期刊
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
卷 89, 期 -, 页码 83-92出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijnonlinmec.2016.11.013
关键词
Singularity; Bifurcation; Universal unfolding; POD method
类别
资金
- National Basic Research Program (973 Program) of China [2015CB057400]
- National Natural Science Foundation of China [11602070]
- China Postdoctoral Science Foundation [2016M590277]
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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