基于李群局部标架的多柔体系统动力学建模与计算

多柔体系统动力学主要研究由多个具有运动学约束、存在大范围相对运动的柔性部件构成的动力学系统的建模、计算和控制.多柔体系统不仅具有柔体大变形导致的几何非线性,更具有大范围刚体运动引起的几何非线性,其非线性程度远高于计算结构力学所研究的几何非线性问题.本文基于李群局部标架(local frame of Lie group, LFLG),讨论如何发展一套新的多柔体系统动力学建模和计算方法体系, 具体内容包括:基于局部标架的梁、板壳单元,适用于长时间历程计算的多柔体系统碰撞动力学积分算法,结合区域分解技术的大规模多柔体系统动力学并行求解器, 以及若干验证性算例.上述基于李群局部标架的方法体系可在计算中消除刚体运动带来的几何非线性问题,使柔体系统的广义惯性力、广义弹性力及其雅可比矩阵满足刚体运动的不变性,使多柔体系统动力学与大变形结构力学相互统一,有望推动新一代多柔体系统动力学建模和计算软件的发展.      

基于李群局部标架的多柔体系统动力学建模与计算

多柔体系统动力学主要研究由多个具有运动学约束、存在大范围相对运动的柔性部件构成的动力学系统的建模、计算和控制.多柔体系统不仅具有柔体大变形导致的几何非线性,更具有大范围刚体运动引起的几何非线性,其非线性程度远高于计算结构力学所研究的几何非线性问题.本文基于李群局部标架(local frame of Lie group, LFLG),讨论如何发展一套新的多柔体系统动力学建模和计算方法体系,具体内容包括:基于局部标架的梁、板壳单元,适用于长时间历程计算的多柔体系统碰撞动力学积分算法,结合区域分解技术的大规模多柔体系统动力学并行求解器,以及若干验证性算例.上述基于李群局部标架的方法体系可在计算中消除刚体运动带来的几何非线性问题,使柔体系统的广义惯性力、广义弹性力及其雅可比矩阵满足刚体运动的不变性,使多柔体系统动力学与大变形结构力学相互统一,有望推动新一代多柔体系统动力学建模和计算软件的发展.     

多柔体系统动力学建模与优化研究进展

多柔体系统是由柔性部件和运动副组成的力学系统,在航空、航天、车辆、机械与兵器等众多工程领域具有广泛的应用前景, 其典型的代表包括柔性机械臂、直升机旋翼、卫星的可展开天线、太阳帆航天器等. 近年来,随着工程技术的发展,多柔体系统动力学问题日益突出,尤其是含变长度柔性部件的多柔体系统,不仅涉及其动力学 建模与计算,还涉及其动力学优化设计. 事实上,部件柔性对多柔体系统的动力学行为影响很大,直接影响到优化结果,因此需要发展基于多柔体系统动力学的优化设计方法. 本文首先阐述了多柔体系统动力学优化的研究背景及意义,简要回顾了多柔体系统动力学建模的3类方法:浮动坐标方法、几何 精确方法和绝对节点坐标方法,并介绍了含变长度柔性部件的多柔体系统动力学建模方法. 系统概述了多柔体系统动力学响应优化、动力学特性优化和动力学灵敏度分析3个方面的研究进展,并从尺寸优化、形状优化和 拓扑优化 3 个方面综述了多柔体系统部件优化的研究进展. 本文最后提出了在多柔体系统动力学优化研究中值得关注的若干问题.      

多柔体系统动力学建模与优化研究进展

多柔体系统是由柔性部件和运动副组成的力学系统,在航空、航天、车辆、机械与兵器等众多工程领域具有广泛的应用前景,其典型的代表包括柔性机械臂、直升机旋翼、卫星的可展开天线、太阳帆航天器等.近年来,随着工程技术的发展,多柔体系统动力学问题日益突出,尤其是含变长度柔性部件的多柔体系统,不仅涉及其动力学建模与计算,还涉及其动力学优化设计.事实上,部件柔性对多柔体系统的动力学行为影响很大,直接影响到优化结果,因此需要发展基于多柔体系统动力学的优化设计方法.本文首先阐述了多柔体系统动力学优化的研究背景及意义,简要回顾了多柔体系统动力学建模的3类方法:浮动坐标方法、几何精确方法和绝对节点坐标方法,并介绍了含变长度柔性部件的多柔体系统动力学建模方法.系统概述了多柔体系统动力学响应优化、动力学特性优化和动力学灵敏度分析3个方面的研究进展,并从尺寸优化、形状优化和拓扑优化3个方面综述了多柔体系统部件优化的研究进展.本文最后提出了在多柔体系统动力学优化研究中值得关注的若干问题.     

