Bifurcation analysis of reduced rotor model based on nonlinear transient POD method |
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| Affiliation: | 1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China;2. Centre for Engineering Dynamics, School Engineering, University of Liverpool, Liverpool L69 3GH, UK;3. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China;4. School of Astronautics, Harbin Institute of Technology, PO Box 137, Harbin 150001, China;1. Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechanical System, Tianjin University of Technology, Tianjin 300384, China;2. National Demonstration Centre for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China;3. Department of Computational Science Graduate School of System Informatics, KOBE University, Kobe 657-8501, Japan |
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| Abstract: | The singularity theory is applied to study the bifurcation behaviors of a reduced rotor model obtained by nonlinear transient POD method in this paper. A six degrees of freedom (DOFs) rotor model with cubically nonlinear stiffness supporting at both ends is established by the Newton's second law. The nonlinear transient POD method is used to reduce a six-DOFs model to a one-DOF one. The reduced model reserves the dynamical characteristics and occupies most POM energy of the original one. The singularity of the reduced system is analyzed, which replaces the original system. The bifurcation equation of the reduced model indicates that it is a high co-dimension bifurcation problem with co-dimension 6, and the universal unfolding (UN) is provided. The transient sets of six unfolding parameters, the bifurcation diagrams between the bifurcation parameter and the state variable are plotted. The results obtained in this paper present a new kind of method to study the UN theory of multi-DOFs rotor system. |
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| Keywords: | Singularity Bifurcation Universal unfolding POD method |
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