动力刚化与多体系统刚-柔耦合动力学

首先指出当前柔性多体系统动力学的大量工程研究背景,在回顾柔性多体系统动力学研究进展后指出动力刚化的现象揭示了刚－柔耦合的零次建模方法的局限,认为进一步深入进行柔性多体系统刚－柔耦合动力学的研究是多体系统动力学研究的新阶段,文末提出了刚－柔耦合动力学的研究任务。     

刚-柔-热耦合多体系统的动力学分析

本文研究了柔性多体系统刚-柔-热耦合动力学特性。以哈勃天文望远镜(HST)为研究对象,基于柔性多体系统动力学理论,考虑了柔性附件弹性变形引起的热辐射边界条件的变化,建立了中心刚体和太阳能毯柔性附件多体系统的刚-柔-热耦合的动力学方程。通过对热载荷作用下哈勃天文望远镜多体系统的数值仿真研究了热辐射角、阻尼系数、比热容、支撑梁、太阳能毯之间的轴向力等参数对于柔性附件热颤振的影响;并提出增加结构阻尼、减小支撑梁和太阳能毯之间的轴向力、选择阻尼系数和比热容均较大的支撑梁材料、采用柔度较大的主体桶材料等改善热颤振的措施。     

柔性多体系统产生动力刚化原因的研究

传统的柔性多体系统建模理论由于对柔性体的变形及其与大范围运动产生惯性力之间的耦合处理得过于简单,所以在分析存在高速大范围运动柔性多体系统的动力学性态时会得到完全错误的结论.本文将通过对作大范围运动弹性薄板的讨论来揭示产生这种错误的原因及探讨对传统柔性多体系统建模理论作出改进的对策.     

考虑刚弹耦合作用的柔性多体连续系统动力学建模

基于Ｈａｍｉｌｔｏｎ原理建立起一般柔性体连续系统的动力学建模方法,进而以水平面内作大范围回转运动的柔性梁为例,在Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ梁模型的假设前提下,根据轴向不可伸长的柔性梁的几何约束条件;推导出作大范围刚体运动的柔性梁连续系统的一致线性化振动微分方程．采用假设模态法对其离散化,导出考虑刚弹耦合作用的柔性梁有限维离散化动力学模型．最后给出仿真算例,验证了该方法的有效性．     

刚-柔耦合多体系统动力学建模与数值仿真

柔性多体系统动力学传统的混合坐标建模方法忽略了变形位移的高次耦合变形量,是一种零次近似方法,其适用范围受到限制。本文以中心刚体、柔性粱及末端质量组成的刚柔耦合系统为对象,考虑了有粘性阻尼及风阻的情况。在柔性粱的纵向变形位移中计及了横向位移引起的轴向变形,并采用有限元方法和Hamilton变分原理导出了系统的刚柔耦合一次近似的动力学方程。该方程充分计及了中心刚体的大范围运动与柔性粱的弹性变形运动的相互耦合,并采用一致的方法引入了阻尼因素。文中最后提供了一个比“动力刚化”问题更具有一般性的仿真计算反例,进一步说明了零次近似方法在处理某些刚一柔耦合动力学问题时的缺陷,同时表明了由一次近似模型可得到正确合理的结论。     

柔性体的刚-柔耦合动力学分析

对柔性梁的刚-柔耦合动力学特性进行分析.从连续介质力学理论出发,在纵向变形位移中计及了耦合变形量,用Jourdain速度变分原理导出了柔性梁的刚-柔耦合动力学方程.定量地研究了非惯性系下柔性梁的动力学性质,比较了在不同转速下零次近似模型和耦合模型的振动频率的差异.为了确定零次近似模型的适用范围,引入与转速和基点加速度有关的相关系数,提出了零次近似模型的适用判据为相关系数小于0.1.在此基础上,进一步研究在大范围运动是自由的情况下柔性梁的大范围运动和变形运动的耦合机理,计算了带平动刚体的柔性梁的大范围运动规律,揭示零次近似模型和耦合模型的刚-柔耦合动力学性质的根本差异.     

