中心刚体-变截面梁系统的动力学特性研究

对在平面内做大范围转动的中心刚体-变截面梁系统的动力学进行了研究.考虑柔性梁横向弯曲变形和纵向伸长变形, 且在纵向位移中计及由于横向变形而引起的纵向缩短项, 即非线性耦合变形项. 采用假设模态法描述变形, 运用第二类Lagrange方程推导得到系统刚柔耦合动力学方程. 在此基础上对做大范围旋转运动的中心刚体-楔形梁以及中心刚体-梯形梁模型的动力学进行了详细研究. 研究表明: 梁宽比、梁高比以及梯形梁变截面位置都对系统的动力学特性有很大影响.      

考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真

对在平面内做大范围转动的中心刚体柔性梁系统的动力学进行了研究,建立了考虑大变形效应的系统刚柔耦合动力学模型,并进行了动力学仿真.该动力学模型不但考虑了柔性梁横向弯曲变形和纵向变形(包含轴向拉伸变形和横向弯曲变形而引起的纵向缩短项),还考虑了纵向变形对曲率的影响,称为曲率纵向变形效应.在以往的研究中,柔性梁的横向弯曲变形能往往直接使用柔性梁横向弯曲变形来表达,并没有考虑纵向变形的影响.为了考虑柔性梁纵向变形对横向弯曲变形能的影响,在浮动坐标系下使用柔性梁参数方程形式的精确曲率公式来计算柔性梁的弯曲变形能.在此基础上建立了基于浮动坐标系的考虑曲率纵向变形效应的刚耦合动力学模型.论文给出了数值仿真算例,验证了本文所建的动力学模型既能适用于柔性梁的小变形问题,又能适用于大变形问题,且较现有高次刚柔耦合动力学模型更加适用于大变形问题的处理.论文还通过与能处理柔性梁大变形问题的绝对节点坐标法的比较,验证了模型的正确性.      

旋转楔形-回形梁的高次动力学建模和末端变形分析

对四种不同结构中心刚体-柔性Euler Bernoulli梁系统进行刚柔耦合动力学分析．其中以等截面梁、变截面梁、等截面回形梁、变截面回形梁为对象，研究楔形梁及回形梁对系统的末端变形位移影响．变截面梁的宽高尺寸沿着轴向线性变化．梁的变形包含了轴向、横向、耦合变形项（横向弯曲引起的纵向缩短）．采用假设模态法和第二类Lagrange方程建立系统的动力学方程，并用C++编写软件进行动力学仿真．研究表明：在相同条件下，梁的截面尺寸及空心部分对梁末端变形位移影响十分明显，且当梁在较大变形情况下，该高次耦合模型依然能得到正确的结果，因此在针对实际结构建模时，建立符合实际截面的模型至关重要．     

旋转薄板的一种高次动力学模型与频率转向

对固结于转动刚体上柔性薄板的刚柔耦合动力学和频率转向特性进行了深入研究,建立了系统的高次刚柔耦合动力学模型,该动力学模型计入了由于横向变形而引起的面内纵向缩短项,即非线性耦合变形量,并且完整保留了与非线性耦合变形量相关的所有项. 研究表明,高次耦合模型不仅适用于小变形问题,而且还适用于大变形问题,弥补了一次近似耦合模型在处理大变形问题上的不足. 旋转悬臂薄板相邻两阶模态间既有柔和的频率转向现象也有剧烈的频率转向现象. 柔和的频率转向伴随着的振型转换的过程是连续的,而剧烈的频率转向伴随着的振型转换的过程则是不连续的. 相隔多阶模态间存在传递性频率转向,并伴随着振型转移.      

柔性梁刚柔耦合碰撞动力学及变形传播研究

运用柔性多体系统刚柔耦合动力学理论,研究了作大范围回转运动柔性梁的碰撞动力学问题.考虑柔性梁的横向变形,以及横向变形引起的纵向缩短项即非线性耦合变形项.采用基于Hertz接触理论及非线性阻尼理论的非线性弹簧阻尼模型来求解碰撞过程中产生的碰撞力,运用第二类拉格朗日方程建立了系统的刚柔耦合碰撞动力学方程.编制仿真软件进行动力学仿真计算,得到了碰撞力和系统动力学响应,对比分析了不同动力学模型对系统动力学响应的影响.同时研究了碰撞导致的柔性梁横向变形传播的波动特性.     

