Numerical Continuation of Solutions and Bifurcation Analysis in Multibody Systems Applied to Motorcycle Dynamics

It is shown how the equations of motion for a multibody system can be generated in a symbolic form and the resulting equations can be used in a program for the analysis of nonlinear dynamical systems. Stationary and periodic solutions are continued when a parameter is allowed to vary and bifurcations are found. The variational or linearized equations and derivatives with respect to parameters are also provided to the analysis program, which enhances the efficiency and accuracy of the calculations. The analysis procedure is firstly applied to a rotating orthogonal double pendulum, which serves as a test for the correctness of the implementation and the viability of the approach. Then, the procedure is used for the analysis of the dynamics of a motorcycle. For running straight ahead, the nominal solution undergoes Hopf bifurcations if the forward velocity is varied, which lead to periodic wobble and weave motions. For stationary cornering, wobble instabilities are found at much lower speeds, while the maximal speed is limited by the saturation of the tyre forces.     

多体系统动力学逆问题的一种处理方法

首先用控制力法建立多体系统动力学逆问题的运动微分方程，然后给出奇异值分解在求系统动力学响应中的应用及作用在系统中的控制力的解法，最后举了一个算例。     

带约束非线性多体系统动力学方程数值分析方法

Lagrange方法是建立带约束多体系统动力学方程的普遍方法之一 ,其方程的形式为微分 代数方程组 ,数值计算与数值分析是研究多体系统动力学特性的重要方法。本文利用缩并法给出了带约束多体系统动力学方程的隐式数值计算方法和Lyapunov指数的计算方法。将数值仿真、Lya punov指数计算和Poincare映射有机结合 ,分析非线性多体系统动力学行为。通过一个算例 ,说明该方法的有效性     

刚柔耦合约束多体系统的动力分析

本文提出了描述柔性多体系统的牵连坐标系统。该系统由惯性参考系,牵连坐标系,物体坐标系及单元坐标系组成,实现了对刚体平动,刚体转动及弹性运动的连续分解,最大限度地消除了由于刚体大角度转动导致的非线性特性。以有限元法为基础,应用拉格朗日方程建立了在该坐标下的刚柔耦合约束多体系统的动力学控制方程。该方程具有耦合程度小、易于推导、编程及求解等优点,为大规模约束多体系统的动力分析提供了新的途径。本文还讨论了平面铰链约束的约束形式及约束方程,最后给出了一个典型多体系统的数值算例。     

NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM

The nonlinear dynamic equations of a multibody system composed of ?exible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation e?ect is employed and its deformation ?eld is …     

A Variational Approach to Dynamics of Flexible Multibody Systems

Abstract

This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body reference frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed     

A Gluing Algorithm for Distributed Simulation of Multibody Systems

A new gluing algorithm is presented that can be used tocouple distributed subsystem models fordynamics simulation of mechanical systems. Using this gluingalgorithm, subsystem models can be analyzed attheir distributed locations, using their own independent solvers,and on their own platforms. The gluing algorithmdeveloped relies only on information available at the subsysteminterfaces. This not only enables efficientintegration of subsystem models, but also engenders modelsecurity by limiting model access only to the exposedinterface information. These features make the algorithm suitablefor a real and practical distributed simulationenvironment.     

Optimization Problems of Controlled Multibody Systems Having Spring-Damper Actuators

The optimal control of the motion of mechanical systems is studied. A characteristic feature of these systems is the presence of passive actuators (springs, dampers, etc.). Energy-optimal control laws and structural parameters of nonlinear spring–damper actuators are determined analytically, which is necessary to impart arbitrary motion to a controllable mechanical system with n degrees of freedom. As an example, a numerical solution is presented for the problem of designing an energy-optimal spring actuator for a robot manipulator of closed kinematic structure     

多体系统动力学优化设计的增广Lagrange乘子法

针对多体系统的非线性受约束动态优化设计通用模型,基于连续可微目标函数和一阶、二阶灵敏度分析给出多体系统动力学优化设计的增广Lagrange乘子法.其中基于多体系统动力学方程的一阶设计灵敏度采用伴随变量方法进行计算,二阶设计灵敏度使用混合方法进行计算,在设计变量较多时具有较高的计算效率.最后对曲柄-滑块系统数值算例使用增广Lagrange乘子方法进行约束优化,通过对使用不同方法进行一阶灵敏度分析和二阶灵敏度分析所得的最优值、迭代次数及运行时间的比较,得出一阶灵敏度分析中使用变尺度方法效率较高,而使用二阶灵敏度分析可以进一步提高优化效率.     

