旋转柔性梁的动力学建模及运动数值仿真
关键词 多体系统 动力刚化 Green应变 Kichhoff应力 差时初应力法
毕业设计说明书（论文）外文摘要
Title Rotating Flexible Beam Dynamics Modeling and Numerical Simulation
Abstract
In flexible multibody systems，the rotation of some parts with little specific gravity at high speed always cause the phenomenons of dynamic stiffening. At this time，the effect of elastic movement of parts on dynamic behavior of systems can not be ignored. Factually，because the deformation of most of the elastic parts are very little，the linear finite element theory is often used to establish dynamic model in the classical multibody system theory，and coupling of space movement in large scale and elastic deformation of parts is ignored. The dynamic stiffening is exactly caused by such coupling.
In this article， several existing main compensation methods for the term of dynamic stiffening are reviewed; deseribing method of material coordinate is introduced on the basis of the principle theorem of mechanics of continuum；and the dynamic equation of flexible body is derived from nonlinear Green strain tensor and Kichhoff stress tensor，which are based on initial configuration. A new compensation method，‘Belated initial stress method’，is developed for term of dynamic stiffening by synthesizing the existing method. The main idea of this method is using internal stress of last moment to construct the term of dynamic stiffening caused by rotation at high speed.Then the effect of dynamic stiffening can be simulated at lower cost when the equation of motion of elastic parts is linear.
Keywords Multibody system Dynamic stiffening Green strain Kichhoff stress Belated initial stress method
目 次
1 引言 1
1．1 工程背景 1
1.2 国内外相关领域的研究情况 4
1.3 柔体动力学中“动力刚化”的研究状况 6
1.4 本文的主要工作 8
2 柔性梁的动力刚化 9
2.1 动力刚化的引出 9
2.2 弹性体的应力和应变 11
3 动力刚化的分析方法 13
3.1 有限元模态分析 13
3.2 动力刚化项的补偿方法——差时初应力法 14
4 算例分析 16
结论．20
致谢．21
参考文献．22
1 引言
1．1 工程背景
随着科学技术的进步和生产力水平的提高,在船舶、车辆、机车、航天航空和机器人等众多工程领域中,出现了许多轻质、柔性、高速运动的多体系统。一方面，这类系统在经历大范围刚体运动的同时还存在着柔性构件的变形运动，且刚体运动和变形运动相互耦合，加上系统在运行过程中所处的环境十分恶劣，所呈现的动力学行为十分复杂，另一方面，人们对其又有十分严格的安全性及可靠性要求。由此，对其运动过程中所呈现的动力学行为的研究及控制就显得尤为重要。目前,这些问题的研究方法主要有多刚体动力学和多柔体动力学这两大类。其中,多刚体系统动力学侧重研究各个物体刚性运动之间的相互作用及其对整个系统动力学的影响,且其在理论研究、数值计算以及软件开发应用方面已经非常成熟。多柔体系统动力学则侧重研究物体的弹性变形和系统整体的刚体运动之间的相互耦合作用以及由此所产生的独特且复杂的动力学效应。多柔体动力学的研究起步相对较晚,但是近几十年来发展相当迅速。且由于多柔体动力学体系中模型的假设条件和计算仿真结果更切合实际,已经有逐渐取代多刚体动力学成为动力学研究主要体系的趋势。多柔体动力学的研究对象是经历大范围空间运动的柔性系统动力学,是多刚体动力学研究的自然延伸和发展。其柔体的弹性变形运动和大范围空间刚体运动的同时出现及其相互耦合是多柔体动力学的本质特征,也是多刚体动力学和结构动力学的结合与推广。
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