AN AUTOMATIC CONSTRAINT VIOLATION STABI- LIZATION METHOD FOR DIFFERENTIAL/ ALGEBRAIC EQUATIONS OF MOTION IN MULTIBODY SYSTEM DYNAMICS

A new automatic constraint violation stabilization method for numerical integration of Euler_Lagrange equations of motion in dynamics of multibody systems is presented. The parameters α,β used in the traditional constraint violation stabilization method are determined according to the integration time step size and Taylor expansion method automatically. The direct integration method, the traditional constraint violation stabilization method and the new method presented in this paper are compared finally.

Numerical Solution for Stiff Dynamic Equations of Flexible Multibody System

A nonlinear numerical integration method, based on forward and backward Euler integration methods, is proposed for solving the stiff dynamic equations of a flexible multibody system, which are transformed from the second order to the first order by adopting state variables. This method is of A0 stability and infinity stability. The numerical solutions violating the constraint equations are corrected by Blajer＇s modification approach. Simulation results of a slider-crank mechanism by the proposed method are in good agreement with ones from other literature.

MODELLING OF MECHANICAL MECHANISM OF CHROMATOGRAPHIC SYSTEM AND THEORETICAL EQUATIONS SHOWING DYNAMICAL CHARACTERISTICS OF CHROMATOGRAPHY

A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.

Solution for Output Coordination Equations of Several Typical Parallel Six-Dimensional Acceleration Sensing Mechanisms

Aiming at the problem that it is difficult to generate the dynamic decoupling equation of the parallel six-dimensional acceleration sensing mechanism,two typical parallel six-dimensional acceleration sensing mechanisms are taken as examples.By analyzing the scale constraint relationship between the hinge points on the mass block and the hinge points on the base of the sensing mechanism,a new method for establishing the dynamic equation of the sensing mechanism is proposed.Firstly,based on the scale constraint relationship between the hinge points on the mass block and the hinge points on the base of the sensing mechanism,the expression of the branch rod length is obtained.The inherent constraint relationship between the branches is excavated and the branch coordination closed chain of the“12-6”configuration is constructed.The output coordination equation of the sensing mechanism is successfully derived.Secondly,the dynamic equations of“12-4”and“12-6”configurations are constructed by the Newton-Euler method,and the forward decoupling equations of the two configurations are solved by combining the dynamic equations and the output coordination equations.Finally,the virtual prototype experiment is carried out,and the maximum reference errors of the forward decoupling equations of the two configuration sensing mechanisms are 4.23%and 6.53%,respectively.The results show that the proposed method is effective and feasible,and meets the real-time requirements.

Variational principle and dynamical equations of discrete nonconservative holonomic systems

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler Lagrange equations and Hamilton＇s canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.

Numerical Integration for DAEs of Multibody System Dynamics

During the simulation of constrained multibody system,numerical integration is important for solving the Euler-Lagrange equation of multibody system dynamics,which is usually a Differential-Algebraic Equations(DAEs).Using the discrete Hamilton principle,discrete EulerLagrangian equation is obtained first based on Lagrange Interpolation.Then the Romberg,Gauss integral is used to solve the DAEs.At last,numerical results are compared by using Euler method,Runge-Kutta method,Romberg method and Gauss method for a double pendulum system.

A New Flexible Multibody Dynamics Analysis Methodology of Deployable Structures with Scissor-Like Elements

There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.

Synchronization of networked multibody systems using fundamental equation of mechanics

From the analytical dynamics point of view, this paper develops an optimal control framework to synchronize networked multibody systems using the fundamental equation of mechanics. A novel robust control law derived from the framework is then used to achieve complete synchronization of networked identical or non-identical multibody systems formulated with Lagrangian dynamics. A distinctive feature of the developed control strategy is the introduction of network structures into the control requirement. The control law consists of two components, the first describing the architecture of the network and the second denoting an active feedback control strategy. A corresponding stability analysis is performed by the algebraic graph theory. A representative network composed of ten identical or non-identical gyroscopes is used as an illustrative example. Numerical simulation of the systems with three kinds of network structures, including global coupling, nearest-neighbour, and small-world networks, is given to demonstrate effectiveness of the proposed control methodology.

Dynamic Response of Fluid-Single Leg Gravity Platform-Soil Interaction System

An approximate method is presented to investigate the earthquake response of the fluid-single leg (shortened for S. L.) gravity platform-soil interaction system. By assuming a suitable form of the velocity potential of the radiation waves and by using the motion equation and the boundary conditions, the unknown coefficients can be obtained. Thereafter the function of frequency for the interaction system may also be obtained. In this paper, the difference of the system dynamic response between rigid foundation is analyzed and the influences of the various foundation geometric dimension and the various water-depth on the hydrodynamic loading and dynamic response of the system is illustrated.

Stability for the Manifold of Equilibrium State of the Autonomous Birkhoff System

Studies the stability for them manifold of equilibrium state of the autonomous Birkhoffsystem. Uses the Liapunov's direct method and the first approximation method to obtain thestability criterion for the manifold of equilibrium state of the system. Gives an example toillustrate the application of the result.