基于径向基点插值法的旋转Mindlin板高次刚柔耦合动力学模型

将无网格径向基点插值法(radial point interpolation method,RPIM)用于中心刚体?旋转柔性板的动力学分析.基于浮动坐标系方法和一阶剪切变形理论即Mindlin板理论,考虑剪切变形的影响,并计入板面内变形的非线性耦合变形项,采用径向基点插值法描述板的变形场,保留动能中有关非线性耦合变形项...     

耦合变形对大范围运动柔性梁动力学建模的影响

柔性梁在作大范围空间运动时,产生弯曲和扭转变形,这些变形的相互耦合形成了梁在纵向以及横向位移的二次耦合变量。本文考虑了变形产生的几何非线性效应对运动柔性梁的影响,在其三个方向的变形中均考虑了二次耦合变量,利用弹性旋转矩阵建立了准确的几何非线性变形方程,通过Lagrange方程导出系统的动力学方程。仿真结果表明,在大范围运动情况下,仅在纵向变形中计及了变形二次耦合量的一次动力学模型,与考虑了完全几何非线性变形的模型具有一定的差异。     

旋转悬臂梁的刚柔耦合动力学建模与频率分析

对固结于转动刚体上外接柔性梁的刚柔耦合动力学建模和频率特性进行了研究,在精确描述柔性梁非线性变形的基础上,利用Hamilton变分原理和假设模态法,在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下,推导出考虑"动力刚化"项的一次近似耦合模型。首先忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型做无量纲化处理,分析梁固有频率对模态截断数的依赖性;其次研究在一次近似简化模型和零次近似简化模型下,调谐角速度与共振现象的关系;最后分析一次近似耦合模型的动力特性。研究发现,为保证计算的精度,模态截断数应随无量纲角速度的增大而增加,合理的模态截断数具有收敛值;一次近似简化模型下悬臂梁横向弯曲振动不存在共振调谐角速度,一次耦合模型下柔性梁并没有出现屈曲失稳现象。现有典型文献的相关结论是值得商榷的。     

An image encryption algorithm based on compound homogeneous hyper-chaotic system

A new dynamic model of a rotating flexible beam with a concentrated mass located in arbitrary position is derived based on the absolute nodal coordinate formulation, and its modal characteristics are investigated in this paper. To consider the concentrated mass at an arbitrary location of the beam, a Dirac’s delta function is used to express the mass per unit length of the beam. Based on the proposed dynamic model, the frequency analysis is performed. The nonlinear equation is transformed into the linear one via employing the linear perturbation analysis method. The stiffness matrix of static equilibrium of the system under the deformed condition is obtained, in which the effect of coupling between the longitudinal deformation and transversal deformation is included. This means even if only the chordwise bending equation is solved, the longitudinal vibration effect can be still considered. As we know, once the longitudinal deformation is large, it will significantly affect the chordwise bending vibration. So the proposed model in this paper is more accurate than the traditional dynamic models which are usually lack of the coupling terms between the longitudinal deformation and transversal deformation. In fact, the traditional dynamic models for the chordwise vibration analysis in the existing literature are usually linear due to neglecting the coupling terms, and consequently, they are only suitable for the modal characteristic analysis of a beam under small deformations. In order to get some general conclusions of the natural frequencies and mode shapes, the equation which governs the chordwise bending vibration of the rotating beam is transformed into a dimensionless form. The dynamic model presented in this paper is nonlinear and can be conveniently used to analyze the modal characteristics of a rotating flexible beam with large deformations. To demonstrate the power of the new dynamic model presented in this paper, the dynamic simulations involving the comparisons between the different frequencies obtained using the model proposed in this paper and the models in the existing literature and the investigating in frequency veering and mode shift phenomena are given. The simulation results show that the angular velocity of the flexible beam will give rise to the phenomena of the natural frequency loci veering and the associated mode shift which is verified in the previous studies. In addition, the phenomena of the natural frequency loci veering rather than crossing can be observed due to the changing of the magnitude of the concentrated mass or of the location of the concentrated mass which are found for the first time. Furthermore, there is an interesting phenomenon that the natural frequency loci will veer more than once due to different types of mode coupling between the bending and stretching vibrations of the rotating beam. At the same time, the mode shift phenomenon will occur correspondingly. Additionally, the characteristics of the vibration nodes are also investigated in this paper.     

径向基点插值法在旋转柔性梁动力学中的应用

将无网格径向基点插值法用于旋转柔性梁的动力学分析. 利用无网格方法对柔性梁的变形场进行离散,考虑梁的纵向拉伸变形和横向弯曲变形,并计入横向弯曲变形引起的纵向缩短,即非线性耦合项,运用第二类拉格朗日方程推导得到系统刚柔耦合动力学方程. 将无网格径向基点插值法的仿真结果有限元法和假设模态法进行比较分析,说明假设模态法的局限性,并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性,并讨论了径向基形状参数的影响. 同时运用3 种求解系统动力学方程的方法:纽马克方法、4阶龙格库塔法、亚当姆斯预报校正法,并比较各方法的计算效率, 结果表明纽马克方法最快.      

