MODEL SMOOTHING METHODS IN NUMERICAL ANALYSIS OF FLEXIBLE MULTIBODY SYSTEMS
QiZhaohui1,*,, CaoYan1, WangGang2,*, 1Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China2School of Ocean Science and Technology, Dalian University of Technology, Panjin 124221, Liaoning, China ; 中图分类号:O313.7 文献标识码:A
关键词:多柔体系统;模型光滑化;刚性微分方程;变形虚功率;虚功率方程 Abstract Dynamic equations of flexible multibody systems are usually a set of stiff differential equations. At present, the common numerical method for solving the stiff differential equations filters out the high frequency by using the numerical damping. The computational efficiency of this method is still unsatisfactory. In order to reduce the stiffness of dynamic equations of flexible multibody systems so greatly that the equations can be solved by regular ordinary differential equation (ODE) solvers such as MATLAB ODE45 solver, methods of filtering high frequency vibrations during the process of modeling are studied. Stresses of flexible bodies are homogenized by their mean value over a time interval from now to a short time later. The homogenized stress is then employed to replace its origin when computing the virtual deformation power. In this way, the obtained model of the flexible multibody system will not contain harmful high frequency elastic vibrations. The range of frequencies can be controlled by the length of the time interval used to homogenize stresses. As validated by the numerical examples in this paper, the precision and efficiency of the proposed method are comparable to some stiff ODE solvers. Moreover, it works well when the stiff ODE solver fails to give correct solutions in a reasonable time. Comparisons of numerical examples show that the proposed method can be a new available approach to numerical analysis of flexible multibody systems.
分别采用MATLAB的刚性方程求解器radau5 和ODE45求解器分别对该问题进行数值积分, 取精度控制参数和. 得到双摆机构上末端点在竖直方向和水平方向的位移, 分别如图6和图7所示. 显示原图|下载原图ZIP|生成PPT 图6末端点的轴向变形. -->Fig.6Axial deformation of the end point -->
显示原图|下载原图ZIP|生成PPT 图7末端点的横向挠度. -->Fig.7Lateral deflection of the end point -->
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