Fuzzy–chaotic modelling for nonlinear vibration systems under parameter uncertainty

Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Yogeesh Nijalingappa
Department of Mathematics, Government First Grade College, Tumkur 572102, India; Research Fellow, INTI International University, INTI International University, Nilai 71800, Malaysia
Soon Eu Hui
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Zetty Pakir Mastan
Faculty of Engineering and Quantity Surveying, INTI International University, Nilai 71800, Malaysia
Choo Wou Onn
International Relations and Collaborations Centre, INTI International University, Nilai 71800, Malaysia
Mohammed El Khider
Department of General Undergraduate Curriculum Requirements, University of Dubai, Dubai P.O. Box 14143, United Arab Emirates

Article ID: 4010

Keywords: nonlinear dynamics, fuzzy set theory, chaotic response, uncertainty propagation, Lyapunov indicators, nonlinear vibration modelling, numerical integration, dynamic testing uncertainty

Abstract

Chaotic responses arise in many nonlinear dynamical systems and can strongly influence practical engineering decisions when measurements, parameters, or operating conditions are imprecise. This paper presents a vibration-oriented fuzzy-parameter uncertainty framework in which uncertain parameters and initial conditions are represented by fuzzy numbers and propagated through a Lorenz-type nonlinear model by means of α-cuts. The novelty claimed here is not the introduction of fuzzy uncertainty itself, but the use of a single workflow that links α-cut propagation, response envelopes, and the interpretation of chaos-sensitive indicators for uncertainty-aware nonlinear vibration analysis. Conventional dynamical descriptors such as phase portraits, stability trends, and bifurcation-related behavior are therefore interpreted as bounded families of trajectories rather than as a single deterministic path. A numerical workflow based on standard time integration is outlined to generate response envelopes that quantify the sensitivity of the dynamics to imprecise inputs. As a basic consistency check, the framework reduces to the classical deterministic model when the fuzzy spreads vanish. The approach provides a mathematically tractable route to uncertainty-aware nonlinear dynamics, with clear relevance to vibration and noise engineering, where nonlinear oscillators, self-excited responses, and test-data uncertainty often coexist. Practical considerations for calibration and validation are also summarized.

Published

2026-07-22

How to Cite

Vasudevan, A., Nijalingappa, Y., Hui, S. E., Mastan, Z. P., Onn, C. W., & Khider, M. E. (2026). Fuzzy–chaotic modelling for nonlinear vibration systems under parameter uncertainty. Sound & Vibration, 60(4). https://doi.org/10.59400/sv4010

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Vol. 60 No. 4 (2026)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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