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．     

旋转中心刚体-FGM梁刚柔热耦合动力学特性研究

对旋转中心刚体-功能梯度材料(functionally graded material,FGM)梁刚柔热耦合动力学特性进行研究.FGM梁为物理性能参数沿厚度方向呈幂律分布的欧拉伯努利梁.考虑柔性梁的横向弯曲变形和轴向拉伸变形, 并计入横向弯曲变形引起的纵向缩短,即非线性耦合变形量.考虑变截面空心梁在外部高温、内冷通道冷却情况下的热力耦合对系统动力学特性的影响,求解得到FGM梁沿厚度方向分布的温度场, 进而在本构关系中计入热应变.采用假设模态法对柔性梁变形场进行离散,运用第二类拉格朗日方程推导得到系统的刚柔热耦合动力学方程,并编制动力学仿真软件, 然后通过仿真算例对系统的动力学问题进行研究.结果表明:不同截面梁动力学响应差异较大, 因此需对实际系统合理建模;大范围运动已知时, 考虑热冲击载荷的FGM梁将有效抑制横向弯曲变形,而大范围运动恒定时随热冲击的叠加会出现高频振荡; 大范围运动未知时,外力矩和热冲击载荷相互作用产生热力耦合效应, 导致系统呈现高频振荡,同时与中心刚体大范围旋转运动产生刚柔热耦合效应.      

基于变形场不同离散方法的柔性机器人动力学建模与仿真

研究了基于变形场不同离散方法的柔性机器人动力学建模和仿真问题. 针对多杆空间链式柔性机器人系统,采用假设模态法、有限元法、Bezier 插值方法和B 样条插值方法对柔性杆变形场进行描述,构造统一形式,运用Lagrange 方法,结合4×4 齐次变换矩阵,在计入柔性杆横向弯曲变形引起的纵向缩短的情况下,推导得到多杆空间柔性机器人动力学方程,并编制基于4 种变形场不同离散方法的多杆空间链式柔性机器人仿真软件.通过仿真算例对柔性机器人系统的动力学问题进行研究. 仿真结果表明:有限元法的计算效率较低;假设模态法在处理较大变形问题时其精度低于Bezier 插值方法和B 样条插值方法的精度;作为新的变形体离散方法,Bezier 插值方法和B 样条插值方法可以有效地描述柔性杆的变形场,并能运用到多杆空间柔性机器人动力学建模中.      

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

中心刚体-柔性梁系统的最优跟踪控制

对考虑阻尼影响的中心刚体-柔性梁系统的动力特性和主动控制进行研究. 研究 中考虑了3种动力学模型：一次近似耦合模型、一次近似简化模型和线性化模型. 一次近 似模型中同时考虑了柔性梁的轴向变形和横向变形. 若在一次近似耦合模型中忽略轴向变 形的影响，则可得出一次近似简化模型. 线性化模型是对一次近似简化模型的线性化处理. 另外研究中考虑了3种阻尼因素：结构阻尼、风阻、中心刚体轴承处的阻尼. 控制设计采 用最优跟踪控制方法. 给出了从物理测量中提取模态坐标的滤波器方法. 研究结果显 示，一次近似简化模型能够有效地对系统的动力学行为进行描述；阻尼对系统的动力学特 性有着重要影响；当系统大范围运动为低速时，模态滤波器能够较好地提取出控制律所需 的模态坐标，最优跟踪控制方法能够使得系统跟踪所期望的运动轨迹，并且柔性梁的弹性 振动可得到抑制.     

Dynamic modeling and modal truncation approach for a high-speed rotating elastic beam

Summary  In the classical finite element analysis of beams, the nonlinear terms of deformation are ignored due to the linearization of deformation based on the assumptions of structural dynamics. Since the number of generalized coordinates is large in flexible bodies when using the finite element method (FEM), the modal truncation approach (MTA) is usually used for improving computational efficiency, and only lower-order transverse modes are chosen. In this paper, dynamic modeling and application of the MTA to a high-speed rotating beam are studied. The foreshortening displacement is included in the longitudinal displacement, therefore the dynamic modeling takes account of the effect of geometric nonlinearity. Equations of a rotating beam are obtained and the FEM and MTA are used for discretization. The applicability of the MTA to a high-speed rotating elastic beam is verified. The comparison of the results obtained by the FEM and MTA shows that in the case of a high-speed rotation, the centrifugal force can excite high-order transverse modes. Since using lower-order transverse modes for modal truncation obviously can cause error, addition of more transverse modes may improve the result. Furthermore, a coupling effect between axial and transverse displacements is revealed. It is shown that in the case of a sudden change of the axial displacement, the inclusion of the axial modes can significantly improve the response. Received 10 April 2001; accepted for publication 26 March 2002 This work was supported by the National Science Foundation of China (19832040) and the National Education Ministry of China (2000024818), for which the authors are grateful.     

