含不确定性区间参数的刚柔耦合多体系统动力学建模与分析

项目名称： 含不确定性区间参数的刚柔耦合多体系统动力学建模与分析

项目编号： No.11472042

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： 田强

作者单位： 北京理工大学

项目金额： 90万元

中文摘要： 基于确定性刚柔耦合多体系统动力学研究的绝对坐标方法（绝对节点坐标方法+自然坐标方法）并利用区间算术，仿射算术以及计算连续介质力学理论，深入研究含不确定性区间参数的刚柔耦合多体系统动力学精确建模与高效计算方法，揭示不确定性区间参数对系统动响应的影响规律，通过数值模拟和地面实验的相互引证和补充，形成一个不确定性刚柔耦合多体系统动力学研究新理论框架，发展多体系统动力学理论。主要研究内容包括：含区间不确定性参数的刚柔耦合多体系统动力学精确建模方法，如：区间参数的防扩张描述、绝对节点坐标区间有限单元等；不确定性刚柔耦合多体系统动力学方程的高效非侵入式区间并行算法；不确定性区间参数（如：惯量、材料参数、运动副间隙尺寸等）对系统动力学性态的影响分析；建模与计算方法的验证实验。重点解决如下关键问题：区间参数的防扩张表达问题；区间动力学方程的精确、高效求解问题；运动副间隙尺寸不确定性问题的建模与计算问题。

中文关键词： 刚柔耦合多体系统；不确定性；区间参数；绝对节点坐标法；实验

英文摘要： Based on the Absolute Coordinate Based method (Absolute Nodal Coordinate Formulation + Natural Coordinate Formulation) for studying the dynamics of deterministic rigid-flexible coupling multibody system, and using the interval arithmetic, affine arithmetic and computational continuum mechanics, the project aims at the accurate modeling and efficient computation algorithm for rigid-flexible coupling multibody system with uncertain interval parameters so as to reveal the effects of the uncertain interval parameters on the system dynamic responses. The results of numerical simulation and those of ground experiments will be validated and amended mutually. These researches can be considered as a new theoretical framework for the dynamics of the uncertain rigid-flexible coupling multibody system, and can develop the mutlibody system dynamics theory. The major studies of the project include: the accurate modeling method of the rigid-flexible coupling multibody system with uncertain interval parameters( for example, the anti-expansion description of the interval parameters and the interval finite element of the Absolute Nodal Coordinate Formulation), the efficient non-intrusive interval parallel algorithm for solving the equations of motions of the multibody system with uncertain interval parameters, the effect of the uncertain interval parameters (inertia parameters, material parameters, and joint clearance size) on the system's dynamic responses, and the verification experiments of the above modeling and computational algorithms. The project will focus on solving the following key problems: how to describe interval parameters without interval expanding, how to accurately and efficiently solving the interval equations of motion, and how to model and compute the dynamics of rigid-flexible coupling multibody system with uncertain uncertain joint clearance size.

英文关键词： Rigid-flexible coupling multibody system;uncertainty;interval parameter;absolute nodal coordinate formulation;experiment