多自由度碰撞振动系统的奇异性与混沌控制研究

项目名称： 多自由度碰撞振动系统的奇异性与混沌控制研究

项目编号： No.11272268

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 乐源

作者单位： 西南交通大学

项目金额： 86万元

中文摘要： 多自由度碰撞振动系统属于高维强非线性动力系统。考虑从非碰撞区域向碰撞区域的转换和过渡（奇异性），碰撞振动系统又是一类非光滑动力系统。碰撞振动系统的奇异性将会导致诸多非常规分岔形式，对其动力学行为产生深刻影响。碰撞振动系统的奇异性包括擦边碰撞导致的奇异性以及粘滞运动导致的奇异性。根据不连续映射方法、普适开折方法以及其它非光滑系统动力学研究方法，通过理论分析、数值模拟以及实验验证等手段全面深入研究多自由度碰撞振动系统的两种奇异性。OGY方法只需要对参数作微小的扰动，就能把系统的混沌运动控制到原系统的不稳定周期轨道，对于动力系统的混沌控制具有重要意义。本项目根据OGY方法及其改进方法研究多自由度碰撞振动系统的混沌控制。考虑轮轨互相作用，可把铁道车辆系统简化为复杂的多自由度碰撞振动系统。把上述研究成果运用于高速铁道车辆系统，深入探讨奇异性对铁道车辆系统动力学行为的重要影响，并有效控制其混沌性态.

中文关键词： 碰撞振动系统；奇异性；混沌控制；转向架；

英文摘要： Multidegree of freedom vibro-impact systems are high dimensional and strong nonlinear. Considering the transition from nonimpacting to impacting (singularity), vibro-impact systems are also nonsmooth dynamic systems. The singularity of the vibro-impact system will induce various unconventional bifurcations, and has qualitative influences on the dynamics of the vibro-impact system. The singularities of the vibro-impact system include the singularity induced by the grazing impact and that induced by the stick motion. According to the discontiniuty mapping approach、universal unfold method and other research approach of nonsmooth dynamic system, based on theory analysis, computer simulations and experimental approach, the singularities of the multidegree of freedom vibro-impact system will be investigated in the round. The OGY method stabilizes the unstable periodic orbits with small parameter perturbation, which has important significance for chaos control. This project will research into the chaos control of the multidegree of freedom vibro-impact system based on the OGY method and its improving approach. Considering the wheel-rail interaction, the railway vehicles can be modeled by a complex multidegree of freedom vibro-impact system. The above research findings will be applied to the the dynamics of the railway

英文关键词： Vibro-impact system；Singularity；Chaos control；Bogie；