基于微分包含干摩擦碰撞系统的分岔分析
发布时间：2019-03-25 10:15
【摘要】：干摩擦碰撞是一类重要的非光滑动力系统,广泛存在于工程设计和机械制造中。由于干摩擦碰撞的存在,增加了系统的不确定性和研究的复杂性,使得传统的动力系统研究方法不能直接应用到干摩擦碰撞系统中。微分包含理论是研究非光滑动力系统的重要工具,且在动力系统的控制、多胞系统、脉冲系统中均有所应用。本文基于微分包含理论系统分析了皮带轮上干摩擦碰撞系统的动力学特性,探究了不同参数引起的分岔现象。结合微分包含理论分析各种运动的存在条件,借助C语言和MATLAB进行仿真。本文共有六章,主要如下:第一章:本章对干摩擦碰撞系统的研究背景意义、主要的研究方法、存在的问题及微分包含理论在干摩擦碰撞系统中的应用进行了简述,并概述了本文的主要内容。第二章:本章给出了集值映射、微分包含理论等相关的基本定义、定理,主要介绍非光滑动力系统微分包含解的存在性和稳定性;建立了非光滑系统的运动模型,推导并计算出系统中滑膜解存在的必要条件、滑膜指数及跳跃运动的跳跃矩阵;最后介绍了Poincaré映射及Poincaré截面图与周期运动系统稳定性的关系。第三章:分析了两种单自由度干摩擦系统的动力学特征,使用凸包的知识将系统方程微分包含标准化,探究了系统平衡点的稳定性;计算出系统滑膜跳跃运动的产生条件及系统轨线滑膜、跳跃运动的范围,并得出无外激励系统不可能发生跳跃运动的结论;数值模拟考虑振幅对滑膜跳跃运动的影响,仿真出滑膜跳跃分岔图,发现了随着振幅的增大,系统有向跳跃运动移动的趋势;考虑了外激励振幅、频率对系统稳定性的影响。第四章:分析了双自由度碰撞系统,建立了碰撞的微分方程模型;推导了质块碰撞过程的转移矩阵、横截指数,并判断出碰撞系统中轨线不可能越过碰撞面;数值模拟了系统在不同参数变化下的分岔图,并发现了参数振幅、频率对系统的稳定性影响较大。第五章:建立了双自由度干摩擦碰撞系统的微分方程模型,使用凸包和集值映射将方程转化为微分包含标准型;分析了非光滑可能引起系统动力学特征的变化,并推导出干摩擦碰撞过程中的转移矩阵和跳跃矩阵;数值仿真出系统的单参分岔图和双参分岔图,探究了不同参数对干摩擦碰撞系统的影响。第六章:总结了本文的主要内容并给出了干摩擦碰撞系统中参数匹配问题的进一步研究方向。
[Abstract]:Dry friction collision is an important non-smooth dynamic system, which widely exists in engineering design and mechanical manufacturing. Due to the existence of dry friction collision, the uncertainty of the system and the complexity of the research are increased, so the traditional research method of dynamic system can not be directly applied to the dry friction collision system. Differential inclusion theory is an important tool for the study of nonsmooth dynamical systems, and it has been applied in the control of dynamical systems, multi-cell systems and impulsive systems. In this paper, the dynamic characteristics of dry friction collision system on pulley are systematically analyzed based on differential inclusion theory, and the bifurcation caused by different parameters is discussed. Based on the differential inclusion theory, the existing conditions of various motions are analyzed, and the simulation is carried out with the help of C language and MATLAB. There are six chapters in this paper, which are as follows: chapter one: the background significance, the main research methods, the existing problems and the application of differential inclusion theory in dry friction collision system are briefly described in this chapter, the research background, the main research methods, the existing problems and the application of differential inclusion theory in dry friction collision system are briefly described. The main contents of this paper are also summarized. In chapter 2, the basic definitions and theorems of set-valued mapping, differential inclusion theory and so on are given, which mainly introduce the existence and stability of differential inclusion solutions for nonsmooth dynamical systems. In this paper, the motion model of the nonsmooth system is established, and the necessary conditions for the existence of the sliding film solution, the sliding film index and the jump matrix of the jumping motion are derived and calculated. Finally, the relations between the Poincar茅 map and the Poincar茅 section diagram and the stability of the periodic motion system are introduced. In chapter 3, the dynamic characteristics of two kinds of single degree of freedom dry friction systems are analyzed, and the differential inclusion of the system equations is standardized by using convex hull knowledge, and the stability of the equilibrium point of the system is explored. The generating conditions of the jump motion of the slide film and the range of the jump motion of the system are calculated, and the conclusion is drawn that the jump motion cannot occur in the system without external excitation. The numerical simulation takes into account the influence of amplitude on the slip jump motion, and simulates the slip bifurcation diagram. It is found that with the increase of the amplitude, the system moves toward the jump motion, and the influence of the external excitation amplitude and frequency on the stability of the system is considered. In chapter 4, the two-degree-of-freedom collision system is analyzed, the differential equation model of collision is established, the transfer matrix and cross-section index of mass collision process are deduced, and the trajectory of collision system is determined that it is impossible to cross the collision surface. The bifurcation diagrams of the system under different parameters are numerically simulated, and it is found that the amplitude and frequency of the parameters have a great influence on the stability of the system. In chapter 5, the differential equation model of two-degree-of-freedom dry friction collision system is established, and the equation is transformed into differential inclusion standard form by convex hull and set-valued mapping. The variation of the dynamic characteristics of the system caused by non-smoothing is analyzed, and the transfer matrix and jump matrix in dry friction collision are derived. The single-parameter bifurcation diagram and the two-parameter bifurcation diagram of the system are numerically simulated, and the effects of different parameters on the dry friction collision system are investigated. Chapter 6: the main contents of this paper are summarized and the further research direction of parameter matching in dry friction collision system is given.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19