Dynamic Analysis of Propulsion Mechanism Directly Driven by Wave Energy for Marine Mobile Buoy

Marine mobile buoy（MMB） have many potential applications in the maritime industry and ocean science.Great progress has been made,however the technology in this area is far from maturity in theory and faced with many difficulties in application.A dynamic model of the propulsion mechanism is very necessary for optimizing the parameters of the MMB,especially with consideration of hydrodynamic force.The principle of wave-driven propulsion mechanism is briefly introduced.To set a theory foundation for study on the MMB,a dynamic model of the propulsion mechanism of the MMB is obtained.The responses of the motion of the platform and the hydrofoil are obtained by using a numerical integration method to solve the ordinary differential equations.A simplified form of the motion equations is reached by omitting terms with high order small values.The relationship among the heave motion of the buoy,stiffness of the elastic components,and the forward speed can be obtained by using these simplified equations.The dynamic analysis show the following：The angle of displacement of foil is fairly small with the biggest value around 0.3 rad;The speed of mobile buoy and the angle of hydrofoil increased gradually with the increase of heave motion of buoy;The relationship among heaven motion,stiffness and attack angle is that heave motion leads to the angle change of foil whereas the item of speed or push function is determined by vertical velocity and angle,therefore,the heave motion and stiffness can affect the motion of buoy significantly if the size of hydrofoil is kept constant.The proposed model is provided to optimize the parameters of the MMB and a foundation is laid for improving the performance of the MMB.

3D dynamic motion of a dielectric micro-sphere within optical tweezers

Known as laser trapping,optical tweezers,with nanometer accuracy and pico-newton precision,plays a pivotal role in single bio-molecule measurements and controllable motions of micro-machines.In order to advance the flourishing applications for those achievements,it is necessary to make clear the three-dimensional dynamic process of micro-particles stepping into an optical field.In this paper,we utilize the ray optics method to calculate the optical force and optical torque of a micro-sphere in optical tweezers.With the influence of viscosity force and torque taken into account,we numerically solve and analyze the dynamic process of a dielectric micro-sphere in optical tweezers on the basis of Newton mechanical equations under various conditions of initial positions and velocity vectors of the particle.The particle trajectory over time can demonstrate whether the particle can be successfully trapped into the optical tweezers center and reveal the subtle details of this trapping process.Even in a simple pair of optical tweezers,the dielectric micro-sphere exhibits abundant phases of mechanical motions including acceleration,deceleration,and turning.These studies will be of great help to understand the particle-laser trap interaction in various situations and promote exciting possibilities for exploring novel ways to control the mechanical dynamics of microscale particles.

DYNAMIC ANALYSIS OF A LATE-MODEL DOBBY SHEDDING MECHANISM

This paper presents the dynamic analysis of a dobby shedding mechanism. Taking theoscillatory slider as a moving reference frame, relative motion relations of the cam-rocker mech-anism are established in the kinematic analysis. A non-linear equation is solved by indirectmethod to obtain its numerical solutions expressed in algebraic power series for the six-barlinkage. In dynamic analysis, the authors have set up dynamic equations for the entire mecha-nism to find the solutions. From the results of dynamic analysis, it can be seen that the mecha-nism is suitable for operation at high speed and under heavy load.

Multibody Dynamics Formulations Based on Variational Principle

The formulation of multibody dynamics was studied based on variational principle. The body coonection matrix was introduced to define the connection configuration. The expression for the system kinematics was obtained by using the body connection matrix. From variational principle the general dynamical equations for multibody system were derived and the dynamical equations were given for multibody system subjected to the constraints.

COMPUTER AIDED ANALYSIS OF FLEXI－BLE MEMBER IN CONSIDERATION OF THE EFFECTS OF DYNAMIC STI－FFEN－ING

A recently developed procedure to capture the dynamic stiffening of an arbitrary flexiblemember in large overall motion accompanied by small elastic vibrations is presented. A mechanicalsystem that consists of one or more flexible members is called a flexible mechanical system. If thesystem is considered as a multibody system, the flexiblemember can be considered as a flexible bodyin a flexible multibody system. Having retained the nonlinearitites up to an appropriate point in theanalysis, the linearization is then performed properiy so that the dynamic stiffening terms can befound naturally, while the explicit formulation of the governing equations for the deformation mo-tion is ultimately linear. Based on the procedure, the effects of dynamic stiffening are investigatedqualitatively and quantitatively with analytical and numerical examples. The results are useful incomputer aid analysis of the dynamic behavior of flexible mechanical systems.

