationary and stationary excitations, revealing the coupled effects of structural parameters and excitation characteristics on the statistical behavior of the response. The results demonstrate the method's superior performance in computational accuracy, numerical robustness, and practical engineering applicability, while successfully capturing both the nonstationary characteristics and non-Gaussian statistical properties of the system response.

Keywords: Nonlinear stochastic dynamics; Transient response; Nonstationary excitation; Complex fractional moment method; Stochastic averaging (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925015036
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925015036

DOI: 10.1016/j.chaos.2025.117490

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().