多自由度碰撞系统的动力学研究

发布时间：2018-10-14 13:32

【摘要】：近几年来,国内外专家对单自由度或单侧刚性约束两自由度碰撞振动系统周期运动的Hopf分岔问题研究已经取得了较大进展,而对于系统参数比较复杂、动态响应式较繁琐、参数对系统的稳定性影响较敏感的多自由度碰撞振动系统的研究甚少,研究方法也主要为数值分析。然而,冲击振动问题在机械、车辆等工程实践中经常存在,迫切需要对此类系统的动态行为有更全面的了解。因此,在工程实践中,对含间隙多自由度碰撞振动系统的研究有重要的意义,因而本文就对两自由度碰撞振动系统和四自由度碰撞振动系统的情况做了全面的分析。本文主要内容为： 1.本文全面分析了两类典型的两自由度碰撞振动系统和一类四自由度碰撞振动系统的动力学行为。通过建立碰撞振动系统的物理模型和数学模型,利用正则模态矩阵法对碰撞振动系统进行解耦,并用解析法求解了碰撞振动系统周期运动的解析解和线性化矩阵和各个系统的Poincare映射。 2.利用Poincare映射理论对平面映射不动点失稳和分岔情况进行分析。当线性化矩阵的某个特征值为1或-1时,系统可能会发生鞍结或倍化分岔：当线性化矩阵有二重特征值穿越单位圆时,系统会发生余维二分岔现象。选择适当的系统参数,结合线性化矩阵特征值横截单位圆周的趋势图,分析线性化矩阵特征值在上述情况下,系统发生分岔与混沌演化的动力学行为。 3.针对具体的多自由度碰撞振动系统的物理模型,研究了系统在何时参数下发生Hopf分岔和混沌的复杂动力学行为,给出了系统历经概周期运动、周期运动和环面倍化向混沌演化的Poincare截面图。 4.利用数值仿真的结果,分析了系统的主要控制参数对系统周期运动的影响,发现高维碰撞振动系统的敏感性较高,尤其激励频率,间隙和恢复系数等参数对系统周期运动对系统周期运动的影响较大,因此,选取系统的最优参数对机械碰撞振动系统得优化设计是必要的。
[Abstract]:In recent years, experts at home and abroad have made great progress in the study of the Hopf bifurcation of the periodic motion of the two-degree-of-freedom collision vibration system with one degree of freedom or one side rigid constraint, but the system parameters are more complex and the dynamic response formula is more complicated. There is little research on the multi-degree-of-freedom impact vibration system which is sensitive to the stability of the system, and the research method is mainly numerical analysis. However, the problem of shock vibration often exists in engineering practice, such as machinery, vehicle and so on. It is urgent to understand the dynamic behavior of this kind of system more comprehensively. Therefore, in engineering practice, it is of great significance to study the impact vibration system with multiple degrees of freedom with clearance, so this paper makes a comprehensive analysis of the impact vibration system with two degrees of freedom and the impact vibration system with four degrees of freedom. The main contents of this paper are as follows: 1. In this paper, the dynamic behaviors of two typical two degree of freedom impact vibration systems and a four degree of freedom impact vibration system are analyzed. By establishing the physical and mathematical models of the impact vibration system, the regular mode matrix method is used to decouple the impact vibration system. The analytical solution and linearization matrix of the periodic motion of the collisional vibration system and the Poincare map of each system are obtained by using the analytical method. 2. The instability and bifurcation of fixed point of planar mapping are analyzed by using Poincare mapping theory. When the eigenvalue of the linearization matrix is 1 or -1, the saddle node or doubling bifurcation may occur. When the linear matrix has a double eigenvalue passing through the unit circle, the system will have a codimensional two-bifurcation phenomenon. By selecting appropriate system parameters and combining with the trend diagram of linear matrix eigenvalue traversing unit circle, the dynamical behavior of bifurcation and chaotic evolution of linear matrix eigenvalue in the above cases is analyzed. 3. In this paper, the complex dynamical behavior of Hopf bifurcation and chaos is studied for the physical model of a specific multi-degree-of-freedom collisional vibration system, and the ergodic almost periodic motion of the system is given. Poincare section of periodic motion and torus doubling to chaos. 4. Based on the results of numerical simulation, the influence of the main control parameters on the periodic motion of the system is analyzed. It is found that the high dimensional impact vibration system has a high sensitivity, especially the excitation frequency. The parameters such as clearance and recovery coefficient have great influence on the periodic motion of the system. Therefore, it is necessary to select the optimal parameters of the system for the optimal design of the mechanical impact vibration system.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113.1

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