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含摩擦与碰撞平面多刚体系统动力学线性互补算法

王晓军 王琪

王晓军, 王琪. 含摩擦与碰撞平面多刚体系统动力学线性互补算法[J]. 力学学报, 2015, 47(5): 814-821. doi: 10.6052/0459-1879-15-168
引用本文: 王晓军, 王琪. 含摩擦与碰撞平面多刚体系统动力学线性互补算法[J]. 力学学报, 2015, 47(5): 814-821. doi: 10.6052/0459-1879-15-168
Wang Xiaojun, Wang Qi. A LCP METHOD FOR THE DYNAMICS OF PLANAR MULTIBODYSYSTEMS WITH IMPACT AND FRICTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 814-821. doi: 10.6052/0459-1879-15-168
Citation: Wang Xiaojun, Wang Qi. A LCP METHOD FOR THE DYNAMICS OF PLANAR MULTIBODYSYSTEMS WITH IMPACT AND FRICTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 814-821. doi: 10.6052/0459-1879-15-168

含摩擦与碰撞平面多刚体系统动力学线性互补算法

doi: 10.6052/0459-1879-15-168
基金项目: 国家自然科学基金资助项目(11372018).
详细信息
    通讯作者:

    王琪,教授,主要研究方向:多体系统动力学与控制.E-mail:bhwangqi@sina.com

  • 中图分类号: O313.7

A LCP METHOD FOR THE DYNAMICS OF PLANAR MULTIBODYSYSTEMS WITH IMPACT AND FRICTION

Funds: The project was supported by the National Natural Science Foundation of China (11372018).
  • 摘要: 基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.

     

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出版历程
  • 收稿日期:  2015-05-11
  • 修回日期:  2015-06-24
  • 刊出日期:  2015-09-18

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