Frictionless multiple impacts in multibody systems. I. Theoretical framework
Frictionless multiple impacts in multibody systems. I. Theoretical framework
复制标题
多体系统中的无摩擦多重碰撞。
DOI：
10.1098/rspa.2008.0078
复制
发表时间：
2008-12-08
影响因子：
3.5
通讯作者：
Brogliato, Bernard
中科院分区：
文献类型：
--
作者：
Liu, Caishan;Zhao, Zhen;Brogliato, Bernard
提出了一种新的方法，可以处理多碰撞问题，并产生能量一致和唯一的碰撞后速度。通过将时间尺度映射到脉冲尺度，发现了与率无关物质组成的物体的能量色散分布规律。结果表明，冲击过程中动能的演化与接触点的相对接触刚度和相对势能密切相关。该分布律与达布-凯勒方法相结合，达布-凯勒方法将正常脉冲作为独立的“类时”变量，其服从用于选择独立正常脉冲的准则。在每个接触点的能量恢复系数建模的本地能量损失。本文第一部分介绍了理论发展。第二部分是专门的数值模拟，大量和准确的结果证明了该方法的有效性。
A new method is proposed that can deal with multi-impact problems and produce energetically consistent and unique post-impact velocities. A distributing law related to the energy dispersion is discovered by mapping the time scale into the impulsive scale for bodies composed of rate-independent materials. It indicates that the evolution of the kinetic energy during the impacts is closely associated with the relative contact stiffness and the relative potential energy stored at the contact points. This distributing law is combined with the Darboux - Keller method of taking the normal impulse as an independent ' time-like' variable, which obeys a guideline for the selection of an independent normal impulse. Local energy losses are modelled with energetic coefficients of restitution at each contact point. Theoretical developments are presented in the first part in this paper. The second part is dedicated to numerical simulations where numerous and accurate results prove the validity of the approach.