多体机械手的一般动力学模型

本文建立了多体机械手的一般动力学方程.设多体系统是由任意数目的刚体组成的树形拓扑结构,并认为铰是柱铰链,允许具有相对转动和滑动.考虑到实际问题中摩擦力的影响,采用Newton-Euler方法,建立了运动方程.进一步通过构造分配矩阵,将动力学方程分离,得到了一组实用的力方程和运动方程.     

双臂空间机器人姿态、关节协调运动基于RBF神经网络的自适应控制算法

讨论了载体位置无控、姿态受控情况下,双臂空间机器人姿态、关节协调运动的控制问题．由Lagrange第二类方法及系统动量守恒关系,建立了漂浮基双臂空间机器人的系统动力学方程．以此为基础,借助于RBF神经网络技术、GL矩阵及其乘积算子定义,对双臂空间机器人系统进行了神经网络系统建模;之后针对双臂空间机器人所有惯性参数均未知的情况,设计了双臂空间机器人载体姿态与机械臂各关节协调运动基于RBF神经网络的自适应控制算法．提出的控制算法不要求系统动力学方程具有惯常的关于惯性参数的线性性质,且无需预知系统惯性参数的任何信息,也无需对神经网络进行离线训练、学习,因此更适于实时应用．一个平面漂浮基双臂空间机器人系统的数值仿真,证实了该控制算法的有效性．     

多杆空间柔性机器人递推Lagrange动力学建模和仿真

研究了多杆空间柔性机器人的动力学问题.运用Lagrange方法,结合齐次变换矩阵,推导得到了多杆空间柔性机器人动力学方程,在推导过程中采用了运动学递推策略以提高计算效率.建模时除考虑柔性构件的横向弯曲变形外,还计及了构件的扭转变形.基于上述理论研制了多杆空间柔性机器人动力学仿真软件,并对一空间柔性机器人进行了动力学仿真计算,验证了理论和软件的先进性能.     

一维非线性周期结构中弹性波传播的辛数学方法

利用辛数学方法分析了质量-弹簧非线性周期结构链中弹性波的传播问题．首先利用能量方法得到频域动力方程,随后通过小量变换将非线性动力方程线性化,得到辛矩阵,进而通过求解辛矩阵的本征值问题来研究波的传播性能．质量-弹簧模型中的弹簧刚度非线性对结构链的传播特性影响很大,研究发现非线性明显改变了周期结构的传播性能,而且不同于线性结构,非线性结构的传播特性与入射波强度有关．数值算例表明随着非线性强度及入射波强度的增大,传播通带宽度逐渐减小,禁带宽度逐渐增大．当入射波强度增大到一定值时,弹性波无法在结构中进行传播．与一般递归方法的比较分析,验证了辛数学方法在非线性周期结构波传播问题中的有效性与优越性．     

水平振动下桩基的非线性动力学特性

将桩-土系统看成一个嵌入桩基的粘弹性半空间,利用连续介质力学的方法,在空间柱坐标系中建立了非线性桩-土相互作用的数学模型——桩土耦合的非线性边值问题．在频率域内研究了水平振动下桩基的非线性动力学特性,考察了轴力对桩基非线性动力学特性的影响．研究了多种参数对桩基动力学特性的影响,特别是轴力对桩基刚度的影响A·D2结果表明:在轴力作用下桩基可能丧失承载能力．因此,研究桩基水平振动的力学行为时,必须考察轴力的影响．     

具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析

研究了一类具有缺陷的不可压缩超弹性材料球壳的径向对称运动问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压缩的neo-Hookean材料．得到了描述球壳内表面运动的二阶非线性常微分方程,并给出了方程的首次积分．通过对微分方程的解的动力学行为的分析,讨论了材料的缺陷参数和球壳变形前的内外半径的比值对解的定性性质的影响,并给出了相应的数值算例．特别地,对于一些给定的参数,证明了存在一个正的临界值,当内压与外压之差小于临界值时,球壳内表面随时间的演化是非线性周期振动;当内压与外压之差大于临界值时,球壳的内表面半径随时间的演化将无限增大,即球壳最终将被破坏．     

非线性非完整约束空间准坐标表示的系统的基本动力学方程

用与准坐标表示的一阶非线性非完整约束超曲面的基矢量共线的量和米歇尔斯基方程点来作为一阶非线性非完整约束变质量系统的基本动力学方程．由此可导出用准坐标表示的各种形式的运动微分方程．和约登（Jourdain）原理相容．举了例子．     

KdV方程的延拓结构

利用外微分形式系统和Lie代数表示理论提出了求解非线性波方程Lax对的延拓结构理论,该方法是构造非线性波方程Lax对的系统最有效的方法.其关键在于如何给出延拓代数的具体表示,如微分算子表示或矩阵表示.如果一个非线性波方程具有非平凡的延拓代数,则称其延拓代数可积,本篇论文主要利用延拓结构理论,讨论KdV方程的解,同时给出...     