考虑尺度效应的微梁刚柔耦合动力学分析

摘要：不少微观实验已经证实,微尺度领域材料的力学性能存在尺度效应。文章以转动刚体、柔性微梁组成的刚柔耦合系统为研究对象,采用偶应力理论（又称 Cosserat理论）研究微梁动力学特性的尺度效应,运用拉格朗日方程推导出系统考虑尺度效应的一次近似刚柔耦合动力学方程。仿真结果表明,较本文提出的一次近似耦合模型,传统的零次近似耦合模型在刚体作高速旋转时不能正确地描述微梁的动力学行为;尺度效应使微梁振动的振幅减小,频率增大。     

考虑几何非线性和热效应的刚-柔耦合动力学

温度增高和温度梯度会引起梁的纵向、横向变形位移,在一定程度上对刚-柔耦合规律产生影响.该文考虑热应变,从平面梁的非线性的应变与位移关系式出发,建立了刚体运动、弹性变形和温度相互耦合的有限元离散的热传导方程和动力学方程.研究热流作用下的中心刚体-简支梁系统的刚-柔耦合动力学性质,揭示了几何非线性项和热应变对弹性变形和刚体运动影响.     

Dynamic analysis of a flexible hub-beam system with tip mass

For a dynamic system of a rigid hub and a flexible cantilever beam, the traditional hybrid coordinate model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zeroth-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of some rigid–flexible coupling systems with high rotational speed. In this paper, characteristics of a flexible hub-beam system with a tip mass is studied. Based on the Hamilton theory and the finite element discretization method, and in consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam, the rigid–flexible coupling dynamic model (referred as the first-order approximation coupling (FOAC) model in this paper) and the corresponding model in non-inertial system for the flexible hub-beam system with a tip mass are presented firstly, then the dynamic characteristics of the system are studied through numerical simulations under twos cases: the large motion of the system is known and is unknown. Simulation and comparison studies using both the traditional zeroth-order model and the proposed first-order model show that even small tip mass may affect dynamic characteristics of the system significantly, which may result in the largening of vibrating amplitude and the descending of vibrating frequency of the beam, and may affect end position of the hub-beam system as well. The effect of the tip mass becomes large along with the increasing of rotating speed of large motion of the system. When the large motion of the system is at low speed, the traditional ZOAC model may lead to a large error, whereas the proposed FOAC model is valid. When the large motion is at high speed, the ZOAC model may result in divergence to the dynamic problem of the flexible hub-beam system, while the proposed second model can still accurately describe the dynamic hub-beam system.     

大型柔性航天器动力学与振动控制研究进展

随着航天重大工程的逐步实施,航天器正朝着超高速、超大尺度、多功能的方向发展,其面临的发射和运行环境也更加恶劣.航天器发射过程中的振动及其主/被动控制、在轨运行中大型柔性航天器动力学建模与动态响应分析、结构振动与飞行器姿态的混合控制等问题越来越复杂且难于处理;航天器结构的大型化和柔性化(如大阵面天线和太阳翼等)也对其地面试验和半实物仿真提出了挑战.本文着重介绍大型柔性航天器涉及到的动力学与振动控制问题,包括航天器发射过程中的整星隔振,大型柔性结构动力学建模与振动响应分析,大型柔性航天器的结构振动与姿轨控耦合动力学及其混合控制等.提炼出航天动力学与控制领域中亟待解决的若干基础科学问题,包括:多刚柔体系统动力学建模与模型降阶(涉及大变形柔性体动力学建模、多求解器合作仿真、模型降阶、组合结构动力学建模的解析方法等);复杂结构状态空间模型构建方法与能控性(涉及状态空间模型构建的理论与实验方法、复杂结构振动控制系统的能观性与能控性等);航天器姿态运动与大型柔性结构振动的混合控制律设计(涉及姿态机动与结构振动的鲁棒混合控制、执行机构与压电控制器的协同控制等).