直升机下落碰撞的动力学响应研究

利用碰撞弹簧概念,结合多柔体系统动力学方法,建立了多体系附落碰撞的动力学模型。并通过求出响应,可详细描述碰撞过程。     

柔性多体系统刚-柔耦合动力学

首先指出大量复杂系统动力学与控制性态分析与优化等工程问题对柔性多体系统动力学领域的进一步需求,在回顾柔性多体系统动力学研究的若干阶段与当前的研究现状后指出:柔性多体系统刚- 柔耦合动力学的研究是多体系统动力学的一个新的阶段．文末提出了刚- 柔耦合动力学的研究任务。      

柔性多体系统动力学研究现状与展望

对柔性多体系统动力学的研究现状进行了概括和总结,主要从柔性体建模方法、刚柔耦合动力学、接触碰撞问题、多物理场耦合、微分代数方程求解技术、控制方法、设计优化及软件开发和实验研究等几个研究方向进行总结,并对未来的研究方向做了展望.     

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。     

柔性多体系统接触/碰撞动力学的若干关键问题

归纳了柔性多体系统接触/碰撞动力学中的4个关键问题: 接触区域的处理方法、 接触作用的力学模型、 柔性体的运动学描述和约束问题的数值方法. 针对这4个问题, 综述了柔性多体领域和有限元领域的现有方法, 指出了这些方法的优点和不足. 进一步提出了柔性多体系统接触/碰撞问题的发展趋势.     

作大范围回转运动柔性梁斜碰撞动力学研究

为正确估计由于碰撞引起的多柔体系统动力学特性的变化,针对作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况,在考虑刚柔耦合效应的多柔体系统动力学建模理论的基础上,利用假设模态法建立起重力场作用下的柔性梁一致线性化动力法向碰撞过程中系统的动力行为。基于Ｈｅｒｔｚ接触理论和非线性阻尼项建立法向碰撞接触模型,基于线性切向接触刚度建立柔性梁切向碰撞接触模型,提出的数值算法保证了计算结果的合理性,给出的仿     

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)     

Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.     

Dynamic characteristic and stability analysis of a beam mounted on a moving rigid body

The phenomenon of dynamic stiffening has drawn general interest in flexible multi-body systems. In fact, approximately analytical, numerical and experimental research have proved that both dynamic stiffening and dynamic softening can occur in flexible multi-body systems. In this paper, the nonlinear dynamic model of a beam mounted on both the exterior and the interior of a rigid ring is established by adopting the general Hamiltons variational principle. The dynamic characteristics of the system are studied using a theoretical method when the rigid ring translates with constant acceleration or rotates steadily. The research proves theoretically that both dynamic stiffening and dynamic softening can occur in both the translation as well as the rotation state of multi-body systems. Furthermore, the approximate vibration frequency, critical value and post-buckling equilibria of the translational beam with constant acceleration are obtained by employing the assumed modes method, which validates the theoretical results. The L² norm stability of the trivial equilibrium of the system with the external beam and the L norm stability of the bending of the external beam are proved by employing the energy–momentum method.This research was supported by the National Natural Science Foundation of China (10272002) and the Doctoral Program from the Ministry of Education of China (20020001032).     

