两自由度刚性碰撞的动力学研究.docx

兰州交通大学毕业设计（论文） PAGE PAGE 51 摘 要 在实际工程系统中，有许多问题的数学模型和动力学方程都可用非线性系统来描述。非线性系统由于参数的变化会引起系统响应的本质变化，从而产生分岔现象，甚至导致混沌运动。混沌是某些非线性动力学系统特有的内在属性，它与机械振动理论相结合而形成新的学科——混沌振动，正在成为一个日趋活跃的研究领域。 本文建立了一类两自由度机械碰撞振动系统的力学模型，取碰撞前瞬时的定相位面为Poincaré截面，构造Poincaré映射并给出其Jacobi矩阵，利用正交化，范数归一化等方法得出两自由度碰撞振动系统的计算方法。并通过理论分析和Matlab数值仿真相结合的方法，研究了该系统在适当参数下发生混沌和分岔的动力学行为。并且揭示了系统主要参数对碰撞振动系统全局分岔的影响，为实际应用中两自由度碰撞振动系统的动力学优化设计提供了理论参考。 关键词：碰撞振动；周期运动；混沌；分岔 Abstract In practical engineering systems, many of the problems of the mathematical model and the kinetic equation can be described by nonlinear systems. Nonlinear systems due to changes in parameters will cause fundamental changes in the system response, resulting in bifurcations, and even lead to chaotic motion. Chaos is the attribute of some nonlinear dynamic system. Chaotic vibration formed from the combining of chaos and mechanical vibration is becoming an active field. In this paper, a two-degree-of-freedom vibro-impact system is investigated. By using a constant phase surface in the pre-impact instantaneous as the Poincaré section and introducing the local maps, the Poincaré section is constructed and the corresponding Jacobi matrix is obtained. Using the Gram-Schmidt ortho-normalization and the iterative method, we obtain the method for calculating the vibro-impact system. And through the combination of theoretical analysis and Matlab numerical simulation method to study the dynamic behavior of the system which occur Chaos and bifurcation with appropriate parameters. And reveals the influence of the main parameters of the system to vibro-impact system global bifurcation, which give a theoretical reference for the dynamical optimal design of vibro-impact system in practical application. Key words: Vibro-impact; Periodic motion; Bifurcation; Chaos 目 录 TOC \o 1-3 \h \z \u 摘 要 I Abstract II 第一章 绪 论 1 1.1 课题背景 1 1.2 混沌理论的发展概述 1 1.3非线性振动系统的研究现状 2 1.4本文研究的问题 3 第二章 混沌理论及算法介绍 5 2.1 混沌的基本概念 5 2.1.1 混沌的定义 5 2.1