动力刚化多体系统动力学

本文利用几何非线性的应变－－位移关系，在小变形假设条件下，得到了一般柔性构件弹性有的广义价值标二阶小量表达式。在此基础上，利用Ｋａｎｅ方程的Ｈｕｓｔｏｎ方法，在推导偏（角）速度表达式后，作适当的线性化处理，以使动力刚度项得以保留，从而建立了动力刚化多体系统的动力学方程，仿真算例证明了该理论的正确性和有效性。     

刚-柔耦合动力学系统的建模理论研究

刚－柔耦合动力学系统的传统的混合坐标方法是零次近似方法,在建模过程中,直接套用的结构动力学的小变形假设,忽略了变形位移的高次耦合变形量．本文对柔性梁建立较零次近似更精确的高次耦合动力学模型,从连续介质力学理论出发,在变形位移中,计及横向位移引起的轴向缩短,导出变形位移的二次耦合量．用一致质量有限元方法对梁进行离散,基于Jourdain速度变分原理导出大范围运动为自由的柔性梁的刚－柔耦合动力学方程．计算了柔性重力摆的角速度和摆端点的横向变形,揭示零次近似模型和耦合模型的刚－柔耦合动力学性质的根本差异．     

柔性多体系统动力学的若干热点问题

全面综述了柔性多体系统动力学近年来的研究成果．对建模方法、模态选取及模态综合、动力刚化及柔性多体系统动力学中微分－代数方程的数值方法等研究热点进行了详细的阐述,并简要展望了柔性多体系统动力学今后的发展趋势     

刚柔耦合约束多体系统的动力分析

本文提出了描述柔性多体系统的牵连坐标系统。该系统由惯性参考系,牵连坐标系,物体坐标系及单元坐标系组成,实现了对刚体平动,刚体转动及弹性运动的连续分解,最大限度地消除了由于刚体大角度转动导致的非线性特性。以有限元法为基础,应用拉格朗日方程建立了在该坐标下的刚柔耦合约束多体系统的动力学控制方程。该方程具有耦合程度小、易于推导、编程及求解等优点,为大规模约束多体系统的动力分析提供了新的途径。本文还讨论了平面铰链约束的约束形式及约束方程,最后给出了一个典型多体系统的数值算例。     

Modal test and analysis of cantilever beam with tip mass

The phenomenon of dynamic stiffening is a research field of general interest for flexible multi-body systems. In fact, there are not only dynamic stiffening but also dynamic softening phenomenon in the flexible multi-body systems. In this paper, a non-linear dynamic model and its linearization characteristic equations of a cantilever beam with tip mass in the centrifugal field are established by adopting the general Hamilton Variational Principle. Then, the problems of the dynamic stiffening and the dynamic softening are studied by using numerical simulations. Meanwhile, the modal test is carried out on our centrifuge. The numerical results show that the system stiffness will be strengthened when the centrifugal tension force acts on the beam (i.e. the dynamic stiffening). However, the system stiffness will be weakened when the centrifugal compression force acts on the beam (i.e. the dynamic softening). Furthermore, the equilibrium position of the system will lose its stability when the inertial force reaches a critical value. Through theoretical analysis, we find that this phenomenon comes from the effect of dynamic softening resulting from the centrifugal compression force. Our test results verify the above conclusions and confirm that both dynamic stiffening and softening phenomena exist in flexible multi-body systems. The project supported by the National Natural Science Foundation of China (19972002) and the Doctoral Programme from The State Education Commission China (20010001011)     

矩形薄板的刚柔耦合动力学系统的建模理论研究

以由中心刚体与柔性板构成的刚柔耦合系统为对象,研究了零次近似模型和耦合模型在动力学方程以及实际计算中表现出来的差异.首先,从连续介质理论出发,在变形位移中,计及了在结构动力学中被忽略的变形位移的附加耦合项,建立了由中心刚体与柔性板构成的刚柔耦合系统的一次近似动力学模型.用一致质量有限元法对柔性板进行离散,基于Jourdain速度变分原理推导出大范围运动为自由的柔性板刚柔耦合动力学连续变分方程.通过数值仿真研究中心刚体和柔性板的大范围运动和变形运动的规律,揭示刚柔耦合动力学性质.通过数值对比,指出了零次近似模型的局限性.     

