BIFURCATION AND UNIVERSAL UNFOLDING FOR A ROTATING SHAFT WITH UNSYMMETRICAL STIFFNESS

• 来源期刊: 力学学报（英文版）
• 学科: 物理学
• 关键词: shaft with unsymmetrical stiffness, 1/2 subharmonic resonance,bifurcation, universal unfolding
• 年，卷（期）: 2002,（2）
• 页码范围: 181-187
• 页数: 7页
• 分类号: O3
• 语种: 英文

摘要

The 1/2 subharmonic resonance bifurcation and universal unfolding are studied for a rotating shaft with unsymmetrical stiffness. The bifurcation behavior of the response amplitude with respect to the detuning parameter was studied for this class of problems by Xiao et al. Obviously, it is highly important to research the bifurcation behavior of the response amplitude with respect to the unsymmetry of stiffness for this problem. Here, by means of the singularity theory, the bifurcation and universal unfolding of amplitude with respect to the unsymmetrical stiffness parameter are discussed. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, we study four forms of two parameter unfoldings contained in the universal unfolding. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper show rich bifurcation phenomena and provide some guidance for the analysis and design of dynamic buckling experiments of this class of system, especially, for the choice of system parameters.