WU Feng, GAO Qiang, ZHONG Wan-xie. Iterative Symplectic Perturbation Method for the Dynamic Analysis of Rigid-Flexible Bodies Equations[J]. Applied Mathematics and Mechanics, 2014, 35(4): 341-352. doi: 10.3879/j.issn.1000-0887.2014.04.001
 Citation: WU Feng, GAO Qiang, ZHONG Wan-xie. Iterative Symplectic Perturbation Method for the Dynamic Analysis of Rigid-Flexible Bodies Equations[J]. Applied Mathematics and Mechanics, 2014, 35(4): 341-352.

# Iterative Symplectic Perturbation Method for the Dynamic Analysis of Rigid-Flexible Bodies Equations

##### doi: 10.3879/j.issn.1000-0887.2014.04.001
Funds:  The National Basic Research Program of China (973 Program)（2009CB918501）
• Publish Date: 2014-04-15
• The iterative symplectic perturbation method was proposed for the dynamic analysis of rigid-flexible bodies equations. With the proposed method, the low-frequency motion and high-frequency motion were treated separately. The symplectic perturbation method was applied to the coupling terms jointly caused by the low- and high-frequency motions. The proposed method could give correct numerical results with relatively larger time steps. It overcomes the difficult stiff integral problem. Numerical examples show that the proposed method is valid for the dynamic analysis of rigid-flexible bodies equations.
•  [1] 于清, 洪嘉振. 柔性多体系统动力学的若干热点问题[J]. 力学进展, 1999,29(2): 145-154.(YU Qing, HONG Jia-zhen. Some topics on flexible multibody system dynamics[J]. Advances in Mechanics,1999,29(2): 145-154.(in Chinese)) [2] Newmark N M. A method of computation for structural dynamics[J]. ASCE Journal of the Engineering Mechanics Division,1959,85(3): 67-94. [3] Bathe K J, Wilson E L.Numerical Methods in Finite Element Analysis [M]. Englewood: Prentice-Hall, 1976. [4] Ascher U M, Petzold L R.Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations [M]. Beijing: Science Press, 2009. [5] 吴志桥. 非惯性系下柔性结构动力学研究[D]. 硕士学位论文. 长沙: 国防科学技术大学, 2004.(WU Zhi-qiao. Study on dynamics for flexible structure in non-inertial frame[D]. Master Thesis. Changsha: National University of Defense Technology, 2004.(in Chinese)) [6] 臧永强. 求解多柔体系统动力方程的违约修正零空间法[D]. 硕士学位论文. 西安: 西安电子科技大学, 2009.(ZANG Yong-qiang. The violation correction null space method of dynamical equation of flexible multi-body systems[D]. Master Thesis. Xi’an: Xidian University, 2009.(in Chinese)) [7] 付士慧, 王琪. 多体系统动力学方程违约修正的数值计算方法[J]. 计算力学学报, 2007,24(1): 44-49.(FU Shi-hui, WANG Qi. A numerical method for constraint stabilization of dynamic equations of multi-body systems[J].Chinese Journal of Computational Mechanics,2007,24(1): 44-49.(in Chinese)) [8] 赵玉立, 吴子燕, 邓子辰. 带伸展柔性附件航天器系统动力响应的精细积分算法[J]. 机械科学与技术, 2002,21(2): 196-197, 201.(ZHAO Yu-li, WU Zi-yan, DENG Zi-chen. The precise integration method for calculating the dynamic behavior of spacecraft with extensional flexible appendages[J].Mechanical Science and Technology,2002,21(2): 196-197, 201.(in Chinese)) [9] 张靖姝, 于洪洁, 洪嘉振. 非线性插值精细积分法在刚柔耦合弹簧摆中的应用[J]. 力学季刊, 2013,34(3): 415-422.(ZHANG Jing-shu, YU Hong-jie, HONG Jia-zhen. Nonlinear interpolation precise integration method in rigid-flexible coupling spring pendulum[J].Chinese Quarterly of Mechanics, 2013,34(3): 415-422.(in Chinese)) [10] 钟万勰, 高强. 约束动力系统的分析结构力学积分[J]. 动力学与控制学报, 2006,4(3): 193-200.(ZHONG Wan-xie, GAO Qiang. Integration of constrained dynamical system via analytical structural mechanics[J].Journal of Dynamics and Control,2006,4(3): 193-200.(in Chinese)) [11] 王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2003.(WANG Xu-cheng.Finite Element Method [M]. Beijing: Tsinghua University Press, 2003.(in Chinese)) [12] Hinch E J.Perturbation Methods [M]. Cambridge: Cambridge University Press, 1991. [13] 钟万勰, 孙雁. 三类保辛摄动及其数值比较[J]. 动力学与控制学报, 2005,3(2): 1-9.(ZHONG Wan-xie, SUN Yan. Numerical comparison for three different symplectic perturbation methods[J].Journal of Dynamics and Control,2005,3(2): 1-9.(in Chinese)) [14] 钟万勰, 姚征. 时间有限元与保辛[J]. 机械强度, 2005,27(2): 178-183.(ZHONG Wan-xie, YAO Zheng. Time domain FEM and symplectic conservation[J].Journal of Mechanical Strength,2005,27(2): 178-183.(in Chinese)) [15] 钟万勰, 孙雁. 小参数摄动法与保辛[J]. 动力学与控制学报, 2005,3(1): 1-6.(ZHONG Wan-xie, SUN Yan. Small parameter perturbation method and symplectic conservation[J].Journal of Dynamics and Control,2005,3(1): 1-6.(in Chinese))

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142