Bifurcation analysis of reduced rotor model based on nonlinear transient POD method. (March 2017)

• Record Type: Journal Article
• Authors: Lu, Kuan; Chen, Yushu; Cao, Qingjie; Hou, Lei; Jin, Yulin
• Is Part Of: International journal of non-linear mechanics. Volume 89(2017)
• Page Start: 83
• Page End: 92
• Publication Date: 2017-03
• Subjects: Singularity -- Bifurcation -- Universal unfolding -- POD method; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2016.11.013
• Languages: English
• ISSNs: 0020-7462

Abstract

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. Highlights: The 6-DOFs rotor model is reduced to 1-DOF one by the transient POD method. The POM energy is applied to confirm the dimension of the reduced model. The co-dimension of bifurcation equation is verified. The transient sets and the corresponding bifurcation behaviors are provided.