PERIODIC MOTIONS AND BIFURCATIONS OF VIBRATORY SYSTEMS WITH PLASTIC IMPACTS REPEATED

LUO Guanwei¹  CHU Yandong²  ZHU Xifeng¹  XIE Jianhua ³

(1. School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070；
2. School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070;
3. Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031 )

Abstract: 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 of piecewise 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 Poincaré 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 by numerical analyses.

 Key words: Vibration Impact Periodic motion Sliding bifurcation Grazing bifurcation

CLC No: TH113.1 

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. Received 20051225, received in revised form 20060510