基于轮对系统的激变及多稳态动力学研究
张凯旋，乐源*
（西南交通大学 力学与航空航天学院 应用力学与结构安全四川省重点实验室，四川 成都 610031）
摘要：以两自由度铁道机车轮对自治系统为研究对象，得到行进过程中随速度参数变化的横移分岔图进行数值模拟。基于Floquent乘子刻画周期解稳定性，利用Lyapunov指数刻画混沌运动。将滞后环与多稳态现象联系起来，在滞后环内部，系统存在多稳态共存；在滞后环外部，多稳态共存消失，滞后环边界处产生边界激变现象，边界激变是由于不稳定周期轨道与稳定周期轨道相接触导致分岔图产生的跳跃现象。基于吸引域图，对滞后环内外多稳态共存现象的出现和消失进一步解释并求解了边界处的Floquent乘子和混沌区域的最大Lyapunov指数。
关键词：轮对系统；滞后分岔；激变；多稳态；Floquent乘子
中图分类号：O322；U27 文献标志码：A doi：10.3969/j.issn.1006-0316.2023.08.001
文章编号：1006-0316 (2023) 08-0001-07
Crisis and Multistability of Railway Wheelset System
ZHANG Kaixuan，YUE Yuan
( Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China )
Abstract：Taking a two-degree-of-freedom railway wheelset autonomous system as the research object, the transverse bifurcation diagram varying with the speed parameter during the traveling process is obtained for numerical simulation. The stability of periodic solution is described based on Floquet multipliers, and chaotic motion is described by Lyapunov exponents. The hysteresis loop is connected with the phenomenon of multistability. Inside the hysteresis loop, there is the coexistence of multistability in the system; outside the hysteresis loop, the coexistence of multistability disappears, and the boundary crisis phenomenon occurs at the boundary of the hysteresis loop. The boundary crisis is the jumping phenomenon resulted from the bifurcation diagram, which is caused by the contact between the unstable periodic trajectory and the stable periodic trajectory. Based on the basin of attraction, the appearance and disappearance of the multistability coexistence phenomenon inside and outside the hysteresis loop are further explained. The Floquet multipliers at the boundary and the largest Lyapunov exponents of the chaotic region are solved.
Key words：wheelset system；hysteresis bifurcation；crisis；multistability；Floquet multiplier
———————————————
收稿日期：2023-01-04
基金项目：国家自然科学基金重点项目——非光滑动力系统的全局动力学及其应用研究（11732014）；国家自然科学基金面上项目——非光滑动力系统的吸引子分岔和多稳态动力学研究（12072291）；国家自然科学基金面上项目——非光滑动力系统的遍历论和大范围变分方法研究（12172306）
作者简介：张凯旋（1998－），男，河北沧州人，硕士，主要研究方向为非线性动力学，Email：wenhua_6@163.com。*通信作者：乐源（1974－），男，四川攀枝花人，博士，教授，主要研究方向为非线性动力学，Email：yueyuan2011@home.swjtu.edu.cn。
（西南交通大学 力学与航空航天学院 应用力学与结构安全四川省重点实验室，四川 成都 610031）
摘要：以两自由度铁道机车轮对自治系统为研究对象，得到行进过程中随速度参数变化的横移分岔图进行数值模拟。基于Floquent乘子刻画周期解稳定性，利用Lyapunov指数刻画混沌运动。将滞后环与多稳态现象联系起来，在滞后环内部，系统存在多稳态共存；在滞后环外部，多稳态共存消失，滞后环边界处产生边界激变现象，边界激变是由于不稳定周期轨道与稳定周期轨道相接触导致分岔图产生的跳跃现象。基于吸引域图，对滞后环内外多稳态共存现象的出现和消失进一步解释并求解了边界处的Floquent乘子和混沌区域的最大Lyapunov指数。
关键词：轮对系统；滞后分岔；激变；多稳态；Floquent乘子
中图分类号：O322；U27 文献标志码：A doi：10.3969/j.issn.1006-0316.2023.08.001
文章编号：1006-0316 (2023) 08-0001-07
Crisis and Multistability of Railway Wheelset System
ZHANG Kaixuan，YUE Yuan
( Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China )
Abstract：Taking a two-degree-of-freedom railway wheelset autonomous system as the research object, the transverse bifurcation diagram varying with the speed parameter during the traveling process is obtained for numerical simulation. The stability of periodic solution is described based on Floquet multipliers, and chaotic motion is described by Lyapunov exponents. The hysteresis loop is connected with the phenomenon of multistability. Inside the hysteresis loop, there is the coexistence of multistability in the system; outside the hysteresis loop, the coexistence of multistability disappears, and the boundary crisis phenomenon occurs at the boundary of the hysteresis loop. The boundary crisis is the jumping phenomenon resulted from the bifurcation diagram, which is caused by the contact between the unstable periodic trajectory and the stable periodic trajectory. Based on the basin of attraction, the appearance and disappearance of the multistability coexistence phenomenon inside and outside the hysteresis loop are further explained. The Floquet multipliers at the boundary and the largest Lyapunov exponents of the chaotic region are solved.
Key words：wheelset system；hysteresis bifurcation；crisis；multistability；Floquet multiplier
———————————————
收稿日期：2023-01-04
基金项目：国家自然科学基金重点项目——非光滑动力系统的全局动力学及其应用研究（11732014）；国家自然科学基金面上项目——非光滑动力系统的吸引子分岔和多稳态动力学研究（12072291）；国家自然科学基金面上项目——非光滑动力系统的遍历论和大范围变分方法研究（12172306）
作者简介：张凯旋（1998－），男，河北沧州人，硕士，主要研究方向为非线性动力学，Email：wenhua_6@163.com。*通信作者：乐源（1974－），男，四川攀枝花人，博士，教授，主要研究方向为非线性动力学，Email：yueyuan2011@home.swjtu.edu.cn。
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