Abstract
Purpose: This paper examines the nonlinear behaviour of a flexible rotor-bearing exposed to transverse harmonic excitations owing to mass unbalance.
Design/Methodology/Approach: The equations of motion are obtained, and the behaviour of the rotor system around the resonant region is explored. The set-up is made intensely nonlinear by varying the mass unbalance. The incremental variation is done as multiples of the actual value. This model’s nonlinear dynamical systems analysis is based on bifurcations detected from the analysis trajectories and the Lyapunov calculations. Strange fractal attractors are observed and periodic orbits evolve into chaos. The emergence of a seemingly chaotic behaviour from perfectly deterministic origins in the system is interestingly observed. The computational method used in this work is facilitated with the Dynamics 2 software.
Findings: Findings show a strong dependence by the system’s response on changes in some control parameters, such as mass unbalance, and chaos observed as mass unbalance increases to make the system more nonlinear. The study further establishes that when the parametric excitation term is introduced deliberately, the motion of the system becomes periodic which eliminates vibration.
Research Limitation/Implications: The nonlinear behaviour of the flexible rotor-bearing system studied in this work was given an analytical treatment whose solutions were verified numerically. This numerical validation, therefore, gives an assured guide should an experimental investigation be performed on the subject.
Practical Implication: A practicable appreciation of the nonlinear behaviour of a flexible rotor-bearing system that has been subjected to transverse harmonic excitations owing to mass unbalance is missing in the literature. Results from this study will enhance the body of knowledge already existent in the field/industry of rotor-bearing systems for effective manufacturing.
Social Implication: Stakeholders and industry players can reference results from the study for the efficient design of flexible rotor systems. The methods and results from this study will be essential reference material on flexible rotor systems for the academic community.
Originality/Value: The novelty of this study also lies in the fact that for the first time, a complete analytic and numerical understanding have been given to the nonlinear behaviour of a flexible rotor-bearing system exposed to transverse harmonic excitations caused by mass unbalance.
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Atepor, L., Davis, F., Akangah, P.M. (2022). Effect of Parametric Force on the Chaotic Behaviour of Flexible Rotor System Under the Influence of Mass Unbalanced. In: Mojekwu, J.N., Thwala, W., Aigbavboa, C., Bamfo-Agyei, E., Atepor, L., Oppong, R.A. (eds) Sustainable Education and Development – Making Cities and Human Settlements Inclusive, Safe, Resilient, and Sustainable. ARCA 2021. Springer, Cham. https://doi.org/10.1007/978-3-030-90973-4_39
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DOI: https://doi.org/10.1007/978-3-030-90973-4_39
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