Modified Adams-Moulton Predictor-Corrector Method in Solving Multibody Dynamical Systems

A modified Adams-Moulton predictor-corrector method is proposed to solve multibody dynamical systems. The proposed method is obtained by combining an Adams-Bashforth predictor method and an Adams-Moulton corrector method with derived weighting coefficients. With the modification, the accuracy of the proposed method is almost one order of magnitude better than the Adams-Moulton predictor-corrector method with the same step size. Stability limits of the proposed method are also studied. Because the present method has greater stability limits than Adams-Moulton predictor-corrector methods, the proposed method has good robustness during the process of time integration. A crank-slider mechanism is used as an example to investigate the capability of the proposed method in solving multibody dynamic systems.     

柔性多体系统动力学通用算法研究

柔性多本系统运动学动力学仿真通用软件可广泛服务于工程领域,基于Ｋａｎｅ方程建立一种开发该类软件的一般算法,通过定义的辨识函数解决束识别问题,利用振型描述构件的弹性变形,建立了递推格式的运动学模型,提出了计算偏带度、偏角速度和运动微分方程系数矩阵的“０－１”法,最后给出的算例表明所建立的算法是可行的。     

A Fully Symbolic Model of Multibody Systems Containing Flexible Plates

The modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multi-body dynamics and the area of structural mechanics and vibration theory. As regards the multibody approach, recursive formulations in relative coordinates are quite suitable and efficient for a large variety of applications. Such a formalism is developed here for a general multibody system containing flexible plates and in such a way that its full symbolic generation is possible within the ROBOTRAN program [1].     

Three-Dimensional Large Deformation Analysis of the Multibody Pantograph/Catenary Systems

To accurately model the nonlinear behavior of the pantograph/catenary systems, it is necessary to take into consideration the effect of the large deformation of the catenary and its interaction with the nonlinear pantograph system dynamics. The large deformation of the catenary is modeled in this investigation using the three-dimensional finite element absolute nodal coordinate formulation. To model the interaction between the pantograph and the catenary, a sliding joint that allows for the motion of the pan-head on the catenary cable is formulated. To this end, a non-generalized arc-length parameter is introduced in order to be able to accurately predict the location of the point of contact between the pan-head and the catenary. The resulting system of differential and algebraic equations formulated in terms of reference coordinates, finite element absolute nodal coordinates, and non-generalized arc-length and contact surface parameters are solved using computational multibody system algorithms. A detailed three-dimensional multibody railroad vehicle model is developed to demonstrate the use of the formulation presented in this paper. In this model, the interaction between the wheel and the rail is considered. For future research, a method is proposed to deal with the problem of the loss of contact between the pan-head and the catenary cable.     

柔性多体系统中间隙铰接副的磨损预测

通过集成磨损计算与柔性多体动力学,对柔性系统中间隙铰接副部位的磨损进行了预测.基于绝对节点坐标方法（ANCF）建立了柔性部件的多体动力学模型,引入连续接触力模型计算间隙铰接副部分的接触力,并采用Archard磨损模型的迭代磨损计算程序预测磨损.为了得到在不同接触情况下的磨损系数,本文中采用了径向基神经网络处理试验数据.通过对含柔性连杆的曲柄滑块机构进行仿真计算,发现当考虑部件的柔性时,得到的间隙处的冲击力大幅降低,且预测的磨损量也略有降低,这种区别会随着仿真时间的增加而变得更加明显.     

求解多体系统动力学方程的子系统迭代法

提出一种求解多体系统动力学方程的迭代法，将多体系统分割成一个主子系统和一个或多个辅子系统，各子系统通过分割点的位移、速度、加速度和力的协调相联系，从而大大降低了方程的耦合程度、非线性和刚性。文中详细讨论了迭代法的收敛条件。     

柔性多体系统的递推组集建模与仿真软件的实现

简要地阐述多体系统动力学单向递推组集建模方法，介绍根据这种方法开发而成的仿真软件系统ＤＡＦＭＢ及它的功能与特点。通过双摆算例指出本文提出的模型在计算效率与计算精度方面优于笛卡尔坐标的微分－代数方程。     

随机ARNOLD系统的稳定性与分叉

本文详细讨论了当ｎ＝２时Ａｒｎｏｌｄ系统在小强度的随机参数激励扰动下，系统的运动稳定性及分叉。为了研究系统响应的统计特性，本文使用了Ｍａｒｋｏｖ近似技巧。在线性系统的情形，给出了系统矩稳定及样本稳定的充分必要条件。在非线性情形，本文的结果表明随机扰动可使系统的分叉点发生漂移