树形多刚体系统动力学方程

本文提出描述联结成树形多刚体系统位置与排列的“位形图”.在不需要引入“增广体”和“子系统”等概念的情况下,本文利用“位形矩阵”研究了树形多刚体系统的运动,并推导出其动力学方程.树形多刚体系统的动态参数与其结构的密切关系在这样的动力学方程中明显地表示出来.     

自由漂浮空间非合作目标的运动预测

空间非合作目标的运动预测是航天器在轨服务中的一个重要问题。在获得非合作目标的运动预测结果后,追踪星即可规划运动轨迹以接近目标并对其进行捕获。该文提出了一种自由漂浮空间非合作目标的运动预测方法。该方法的核心思想是首先辨识出目标的姿态动力学参数和目标的质心运动学参数,然后利用参数辨识结果和目标的动力学方程实现对目标的运动预测。在姿态动力学参数的辨识过程中,首先对目标的惯性参数进行初步辨识,然后采用自适应无迹Kalman滤波器对姿态动力学参数进行粗略辨识,最后通过最优化方法进一步提高姿态动力学参数的辨识精度。该文通过数值仿真验证了所提运动预测方法的有效性。仿真结果表明,无论目标是做单轴旋转还是翻滚运动,所提运动预测方法都能够实现对目标的长时间高精度的运动预测。     

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing.     

The Vibrational Behavior of Coupled Bladed Disks with Variable Rotational Speed

Low pressure steam turbine blades are subjected to high static and dynamic loads during operation. These loads strongly depend on the turbine's rotational speed, leading to entirely new load conditions. To avoid high dynamic stresses due to the forced vibrations, a coupling of the blades, such as shrouds or snubber coupling, is applied to reinforce the structure. In this work the influence of the rotational speed on the vibration behavior of shrouded blades is investigated. Two fundamental phenomena are considered: the stress stiffening and the spin softening effect. Both effects are caused by centrifugal forces and affect the structural mechanical properties, i.e. the stiffness matrix K , of the rotating system. Since the rotational speed Ω appears quadratically, it is possible to derive the stiffness matrix as a second order matrix polynomial in Ω² [3]. In the case of shrouded blades, contact forces between neighboring blades must be taken into account. The contact status and the pressure distribution in particular is strongly influenced by the rotational speed, respectively, centrifugal forces, caused by the untwisting and radial deformation of the blades. For the calculation, a three dimensional structural mechanical model including a spatial contact model is considered. The solution of the nonlinear equations of motion is based on the well known Multiharmonic Balance Method [2]. Here, the nonlinear forces are computed in the time domain and transferred in the frequency domain by the use of the Fast Fourier Transformation (FFT), also known as the Alternating Frequency Time method (AFT) [1]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of mass moment of inertia on the normal modes of a preloaded solar array mast

Earth-orbiting spacecraft often contain solar arrays or antennas supported by a preloaded mast. Due to weight and cost considerations, the supporting structures of the spacecraft appendages are made extremely light and flexible. Therefore, it is essential to investigate the influence of all physical and structural parameters on the dynamic behavior of the overall structure. The governing equation of motion and its general solution for the preloaded mast are developed. Furthermore, the mass moment of inertia of the mast subjected to bending vibrations is included in the governing equation of motion to investigate its influence on determining the circular frequencies. To verify the developed formulations, a finite element technique was implemented. The accuracy and limitation of the technique on calculating the circular frequencies are discussed. Although the study described in this paper primarily focuses on the mast for the space station solar arrays, the developed formulations and techniques can be applied to any large and flexible beam in zero gravity.     

Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight

This paper focuses on the nonlinear vibration phenomenon caused by aircraft hovering flight in a rub-impact rotor system supported by two general supports with cubic stiffness. The effect of aircraft hovering flight on the rotor system is considered as a maneuver load to formulate the equations of motion, which might result in periodic response instability to the rotor system even the eccentricity is small. The dynamic responses of the system under maneuver load are presented by bifurcation diagrams and the corresponding Lyapunov exponent spectrums. Numerical analyses are carried out to detect the periodic, sub-harmonic and quasi-periodic motions of the system, which are presented by orbit diagrams, phase trajectories, Poincare maps and amplitude power spectrums. The results obtained in this paper will contribute an understanding of the nonlinear dynamic behaviors of aircraft rotor systems in maneuvering flight.     

