多柔体系统数值分析的模型降噪方法

齐朝晖; 曹艳; 王刚

doi:10.6052/0459-1879-18-111

多柔体系统数值分析的模型降噪方法

doi: 10.6052/0459-1879-18-111

齐朝晖^1,*, ,,
曹艳¹,
王刚^2,*, ,

1大连理工大学工程力学系, 大连 116023
2大连理工大学盘锦校区海洋科学与技术学院, 辽宁盘锦 124221;

基金项目: 国家自然科学基金资助项目(91748203, 11372057).

详细信息

作者简介:
^齐朝晖, 教授, 主要研究方向: 多体系统动力学. E-mail: zhaohuiq@dlut.edu.cn ;^王刚, 讲师, 主要研究方向: 多体系统动力学. E-mail:wanggangdut@dlut.edu.cn

通讯作者:
齐朝晖,王刚

齐朝晖,王刚

中图分类号: O313.7;
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出版历程
- 刊出日期: 2018-07-18

MODEL SMOOTHING METHODS IN NUMERICAL ANALYSIS OF FLEXIBLE MULTIBODY SYSTEMS

Qi Zhaohui^{1,*
, ,},
Cao Yan¹,
Wang Gang^{2,*
, ,}

1Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China
2School of Ocean Science and Technology, Dalian University of Technology, Panjin 124221, Liaoning, China ;

摘要

摘要: 多柔体系统的动力学方程通常是一组刚性微分方程, 目前普遍采用的刚性微分方程数值解法主要通过数值阻尼滤除系统响应中的高频分量, 其求解效率难以令人满意. 为了降低多柔体系统动力学方程的刚性, 从而可采用ODE45等常规微分方程求解器进行求解, 研究了在建模过程中滤除高频振荡分量的方法. 在以当前时刻为起点的短时间内对柔性体的应力进行均匀化, 用均匀化后的应力计算柔性体的变形虚功率, 由此得到的系统动力学方程的解中不含过高频率的弹性振动, 并且可以通过调节均匀化时间区间的长度参数控制滤波的范围. 数值算例表明: 这种模型降噪方法的计算效率和精度均不低于刚性微分方程求解器, 并且在刚性微分方程求解器失效的情况下模型降噪方法仍有良好的精度和效率. 本文所提的模型降噪方法可成为求解多柔体系统动力学方程的新途径.
- 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.
- flexible multibody systems /
- model smoothing /
- stiff ODEs /
- virtual deformation power /
- principle of virtual power

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