THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Yajie Li

,

Zhiqiang Wu

,

Ying Hao

,

Yongtao Sun

NON-LINEAR STOCHASTIC RESPONSE AND BIFURCATION ANALYSIS OF A MULTISTABLE RAYLEIGH SYSTEM WITH A FRACTIONAL ELEMENT SUBJECTED TO NOISE EXCITATION

ABSTRACT
The study examines the stochastic bifurcation phenomenon of a generalized and multistable Rayleigh system subjected to fractional damping driven by Gaussian white noise. First, the harmonic balance technique is employed to minimize the error in terms of mean square, thereby deriving the approximate equal integer-order system from the original system with fractional-order elements. Subsequently, the stationary probability density function of the system is determined using the stochastic averaging method. Subsequently, employing singularity theory, the critical conditions of system parameters for stochastic P-bifurcation of the original system are identified. Finally, a qualitative analysis of the stationary probability density function curves of the system amplitude is conducted in each region delineated by the boundary set curves. The analytical solutions were found to align with the numerical findings obtained from Monte-Carlo simulation, thereby corroborating the theoretical deductions. The methodology and findings presented in this study have the potential to enhance system response control through the design of fractional-order controllers.
KEYWORDS
fractional damping, stochastic P-bifurcation, boundary set curves, stochastic averaging method, Monte-Carlo simulation
PAPER SUBMITTED: 2023-08-07
PAPER REVISED: 2024-07-08
PAPER ACCEPTED: 2024-07-08
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503861L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [1861 - 1870]
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Non-linear stochastic response and bifurcation analysis of a multistable Rayleigh system with a fractional element subjected to noise excitation

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence