二维系统传递矩阵法

以薄板横向振动的振动特性问题为例提出了二维系统传递矩阵法. 从质点和无质量梁的传递 矩阵出发，建立了按列排列的薄板子结构的传递矩阵. 用二维系统传递矩阵法获得了整个板 的总体传递方程，从而可得到板在任意一种边界条件下的特征方程. 数值求解了两种情况下 薄板横向振动的固有振动特性. 计算结果表明，用该方法可用于研究类似薄板的二维系统的 动力学问题，且无需建立系统的总体动力学方程.     

约束层阻尼板动力学问题的半解析解

利用条形传递函数方法(SDTFM)得到了约束层阻尼(CLD)板动力学问题的半解析解.首先对CLD板沿纵向离散成多个条形单元,基于Hamilton原理推导出条形单元的刚度矩阵和质量矩阵,仿照有限元法组集得到系统的总刚度矩阵和总质量矩阵.经Laplace变换后引入状态向量,采用分布参数传递函数方法在状态空间内建立CLD板的控制方程并进行求解.最后以对边固支和悬臂CLD板为例,得到了板的动力学特性和频响曲线,并与NASTRAN或相关文献结果进行了比较,吻合良好,验证了该方法的有效性.从推导过程和算例可以看出,该方法所需的单元数目少,获得的是半解析解,计算效率高且准确可靠.     

Numerical modelling of structure vibrations under inertial moving load

Inertial loading of structures by mass travelling with near-critical velocity has been intensively debated. In the literature a moving mass is replaced by an equivalent force or an oscillator that is in permanent contact with the structure. A direct mass matrix modification method frequently implemented in the finite element approach gives reasonable results only in the range of relatively low velocities and for low mass value if compared with the mass of a structure. However, existing solutions are incorrect and are not implemented in commercial computer codes. In this paper we present the space–time finite element approach to the problem. The interaction of the moving mass/supporting structure is described in a local coordinate system of the space-time finite element domain. Resulting characteristic matrices include inertia, Coriolis and centrifugal forces. Simple modification of matrices in the discrete equations of motion allows us to gain accuracy in a wide range of velocity, up to the over-critical speed. Numerical examples of string and beam vibrations prove the simplicity and efficiency of the method.     

Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work

Inverse dynamics of a general model of a spherical star-triangle (SST) parallel manipulator (Enferadi and Akbarzadeh Tootoonchi, Robotica 27:663–676, 2009) is the subject of this paper. This manipulator is of type 3-RRP, has good accuracy and relatively a large workspace which is free of singularities (Enferadi and Akbarzadeh Tootoonchi, Robotica, Revised paper, 2009). First, inverse kinematics utilizing the angle axis representation is solved. Next, velocity and acceleration analysis as well as link Jacobian matrices are obtained in invariant form. Finally, a systematic approach based on the principle of virtual work and the concept of link Jacobian matrices is presented. This method allows elimination of constraint forces and moments at the passive joints from motion equations. It is shown that the dynamics of the manipulator can be reduced to solving a system of three linear equations with three unknowns. Moreover, a computational algorithm for solving the inverse dynamics is developed. Two examples with different trajectories for the moving spherical platform are presented and motor torques are obtained. Results are verified using a commercial dynamics modeling package.     

多体系统传递矩阵法研究进展

作为一种多体系统动力学新方法, 多体系统传递矩阵法由于其无需系统总体动力学方程和快速计算的特点, 已被广泛用于各种多管火箭、自行火炮、舰炮等复杂大型机械系统动力学分析与设计. 本文介绍了该方法的研究进展, 包括: 线性多体系统传递矩阵法、多体系统离散时间传递矩阵法、二维系统传递矩阵法、受控多体系统传递矩阵法、多体系统传递矩阵法和通常动力学方法的混合方法等, 给出了该方法解决自行火炮、多管火箭武器多体系统动力学的重大工程应用实例.      

完整系统的多刚体系统离散时间传递矩阵法研究

基于多刚体系统离散时间传递矩阵法，采用提高计算精度的方法，研究具有大运动、非线性特征的完整系统在平面、空间中的动力学响应。提出了对部分变量重新赋值的违约修正方法，计算机仿真表明了其有效性。多刚体系统离散时间传递矩阵法不须进行违约修正，体现了该方法建模灵活性较强、程式化程度较高的优点。     

可倾瓦径向滑动轴承完整动特性系数的分析模型

基于可倾瓦径向滑动轴承瓦块的扰动特性,提出了计算轴承完整动力系数的数学解析模型。在由单块瓦和轴颈构成的子系统上建立局部动坐标参考系,全局广义位移向量可以通过简练的步骤转换为局部动坐标系下轴颈的位移向量,利用求解固定瓦轴承动力特性的方法求得的局部动坐标系下的油膜力又可以精确地转换为全局坐标系下的表达形式,全局坐标系下的油膜力向量关于广义位移和广义速度的Jocabian矩阵形成轴承的完整动力特性系数;利用Newton-Raphson方法同时求解瓦块和轴颈在给定的静态载荷下的平衡位置,其中所需用到的系数矩阵恰好为轴承油膜力关于广义位移的Jocabian矩阵的负值,在得到平衡位置的同时可以获得轴承完整的刚度和阻尼矩阵。数值算例证明了此方法的有效性。     

Fast stochastic analysis for non-proportionally damped system

Fundamental principles from structural dynamics, pseudo excitation method and pseudo force method are used to develop a new fast stochastic method for seismic response analysis of non-proportionally damped system. In the method, the mathematical equation of non-proportionally damped system is expressed in the iterative form, based on which the inverse operation of the matrices is avoided. Moreover, the new method does not need the solution of any complex eigenvalue problem, in contrast to other methods found in the literature.     

Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems

The automatic derivation of motion equations is an important problem of multibody system dynamics. Firstly, an overview of the matrix calculus related to Kronecker product of two matrices is presented. A new matrix form of Lagrangian equations with multipliers for constrained multibody systems is then developed to demonstrate the usefulness of Kronecker product of two matrices in the study of dynamics of multibody systems. Finally, the equations of motion of mechanisms are derived using the proposed matrix form of Lagrangian equations as application examples.     

三体轨道动力学研究进展

三体系统轨道动力学问题是航天动力学领域中的经典问题, 具有丰富的理论与工程意义, 并将在人类由近地延伸到深空的航天活动过程中起到至关重要的作用. 本文回顾并总结了三体系统轨道动力学相关研究进展, 并结合未来的深空探测的发展趋势, 展望了三体系统轨道动力学研究中的热点与挑战. 首先阐述了三体问题的研究背景及意义, 简要回顾了三体系统动力学模型的发展历程. 其次, 系统概述了三体系统平衡点附近的局部运动特性, 介绍了平衡点附近周期轨道解析与数值求解方法, 给出了拟周期运动的最新进展. 同时总结了共振轨道、循环轨道、自由返回轨道等三类三体系统全局周期运动的动力学特性与研究进展. 再次, 从不变流形理论和弱稳定边界理论两个方面综述了三体系统中低能量转移与捕获轨道设计的研究进展. 最后, 综述了三体系统轨道动力学在编队飞行、导航星座设计两方面的应用, 并展望了全月面覆盖轨道设计、三体系统下的小推力轨道优化和三体系统的三角平衡点开发利用中值得关注的轨道动力学与控制问题.      

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。     

Libration suppression of tethered space system with a moving climber in circular orbit

This paper studies the dynamics and libration suppression of a tethered system with a moving climber in circular orbits. The tethered system is modeled by a two-piece dumbbell model that consists of one main satellite, one climber and one end-body connected by two straight, massless and inextensible tethers. A new tension control strategy to suppress the libration of the tethered system due to the moving climber is proposed by reeling in-out tether at the end-body without thrust. The control strategy is implemented with the sliding mode control to suppress the libration angle of the climber to zero by the end of climber’s transfer phase. The numerical results show that the proposed control strategy is very effective in suppressing the libration of the climber in the three-body tethered system with tension control only. Furthermore, cases with limited tension control are examined. It reveals that a longer tether between the climber and the end-body is required to supplement the limited tension in suppressing the libration of the climber.     

提高多体系统离散时间传递矩阵法计算精度的研究

深入探讨多体系统离散时间传递矩阵法对平面、空间刚体-光滑铰多体系统运动响应的研究。提出提高该方法计算精度和计算稳定性的方法，导出相应的多端刚体传递矩阵。设计了角坐标的迭代循环，该变量不必采用近似形式，因而提高了计算精度和计算稳定性。其它方法有：1)增加泰勒展开式的高阶项；2)合理选择将速度、加速度表示为位移的线性函数的方法(本文简称线性化方法)；3)合理确定迭代循环的初值等。对4种多体系统进行了计算机仿真研究，表明本文提出的方法有效。     

Using quaternion matrices to describe the kinematics and nonlinear dynamics of an asymmetric rigid body

A set of four quaternion matrices is used to represent the equations of finite rotation theory and to describe the kinematics and nonlinear dynamics of an asymmetric rigid body in space. The results obtained are tested in setting up direction-cosine matrices, calculating three-index symbols, establishing the relationship between the components of angular velocity in body-fixed and space-fixed frames of reference, and using a set of three independent rotations. Euler–Lagrange equations and a set of four quaternion matrices are used to construct a block-matrix model describing the nonlinear dynamics of a free asymmetric rigid body in three-dimensional space. The model gives the matrix Euler’s equations of motion and other special cases. Algorithms adapted to use in a numerical experiment are developed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 133–143, February 2009.     

Nonlinear dynamics of axially moving beam with coupled longitudinal–transversal vibrations

In this study, the nonlinear vibrations of an axially moving beam are investigated by considering the coupling of the longitudinal and transversal motion. The Galerkin method is used to truncate the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. By detuning the axially velocity, the exact parameters with which the system may turn to internal resonance are detected. The method of multiple scales is applied to the governing equations to study the nonlinear dynamics of the steady-state response caused by the internal–external resonance. The saturation and jump phenomena of such system have been reported by investigating the nonlinear amplitude–response curves with respect to external excitation, internal, and external detuning parameters. The longitudinal external excitation may trigger only longitudinal response when excitation amplitude is weak. However, beyond the critical excitation amplitude, the response energy will be transferred from the longitudinal motion to the transversal motion even the excitation is employed on the longitudinal direction. Such energy transfer due to saturation has the potential to be used in the vibration suppression.     

在轨组装空间结构面向主动控制的动力学建模

在轨组装是未来超大型空间结构最有发展潜力的构建方式之一, 组装过程中空间结构尺寸逐渐增长、动力学特性也随之改变, 给结构主动控制任务带来了新的挑战. 针对这一问题, 提出一种在轨组装空间结构面向主动控制的动力学建模方法. 首先, 建立不同类别组装模块的基础模型库, 以用于后续直接调用; 然后, 定义模块的邻接关系矩阵以描述在轨组装过程中空间结构的变化, 并根据在轨组装任务特点, 设计了面向分布式控制的智能组件结构形式; 在有限元建模方法的基础上提出"节点自由度加载"方法, 利用模块的基础模型库与邻接关系矩阵, 分别建立智能组件和空间结构整体的动力学模型, 该模型可随组装的进行同步自适应更新; 最后, 以在轨组装桁架结构为例, 给出组装碰撞冲击下动力学建模与分布式主动控制数值仿真. 结果表明, 在轨组装过程中桁架结构整体的动力学特性有明显的变化, 主动控制非常必要; 基于提出的建模方法, 可高效地建立构型多样的在轨组装空间结构动力学模型; 智能组件的动力学模型在组装过程中可进一步根据邻接关系矩阵限定更新范围, 适用于在轨组装过程中的分布式主动控制系统设计.      

Non-linear global dynamics of an axially moving plate

In the present study, the geometrically non-linear dynamics of an axially moving plate is examined by constructing the bifurcation diagrams of Poincaré maps for the system in the sub and supercritical regimes. The von Kármán plate theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of this gyroscopic system are obtained based on an energy method by means of the Lagrange equations which yields a set of second-order non-linear ordinary differential equations with coupled terms. A change of variables is employed to transform this set into a set of first-order non-linear ordinary differential equations. The resulting equations are solved using direct time integration, yielding time-varying generalized coordinates for the in-plane and out-of-plane motions. From these time histories, the bifurcation diagrams of Poincaré maps, phase-plane portraits, and Poincaré sections are constructed at points of interest in the parameter space for both the axial speed regimes.     

基于Krein空间的鲁棒Kalman滤波在传递对准中的应用研究

基于Krein空间的鲁棒Kalman滤波器与通过其它方法建立的鲁棒Kalman滤波器相比有较高稳态精度。文中将基于Krein空间的鲁棒Kalman滤波方法用于导弹捷联惯导系统动基座传递对准，并与标准Kalman滤波进行了比较。仿真结果表明，在垂直比力参数存在摄动的情况下，如果基于Krein空间的鲁棒Kalman滤波器的参数选取适当，它的精度鲁棒性优于标准Kalman滤波。