采煤机滚筒工作性能优化研究

在实际生产中,截割破碎过程是多作用耦合的结果,离散元法(DEM)与多体动力学(MBD)双向耦合技术可实现煤机设备与煤壁的信息交互,符合实际生产情况,具有较大的优越性。为提高采煤机滚筒的工作性能,基于DEM−MBD双向耦合机理,结合力学性能试验和模拟试验得到实际工况参数,采用仿真软件EDEM和RecurDyn建立了采煤机滚筒截割煤壁的双向耦合模型,对仿真过程中滚筒所受的转矩和截割力进行分析,证明耦合效果和截割效果较好。设计了单因素试验和正交试验,分析了滚筒运行参数对工作性能的影响规律,并利用SPSS软件得到滚筒转速、截割深度、牵引速度对截割比能耗、装煤率、载荷波动系数的影响程度,通过现场试验验证了模型的可行性。构建了以滚筒转速、截割深度、牵引速度为决策变量,以截割比能耗、装煤率和载荷波动系数为目标的多目标优化模型,利用改进多目标灰狼(MOGWO)算法和优劣解距离法(TOPSIS)对模型进行求解,得出当滚筒转速为31.12 r/min、截割深度为639.4 mm、牵引速度为5.58 m/min时,采煤机滚筒的工作性能最优,此时截割比能耗为0.4677 kW·h/^(3),装煤率为43.01%,载荷波动系数为0.3278。

面向联邦学习激励优化的演化博弈模型

针对联邦学习中参与者虚报训练成本导致激励不匹配的现象,提出了面向联邦学习激励优化的演化博弈模型.首先在联邦学习系统中建立了联邦参与者-联邦组织者演化博弈模型,设计模型质量评估算法对参与者提交的模型进行质量评估,去除低质量模型的同时量化参与者训练成本.然后结合信誉度指标提出优化的激励分配方法,通过求解演化博弈的稳定策略得到不同初始状态下的最优收益策略.最后仿真实验表明参与者激励收益方面,与平均分配法和个体收益分享法相比诚实参与者的收益提升了70%和57.4%,虚报参与者收益降低了65%和69.5%,策略选择方面,所提模型能合理选择收益策略.

悬臂同轴双转子系统不平衡耦合振动抑制试验研究

针对悬臂同轴双转子系统不平衡耦合振动突出问题,以某开式转子发动机输出端双转子系统为研究对象,对悬臂双转子系统振动耦合机理进行了理论推导、仿真分析和试验研究。首先,采用有限元法(FEM)建立了双转子系统等效动力学模型和耦合动力学方程,分析了悬臂同轴双转子系统耦合振动机理;然后,利用有限元软件对双转子系统进行了模态分析、临界转速分析以及不平衡响应分析,建立了自敏感系数概念以定量评价系统对不平衡振动的敏感度和耦合状态;最后,根据实际结构设计了悬臂同轴双转子实验台,进行了不同转速比下的不平衡振动抑制实验,并结合实验结果对仿真结果进行了验证。研究结果表明:模拟仿真提出的自敏感系数可作为双转子系统实际振动测点布置和不平衡振动抑制策略的理论依据;通过应用先平衡内转子后平衡外转子的不平衡振动分步抑振策略,可使双转子系统不平衡振动降幅达80%以上。该研究对双转子系统传感器测点布局和系统耦合振动抑制具有一定的指导意义。

3-DOF并联机械腿动力学建模与伺服电机峰值预估

提出了一种结构紧凑、承载能力大、转动解耦性好、运动速度和加速度大的3自由度并联机械腿。为了对其进行驱动参数分析,对机械腿进行了动力学建模,并基于动力学模型进行了伺服电机峰值预估。首先,分析了腿部机构各构件的运动参数,采用Lagrange方程建立了动力学模型,得出了机构驱动力的显式解;接着,在机构动力学模型的基础上,建立了伺服电机驱动转速和驱动力矩的峰值预估模型;最后,通过给定一组结构参数和运动轨迹函数,得出了伺服电机驱动转速和驱动力矩随时间变化曲线,得到了机构的动力学特性,并验证了峰值预估模型的正确性。计算表明,3个伺服电机驱动转速的峰值分别为Nx=19r/s、Ny=17r/s、Nw=27r/s;3个伺服电机驱动力矩的峰值分别为εx=5.8N.m、εy=3.1N.m、εw=4.4N.m。

基于结构方程模型的广州市相对贫困空间分异及动力机制研究

我国农村脱贫攻坚取得全面胜利,相对贫困问题将是未来贫困研究的关键。文章以广州市为例,通过多源综合数据分析相对贫困分布规律和空间聚集特征,并结合结构方程模型探讨相对贫困空间分异的动力机制。研究表明:(1)广州市相对贫困呈现“高—低—高”的圈层分布特征;(2)根据结构方程模型路径分析结果,基础设施、人力资本、经济活力、自然环境等因素对广州市相对贫困空间分异形成了多重路径的影响关系;(3)结合地理区位和城乡差异划分内城衰落型、城乡融合型和乡村滞后型3种贫困模式,并针对不同贫困空间类型提出差异化的贫困治理建议,以期为后扶贫时代城乡相对贫困的精细化治理提供理论基础。