A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint

Impact affects the dynamic characteristics of mechanical multi-body systems and damages those rotating parts, such as the joint rolling element bearings, which are high-precision, defect intolerant components. Based on multi-body dynamic theory, Hertzian contact theory, and a continuous contact model, this study proposed a modelling method that can describe the dynamic behaviour of planar mechanical multi-body systems containing a rolling ball bearing joint under impact. In this method, the rigid bodies and bearing joint were connected according to their joint force constraints; the impact constraint between the multi-body system and the target rigid body was constructed using a continuous contact force model. Based on this method, the reflection relationship between the external impacts of the mechanical multi-body system and the variation law governing the dynamic load on the rolling bearing joint were revealed. Subsequently, an impact multi-body system, which was composed of a sliding–crank mechanism containing a rolling ball bearing joint and the target rigid body with an elastic support, was analysed to explore the dynamic response of such a complex discontinuous dynamic system andthe relevant relationship governing the dynamic load on the rolling bearing joint. In addition, a multi-body dynamic simulation software was used to build a virtual prototype of the impact slider–crank system. Compared with the theoretical model, the prototype had an additional deep groove ball bearing. That is to say, the prototype model took account of the specific geometric structural characteristics and the complex contact relationship of the inner and outer races, rolling balls, and bearing cage. Finally, the effectiveness of the theoretical method proposed in this study was verified by comparative analysis of the results. The results suggested that the external impact of a mechanical multi-body system was prone to induce sudden changes in the equivalent reaction force on its bearing joint and the dynamic load carried on its rolling balls. This study provided an effective method for exploring the distribution characteristics of dynamic loads on rolling ball bearing joints under working impact load conditions. Moreover, it offered support for the parameter optimisation of geometric structure, performance evaluation, and dynamic design of the rolling ball bearings.     

柔性曲梁多体系统的研究现状和展望

本文对近几年来柔性多体系统建模理论的研究进展进行了评述, 详细阐述了曲梁结构多体系统动力学研究的理论背景和工程意义. 结合连续介质力学和多体系统动力学理论, 介绍了平面曲梁、空间曲梁应变位移场的描述以及几何非线性问题研究现状. 通过国内外文献及已有的研究, 综述了现有曲梁的离散化方法, 以及这些方法对于定曲率、变曲率曲梁的适用性. 然后, 总结了曲梁刚柔耦合动力学建模和数值计算中的难点问题, 介绍了平面曲梁、空间曲梁实验研究的现状. 最后, 综合全文, 提出了目前研究存在的难点问题, 以及计划解决这些难点问题的方法.      

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multi-body systems involving impact should consider the local plastic deformation and the strict requirements of the spa-tial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlin-ear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.     

Dynamics of Multi-Body Rotors: Numerical and Experimental FEM Analysis of the Scientific Earth Experiment Galileo Galilei Ground

Some small scientific satellites can be regarded as free, multi-body, supercritical and statorless rotors. Classical rotordynamics does not cover the dynamic behaviour and the stability analysis of such rotating systems, being focused on fixed rotors. Attitude dynamics usually deals with single rigid spacecrafts, sometimes equipped with flexible appendices like solar arrays or antennas. The case of the Galileo Galilei Ground (GGG) test facility is herewith analyzed through a numerical and experimental investigation on the dynamic behaviour of a fixed multi-body fast-spinning rotor in order to validate the design approach proposed for Galileo Galilei (GG) spacecraft.     

柔性多体碰撞问题的多变量方法

针对柔性多体系统碰撞问题的特点, 提出了柔性多体系统碰撞问题的多变量方法. 在未碰撞阶段和分离后的阶段, 多变量方法考虑了物体大范围运动与变形的耦合.在碰撞阶段, 考虑非碰撞区域的变形, 对非碰撞区域用浮动参考系方法求解, 对发生碰撞的局部区域用非线性有限元方法求解. 非碰撞区域采用浮动基位形坐标和柔性体相对浮动基的变形模态坐标描述, 大大减缩了变量的维数,提高了计算效率. 碰撞局部区域采用非线性有限元节点坐标描述, 可以得到碰撞局部区域高精度的应力、应变响应, 而且可以反映碰撞局部区域的大变形、塑性等非线性响应. 该方法既能体现碰撞对系统大范围运动和长期动力学仿真的影响, 又能精确反映出碰撞发生的微小时间段内物体碰撞局部区域的应力、应变响应, 表现出碰撞过程中物体接触区域的演化历程.介绍了两杆正碰撞与铅垂面内双摆撞击自由圆盘的算例, 设计了两柔性杆正碰撞实验,多变量方法的数值仿真结果与实验测量结果很好地吻合.