带有质心运动的挠性空间飞行器运动方程

一、引言随着空间事业的不断发展,空间飞行器的种类不断增多,其动力学结构也越来越复杂.其中绝大部分飞行器既不是单一的刚体,也不是单一的弹性体,而是既有弹性体又有刚体组成的混合体.带有大型太阳帆板的卫星就是其中的一个典型例子.     

Multilayer beams: A geometrically exact formulation

Summary We review and extend our recent work on a new theory of multilayer structures, with particular emphasis on sandwich beams/1-D plates. Both the formulation of the equations of motion in the general dynamic case and the computational formulation of the resulting nonlinear equations of equilibrium in the static case based on a Galerkin projection are presented. Finite rotations of the layer cross sections are allowed, with shear deformation accounted for in each layer. There is no restriction on the layer thickness; the number of layers can vary between one and three. The deformed profile of a beam cross section is continuous, piecewise linear, with a motion in 2-D space identical to that of a planar multibody system that consists of three rigid links connected by hinges. With the dynamics of this multi (rigid/flexible) body being referred directly to an inertial frame, the equations of motion are derived via the balance of (1) the rate of kinetic energy and the power of resultant contact (internal) forces/couples, and (2) the power of assigned (external) forces/couples. The present formulation offers a general method for analyzing the dynamic response of flexible multilayer structures undergoing large deformation and large overall motion. With the layersnot required to have equal length, the formulation permits the analysis of an important class of multilayer structures with ply drop-off. For sandwich structures, an approximated theory with infinitesimal relative outer-layer rotations superimposed onto finite core-layer rotation is deduced from the general nonlinear equations in a consistent manner. The classical linear theory of sandwich beams/1-D plates is recovered upon a consistent linearization. Using finite element basis functions in the Galerkin projection, we provide extensive numerical examples to verify the theoretical formulation and to illustrate its versatility. Dedicated to the memory of Professor Juan Carlos Simo, whose early demise is a great loss for the applied and computational mechanics community This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.     

Global mode method for dynamic modeling of a flexible-link flexible-joint manipulator with tip mass

In this paper, the global mode method (GMM) is proposed to obtain a reduced-order analytical dynamic model for a signal flexible-link flexible-joint (SFF) manipulator. Firstly, the nonlinear partial differential equations (PDE) that govern the motion of the flexible link and flexible joint, respectively, are derived by applying the Hamilton principle. By combining the linearized governing equations of motion for a flexible link and the equation of motion for the flexible joint, the characteristic equation is obtained for the whole system. The natural frequencies and global mode shapes of the linearized model of the SFF manipulator are determined, and orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to truncate the nonlinear PDEs of the SFF manipulator to a nonlinear ordinary differential equation with a few degrees-of-freedom (DOF). For comparison, two other dynamic models of the SFF are derived by employing the assumed mode method (AMM) and finite element method (FEM). To verify the method proposed, the results from the GMM are compared with those obtained from the FEM. The effects of the link length and payload mass on the convergence of AMM model for the first two frequencies are investigated. Based on the dynamic models, obtained by GMM and AMM, dynamical responses for the system with different numbers of modes are worked out numerically, which are compared with those obtained from FEM. These comparisons show a good agreement between the results of the GMM and that of the FEM model, which indeed proved the accuracy and applicability of the GMM model.     

Analytical elastostatic stiffness modeling of parallel manipulators considering the compliance of the link and joint

This paper discusses the analytical elastostatic stiffness modeling of parallel manipulators (PMs) considering the compliance of the link and joint. The proposed modeling is implemented in three steps: (1) the limb constraint wrenches are formulated based on screw theory; (2) the strain energy of the link and the joint is formulated using material mechanics and a mapping matrix, respectively, and the concentrated limb stiffness matrix corresponding to the constraint wrenches is obtained by summing the strain energy of the links and joints in the limb; and (3) the overall stiffness matrix is assembled based on the deformation compatibility equations. The strain energy factor index (SEFI) is adopted to describe the influence of the elastic components on the stiffness performance of the mechanism. Matrix structural analysis (MSA) using Timoshenko beam elements is applied to obtain analytical expressions for the compliance matrices of different joints through a three-step process: (1) formulate the element stiffness equation for each element; (2) extend the element stiffness equation to obtain the element contribution matrix, allowing the extended overall stiffness matrix to be obtained by summing the element contribution matrices; and (3) determine the stiffness matrices of joints by extracting the node stiffness matrix from the extended overall stiffness matrix and then releasing the degrees of freedom of twist. A comparison with MSA using Euler–Bernoulli beam elements demonstrates the superiority of using Timoshenko beam elements. The 2PRU-UPR PM is presented to illustrate the effectiveness of the proposed approach. Finally, the global SEFI and scatter matrix are used to identify the elastic component with the weakest stiffness performance, providing a new approach for effectively improving the stiffness performance of the mechanism.