Homoclinic bifurcations and chaotic dynamics of non-planar waves in axially moving beam subjected to thermal load

• Published in: Applied Mathematical Modelling Vol. 83; pp. 674 - 682
• Main Authors: Wu, Qiliang, Qi, Guoyuan
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.07.2020; Elsevier BV
• Subjects: Axially moving beam; Bifurcations; Chaos theory; Computer simulation; Geometric analysis; Homoclinic bifurcations; Loads (forces); Nonlinear systems; Nonplanar chaotic waves; The Melnikov approach; Thermal analysis; Geometric analysis; Axially moving beam; The Melnikov approach; Homoclinic bifurcations; Nonplanar chaotic waves
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.03.013

•The nonplanar global dynamics of the axially moving beam is investigated via IDGP method for the first time.•The persistent homoclinic orbit of the perturbed system is explored by the Menikov method and geometric analysis.•The critical criterion of chaos is obtained for the axially moving beam.•The mechanism of the external excitation influencing the complex dynamics of the axially moving beam is uncovered. The homoclinic bifurcations and nonplanar chaotic waves in axially moving beam (AMB) under thermal excitation are investigated. By the multiple scale technique, the equivalent nonlinear system is derived to explore qualitatively the dynamical characteristics of AMB system for the case of primary resonance. Using Melnikov approach as well as geometric analysis, the criterion for homoclinic chaos and complex nonplanar motions for AMB system is discussed. The theoretical predictions are tested by the numerical approach. For the design and application of the AMB, some inspiration and guidance are provided by the results from theory and simulation.