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塑性碰撞机械振动系统的周期运动和分岔

ISSN号：0577-6686
期刊名称：《机械工程学报》
时间：0
分类：TH113.1[机械工程—机械设计及理论]
作者机构：[1]兰州交通大学机电工程学院,兰州730070, [2]兰州交通大学数理与软件工程学院,兰州730070, [3]西南交通大学应用力学与工程系,成都610031
相关基金：国家自然科学基金（10572055,50475109）和教育部科学技术研究（206151）资助项目.

关键词：振动, 冲击, 周期运动, Sliding分岔, Grazing分岔, Vibration, Impact, Periodic motion, Sliding bifurcation, Grazing bifurcation

中文摘要：

应用映射的分岔理论研究塑性碰撞机械振动系统特有的两类周期碰撞运动的存在性、分岔和碰撞映射的奇异性,分析两类周期碰撞运动的规律和转迁过程.塑性碰撞振动系统的Poincaré映射具有分段不连续特性和擦边奇异性.塑性碰撞振动系统的部件在碰撞后呈现＂粘贴＂或＂非粘贴＂运动,导致该类系统的Poincaré映射具有分段不连续性;碰撞部件的擦边接触导致系统的Poincaré映射具有擦边奇异性.塑性碰撞振动系统Poincaré映射的分段不连续特性和擦边奇异性导致该类系统的周期碰撞运动发生非常规分岔.描述分段不连续性和擦边接触奇异性对系统周期运动和全局分岔的影响,分析塑性碰撞振动系统混沌运动的形成与退出过程.

英文摘要：

Vibratory systems with repeated impacts are considered. Dynamics of such systems, in inelastic impact cases, are studied with special attention to existence of two different types of periodic-impact motions, bifurcations and singularity by applying bifurcation theory of mapping. Regularity and transition of two types of periodic-impact motions are studied by use of a mapping derived from the equations of motion. The mapping of vibratory systems with repeated inelastic impacts is ofpiecewise property due to synchronous and non-synchronous motions of impact components immediately after the impact, and singularities caused by the grazing contact motions of impact components. The piecewise property and grazing singularity of Poincar6 mapping of such systems lead to non-standard bifurcations of periodic-impact motions. The influence of the piecewise property and singularities on global bifurcations and transitions to chaos is elucidated. The routes from periodic-impact motions to chaos are analyzed bv numerical analyses.

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