Tentative Research for Chaotic Fatigue
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摘要: 引入非线性动力系统分叉与混沌研究方法,探讨疲劳损伤系统的性质突变.基于物理力学观点,提出了疲劳损伤微观系统模型,定性地分析、讨论了疲劳损伤系统的局部分叉(Hopf分叉)与全局分叉(混沌)机制,给出了系统产生局部分叉时的参数取值范围和产生混沌运动的门槛值.Abstract: The bifurcation and chaos theory of dynamic system is introduced to study the sudden change of fatigue behavior. A micro-model to describe the fatigue damage dynamic system is proposed on the basis of physical mechanics. The local saddle-node, Hopf bifurcations and global bifurcations of this fatigue system are analyzed and discussed. The numerical ranges of the parameters in the fatigue damage dynamic system are presented while Hopf bifurcations occuring by means of the normal form theory and Hopf theorem, and the threshold value of the chaotic fatigue system is given by calculating Melinkov function of the perturbed system according to the unperturbed homoclinic orbits.
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