本文编号：2446880
[Abstract]:Dry friction collision is an important non-smooth dynamic system, which widely exists in engineering design and mechanical manufacturing. Due to the existence of dry friction collision, the uncertainty of the system and the complexity of the research are increased, so the traditional research method of dynamic system can not be directly applied to the dry friction collision system. Differential inclusion theory is an important tool for the study of nonsmooth dynamical systems, and it has been applied in the control of dynamical systems, multi-cell systems and impulsive systems. In this paper, the dynamic characteristics of dry friction collision system on pulley are systematically analyzed based on differential inclusion theory, and the bifurcation caused by different parameters is discussed. Based on the differential inclusion theory, the existing conditions of various motions are analyzed, and the simulation is carried out with the help of C language and MATLAB. There are six chapters in this paper, which are as follows: chapter one: the background significance, the main research methods, the existing problems and the application of differential inclusion theory in dry friction collision system are briefly described in this chapter, the research background, the main research methods, the existing problems and the application of differential inclusion theory in dry friction collision system are briefly described. The main contents of this paper are also summarized. In chapter 2, the basic definitions and theorems of set-valued mapping, differential inclusion theory and so on are given, which mainly introduce the existence and stability of differential inclusion solutions for nonsmooth dynamical systems. In this paper, the motion model of the nonsmooth system is established, and the necessary conditions for the existence of the sliding film solution, the sliding film index and the jump matrix of the jumping motion are derived and calculated. Finally, the relations between the Poincar茅 map and the Poincar茅 section diagram and the stability of the periodic motion system are introduced. In chapter 3, the dynamic characteristics of two kinds of single degree of freedom dry friction systems are analyzed, and the differential inclusion of the system equations is standardized by using convex hull knowledge, and the stability of the equilibrium point of the system is explored. The generating conditions of the jump motion of the slide film and the range of the jump motion of the system are calculated, and the conclusion is drawn that the jump motion cannot occur in the system without external excitation. The numerical simulation takes into account the influence of amplitude on the slip jump motion, and simulates the slip bifurcation diagram. It is found that with the increase of the amplitude, the system moves toward the jump motion, and the influence of the external excitation amplitude and frequency on the stability of the system is considered. In chapter 4, the two-degree-of-freedom collision system is analyzed, the differential equation model of collision is established, the transfer matrix and cross-section index of mass collision process are deduced, and the trajectory of collision system is determined that it is impossible to cross the collision surface. The bifurcation diagrams of the system under different parameters are numerically simulated, and it is found that the amplitude and frequency of the parameters have a great influence on the stability of the system. In chapter 5, the differential equation model of two-degree-of-freedom dry friction collision system is established, and the equation is transformed into differential inclusion standard form by convex hull and set-valued mapping. The variation of the dynamic characteristics of the system caused by non-smoothing is analyzed, and the transfer matrix and jump matrix in dry friction collision are derived. The single-parameter bifurcation diagram and the two-parameter bifurcation diagram of the system are numerically simulated, and the effects of different parameters on the dry friction collision system are investigated. Chapter 6: the main contents of this paper are summarized and the further research direction of parameter matching in dry friction collision system is given.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19
【参考文献】
相关期刊论文 前10条
1 焦云迪;王小静;白瑞成;聂周;喻广义;;大比压油润滑条件下C/C复合材料的摩擦特性[J];润滑与密封;2017年01期
2 李琳;刘久周;李超;;航空发动机中的干摩擦阻尼器及其设计技术研究进展[J];航空动力学报;2016年10期
3 姜春霞;邬开俊;;一类摩擦碰撞振动系统动力学行为的数值研究[J];信息通信;2015年11期
4 王树国;陈英;刘大亮;杨昊;翟海峰;;干摩擦下含间隙碰撞振动系统的动力学行为分析[J];武汉科技大学学报;2011年05期
5 张海涛;丁千;;干摩擦自激振动周期解的同伦方法[J];振动与冲击;2011年08期
6 马飞;杜三明;张永振;;干摩擦磨屑的三维形貌特征研究综述[J];润滑与密封;2011年01期
7 张有强;丁旺才;;干摩擦对碰撞振动系统周期运动的影响分析[J];振动与冲击;2009年06期
8 许宏文;薛小平;;约束微分包含的Filippov型定理[J];兰州大学学报(自然科学版);2009年03期
9 魏艳辉;徐洁琼;黄龙生;;两自由度碰撞振动系统的Lyapunov指数谱分析[J];振动与冲击;2009年01期
10 皇甫玉高;李群宏;;一类单侧碰撞悬臂振动系统的擦边分岔分析[J];力学学报;2008年06期
相关博士学位论文 前3条
1 蔡佐威;几类基于微分包含的不连续系统的动力学研究[D];湖南大学;2014年
2 刘磊坡;微分包含系统的几类控制问题研究[D];上海交通大学;2011年
3 秦泗甜;基于微分包含的非光滑动力系统分析及其应用[D];哈尔滨工业大学;2010年
，本文编号：2446880
本文链接：https://www.wllwen.com/kejilunwen/yysx/2446880.html
