含摩擦的多刚体系统碰撞问题的滑动状态步进法

基金项目: 国家自然科学基金资助项目(10532050);国家杰出青年基金资助项目(10625211)

Sliding State Stepping Algorithm Solving Impact Problems of Multi-Rigid-Body System With Joint Friction

1.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. China;

摘要: 研究了含铰摩擦的多刚体系统的碰撞动力学问题．在保留了关于处理冲击问题的经典近似假定的基础上，给出了计算冲击后系统广义速度的滑动模式步进算法．该算法避免了求解变尺度的微分方程的困难，同时由于考虑了切向模式的复杂性，从而使计算结果避免了碰撞前后能量的不协调性．算例描述了该算法的实现过程．
- 多刚体系统 /
- 铰摩擦 /
- 滑动状态 /
- 步进法
Abstract: Impact dynamics of multi-rigid-body systems with joint friction was considered. Based on traditional approximate assumption dealing with impact problem, a general numerical method called sliding state stepping algorithm was introduced. This method can avoid the difficulties in solving di-f ferential equations with variable scale and the result can avoid the energy inconsistency before and a-f ter impact due to considering the complex of the tangential sliding mode. An example was given to describe the concrete details dealing with these difficulties.
- multi-rigid-body system /
- joint friction /
- sliding state /
- stepping algorithm

[1]	黄昭度,钟奉娥.工程系统分析力学[M].北京：高等教育出版社,1992.
[2]	Kane T R, Levison D A.Dynamics: Theory and Applications[M].New York: McGraw-Hill, 1985，150-180.
[3]	Lotstedt P. Coulomb friction in two-dimensional rigid systems[J].Z Angnew Math Mech,1981,61:605-615. doi: 10.1002/zamm.19810611202
[4]	Stronge W J. Generalized impulse and momentum applied to multibody impact with friction[J].Mechanics of Structures and Machines,2001,29(2):239-260. doi: 10.1081/SME-100104482
[5]	赵振，刘才山，陈滨.步进冲量法[J].北京大学学报自然科学版，2006,42(1):41-46.
[6]	Pfeiffer F.Multibody systems with unilateral constraints[J].J Appl Math Mech,2001,65(4):665-670. doi: 10.1016/S0021-8928(01)00070-3
[7]	YAO Wen-li, CHEN Bin, LIU Cai-shan. Energetic coefficient of restitution for planar impact in multi-rigid-body systems with friction[J].International Journal of Impact Engineering,2005,31(3):255-265. doi: 10.1016/j.ijimpeng.2003.12.007