一类两自由度非光滑塑性碰撞系统的擦边分岔研究  

Study on Edge Bifurcation of Two-degree-of-freedom Plastic Impact System

作　　者：郝文鑫 张红兵[1] 李万祥[1] 李雄兵 魏心雨 HAO Wenxin;ZHANG Hongbing;LI Wanxiang;LI Xiongbing;WEI Xinyu(Lanzhou Jiaotong University,Lanzhou 730070,China;Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学,甘肃兰州730070 [2]西北师范大学,甘肃兰州730070

出　　处：《机械制造与自动化》2023年第5期171-175,共5页Machine Building & Automation

摘　　要：研究一类两自由度非光滑塑性碰撞系统动力学模型,推导并利用模态叠加法求解系统,建立Poincaré映射,利用半解析法分析模型运动的整个过程。研究系统的周期和非周期运动;利用分岔图、相图轨迹、Poincaré截面图研究不同参数下以不同路径通往混沌状态下的擦边行为;分析系统的hopf分岔、倍化分岔以及周期突变的“擦边”导致系统的中断以及不连续现象,同时擦边运动导致系统Poincaré映射产生奇异性,最后得出q=p/n周期运动的“擦边”行为通常导致系统的周期运动数不变,碰撞次数增加或减少一次。The dynamic model of a two-degree-of-freedom non-smooth plastic collision system was studied,and its system was solved by means of the mode superposition method.The Poincare mapping was established,and the whole process of the model motion was analyzed by the semi-analytical method.The periodic and aperiodic motions of the system were studied.Bifurcation diagram,phase diagram trajectory and Poincare section diagram were applied to explore the edging behavior in different paths to chaotic state under different parameters.The hopf bifurcation,doubling bifurcation and the interruption of the system and discontinuous phenomenon caused by periodcal tumble mutation of"cluster"were analyzed.And meanwhile fringe movement leads Poincare mapping system to singularity.The final conclusion is drawn that q=p/n periodic motion"fired"behavior often results in the constancy of periodic motion number with one time increase or decrease in collision frequency.

关 键 词：非光滑系统 塑性碰撞 擦边分岔 混沌 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]