刚体单元及其在多体系统动力学中的应用

多体系统动力学分析软件要求人工输入形状复杂物体的质量、质心位置和转动惯量,而实际上这些参量并不容易获得。本文探索了一种以组成物体的刚体单元为基本要素的新方法,并结合实际需要具体构造了刚性四面体和刚性梁单元。以刚体单元为基础并内嵌网格剖分模块的分析软件能够自动获得这些参数,从而具备处理任何复杂系统的能力。仿真结果的对比分...     

Dymamics of a rotating flexible manipulator with tip load

The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic blance, the motion equations of a rotating beam with tip load are established by using Hamilton's principle. By taking into account the effects of dynamic stiffening and dynamic softening, the stability of the system is proved by employing Lyapunov's approach. Furthermore, the method of power series is proposed to find the exact solution of the eigenvalue problem. The effects of rotating speed and tip load on the vibration behavior of the flexible manipulator are shown in numerical results. Supported by National Natural Science Foundation. of China     

Equations of motion of a multibody system and Lie groups

Usually, the methods used for forming the equations relating to the motion of a complex system are based either on the use of general theorems or on the use of conventional techniques of analytical mechanics (Lagrange or Hamilton equations). In this case the formation of the equations of motion was made using a method allowing us to draft these equations in a more synthetic form. It uses the properties of the displacement group as a LIE group. Its main advantage is that it allows a totally intrinsic analytical calculation in the vector space of the wrenches or complex forces [8]. A symbolic calculus code has been designed in order to apply this approach. Initially, we have used and tested it in any open loop multibody system. The symbolic calculus code was applied, for instance, in the context of a study into the crash of a vehicle driven into a barrier.

---

Sommario I metodi più comunemente usati per formulare le equazioni relative al moto di un sistema complesso si basano o su teoremi generali o su tecniche convenzionali della meccanica analitica (equazioni di Lagrange o di Hamilton). Nel presente studio, invece, le equazioni del moto vengono formulate usando una metologia che ne permette la scrittura in una forma più sintetica, sfruttando le proprietà del gruppo degli spostamenti come di un gruppo di Lie: il principale vantaggio del metodo è di permettere un calcolo analitico totalmente intrinseco nello spazio vettoriale delle forze complesse [8]. Per poter applicare questo approccio, è stato sviluppato un codice di calcolo simbolico. Per cominciare, l'approccio è stato usato e sperimentato per un generico sistema multicorpo a loop aperto: per esempio, nel contesto di uno studio sull'urto di un veicolo su di una barriera.

     

On the Use of Implicit Integration Methods and the Absolute Nodal Coordinate Formulation in the Analysis of Elasto-Plastic Deformation Problems

In the general theory of continuum mechanics, the state of rotation and deformation of material points can be uniquely defined from the displacement field by using the nine independent components of the displacement gradients. For this reason, the use of the absolute rotation parameters as nodal coordinates, without relating them to the displacement gradients, leads to coordinate redundancy that leads to numerical and fundamental problems in many existing large rotation finite element formulations. Because of this fundamental problem, special measures that require modifications of the numerical integration methods were proposed in the literature in order to satisfy the principle of work and energy. As demonstrated in this paper, no such measures need to be taken when the finite element absolute nodal coordinate formulation is used since the principle of work and energy are automatically satisfied. This formulation does not suffer from the problem of coordinate redundancy and ensures the continuity of stresses and strains at the nodal points. In this study, the use of the implicit integration methods with the consistent Lagrangian elasto-plastic tangent moduli is examined when the absolute nodal coordinate formulation is used. The performance of different numerical integration methods in the dynamic analysis of large elasto-plastic deformation problems is investigated. It is shown that all these methods, in the case of convergence, yield a solution that satisfies the principle of work and energy without the need of taking any special measures. Semi-implicit integration methods, however, can lead to numerical difficulties in the case of very stiff problems due to the linearization made in these methods in order to avoid the iterative Newton--Raphson procedure. It is also demonstrated that the use of the consistent Lagrangian-plastic tangent moduli derived in this investigation using the absolute nodal coordinate formulation leads to better convergence of the iterative Newton--Raphson procedure used in the implicit integration methods.