碰撞接触中的尺度缩放效应

Compelex responses with the characters of different scales in size and time are often exhibited in the dynamics of mechanical system due to the interactions coming from contact/impact with friction. Understanding the contributions of their effects on the model established at the expected level is crucial in the variety of scientific fields. Obviously, Concluding the ordered structure of the scale effects in modeling depends on the precise experiment observations that could be quantified by a suitable mathematical expression. Due to the limitation in observations, however, we often have to magnify or minify the scales in order to find their effects in modeling. In this project, we focus on three kinds of mechanical systems:(1) bouncing dimers; (2) rolling prisms; and (3) domino effects. By investigating the three systems, we expect to clarify the problems as follows: the ordered structures in the dynamics of the bouncing dimer and the similarities in comparison with the quantum manefication; the connection between the dynamics of rolling prism and rolling friction; the solitary wave induced by the domino effects. Noting that contact/impact and friction are involved in the dynamics in all of three systems, we will base LZB method to deal with those problems. The project will be implemented by presenting the results of a combined experimental and theoretical investigations of the three systems. The results anticipated in this project may have significant implications in developing the thoery of dynamics in complex systems, and also may find possible important applications in the fields of numerous engineering problems.

力学系统往往包含碰撞接触及摩擦作用激发复杂的多尺度效应。理解这些尺度效应在不同层次模型结构中的贡献，是多学科所关注的重要内容之一。归纳不同尺度效应中的有序结构，依赖于精细的实验观测和有效的数学定量化表示。如何对所关注的尺度效应进行合理的缩放，克服观测手段的局限性，是展现尺度特征和建立层次化模型的重要手段。本项目将研究三类具有典型尺度缩放效应的力学系统：（1）跳动哑铃系统；（2）滚动多边柱体。（3）多米诺骨牌。我们期望针对三类系统的研究，关注如下科学问题：跳动哑铃系统中的有序动力学结构及其宏观量子化表现；滚动多边柱体与滚动摩阻效应的关联；多米诺骨牌中的孤立波效应。以上三类系统均包含复杂的碰撞接触及摩擦作用。本项目将基于所发展的LZB方法开展相关的实验和理论研究工作。预期成果不仅有助于动力学基本理论的发展，而且在控制、工程应用等多学科发现重要的应用价值。

力学系统往往包含碰撞接触及摩擦作用激发复杂的多尺度效应。理解这些尺度效应在不同层次模型结构中的贡献，是多学科所关注的重要内容之一。本项目围绕三类具有典型尺度缩放效应的力学系统：（1）跳动哑铃系统；（2）滚动多边柱体；（3）多米诺骨牌， 从实验和理论方面系统研究了所激发的多尺度动力学问题。我们针对三类系统的理论和实验研究，发现了如下由多尺度效应所触发的有序力学行为：（1）在外部谐振激励作用下，跳动哑铃型刚体多点碰撞精细动力学模型，数值发现并实验证实了该系统可自组织形成有序的直线轨道或圆形周期轨道; （2）以多米诺骨牌为对象，研究了临界稳定性系统受小扰动情况下所激发的孤立波行为，并发现了对应的稳定域。（3）建立滚动多边柱运动中的线碰撞规律，并建立了滚动多边柱多尺度动力学与滚动摩阻之间的内在联系。同时，本课题在旋转梁的振动效应，散体动力学及其输运行为等方面均取得了重要的研究进展。供发表学术论文23篇，其中SCI论文19篇。部分研究成果为我国航天嫦娥工程三期月壤钻取等提供了重要的理论支撑。该项目其它研究成果属于基础理论研究成果。这些成果解决了一些基础性科学问题，例如滚动摩阻理论模型，并为相关工程学科提供了重要的理论支撑。