碰撞接触中的尺度缩放效应

项目名称： 碰撞接触中的尺度缩放效应

项目编号： No.11472011

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 刘才山

作者单位： 北京大学

项目金额： 95万元

中文摘要： 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。

中文关键词： 动力学；多体动力学；非线性动力学；动力学建模；振动控制

英文摘要： 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.

英文关键词： dynamics;multibody system dynamics;nonlinear dynamics;modeling of dynamics;vibration control