非保守非线性刚-弹-液-控耦合分析动力学及其应用研究

李海波; 刘世兴; 宋海燕; 梁立孚

doi:10.6052/0459-1879-20-107

非保守非线性刚-弹-液-控耦合分析动力学及其应用研究

李海波^*2), ,,
刘世兴^†,
宋海燕^**,
梁立孚^**3),

^*北京强度环境研究所可靠性与环境工程技术重点实验室, 北京 100076
^†辽宁大学物理学院, 沈阳 110036
^**哈尔滨工程大学力学一级学科博士点,哈尔滨 150001

基金项目: 1)国家自然科学基金(11172046);国家自然科学基金(10272034);国家自然科学基金(11872030)

详细信息

通讯作者:
李海波

李海波,梁立孚

中图分类号: O316
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出版历程
- 收稿日期: 2020-04-13
- 刊出日期: 2020-08-09

NON-CONSERVATIVE NONLINEAR RIGID-ELASTIC-LIQUID- CONTROL COUPLING ANALYTICAL DYNAMICS AND ITS APPLICATIONS

Li Haibo^*2), ,,
Liu Shixing^†,
Song Haiyan^**,
Liang Lifu^**3),

^*Key Laboratory of Reliability and Environmental Engineering Technology, Beijing Institute of Intensity and Environment, Beijing 100076, China
^†College of Physic, Liaoning University, Shenyang 110036, China
^**A Doctoral Program in Mechanics, Harbin Engineering University, Harbin 150001, China

摘要

摘要: 非保守非线性刚-弹-液-控耦合分析动力学是与航天动力学和多体动力学相关的重要研究课题之一, 研究这一理论和应用课题具有重要理论意义和实际应用价值. 本研究建立了非保守非线性两类变量的刚-弹-液-控耦合分析动力学的Hamilton型拟变分原理, 并以该Hamilton型拟变分原理的泛函为依据, 分析了刚-弹-液-控耦合中的刚-弹耦合、刚-液耦合与弹-液耦合、控-刚耦合的特点. 借助于Lagrange-Hamilton体系, 从Hamilton型拟变分原理出发推导出非保守非线性刚-弹-液-控耦合系统的Lagrange方程, 并应用该Lagrange方程推导出系统的控制方程. 进一步以该控制方程为依据, 分析了刚-弹-液-控耦合中的刚-弹耦合、刚-液耦合与弹-液耦合、控-刚耦合的机理. 从两个方面概要地研究了非保守非线性刚-弹-液-控耦合系统的Lagrange方程的应用: 一方面, 应用该Lagrange方程建立了相应的有限元计算模型, 分析了这类计算模型的优越性; 另一方面, 应用系统的控制方程对实际问题进行解析的分析讨论, 说明了应用解析的分析讨论来研究问题与应用数值的、定量的分析方法来研究问题的互补特性. 最后, 讨论了几个相关的问题.
- Lagrange方程 /
- Hamilton原理 /
- 非保守 /
- 非线性 /
- 刚-弹-液-控耦合
Abstract: Non-conservative nonlinear rigid-elastic-liquid-control coupling analytical dynamics is one of the important research subjects related to aerospace dynamics and multi-body dynamics. It is of great theoretical significance and practical value to study this theoretical and applied subject by using analytical dynamics method. Firstly, the non-conservative nonlinear Hamilton-type quasi-variational principle of rigid-elastic-liquid-control coupling dynamics with two types of variables is established. Based on the functional of the Hamilton-type quasi-variational principle with two types of variables, the characteristics of rigid-elastic coupling, rigid-liquid coupling, elastic-liquid coupling and rigid-control coupling are analyzed. Secondly, with the help of Lagrange-Hamilton system, the Lagrange equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system is derived from Hamilton-type quasi-variational principle. Thirdly, the governing equations of the non-conservative nonlinear rigid-elastic-liquid-control coupling system are derived by applying the Lagrange equations. Based on the governing equations, the mechanisms of rigid-elastic coupling, rigid-liquid coupling , elastic-liquid coupling and rigid-control coupling are analyzed. The application of Lagrange equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system is studied in two aspects. On the one hand, the finite element model is established by applying the Lagrange equations. Furthermore, the advantages of this kind of computing model are analyzed. On the other hand, the problems are analyzed by using the governing equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system. It illustrates the complementary characteristics of the application of analytic analysis and discussion to the study of problems and the application of numerical and quantitative analysis methods to the study of problems. Finally, several related issues are discussed.
- Lagrange equation /
- Hamilton principle /
- non-conservative /
- non-linear /
- rigid-elastic-liquid-control coupling

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参考文献(1)

[1]	李青, 王天舒, 马兴瑞. 充液航天器液体晃动和液固耦合动力学的研究与应用. 力学进展, 2012,42(4):471-480
[1]	( Li Qing, Wang Tianshu, Ma Xingrui. Reviews on liquid sloshing dynamics and liquid-structures coupling dynamics in liquid-filled spacecrafts. Advances in Mechanics, 2012,42(4):471-480 (in Chinese))
[2]	岳宝增, 宋小娟. 具有刚-柔-液-控耦合的航天器动力学研究进展. 力学进展, 2013,43(1):163-173
[2]	( Yue Baozeng, Song Xiaojuan. Advances in rigid-flexible-liquid-control coupling dynamics of spacecraft. Advances in Mechanics, 2013,43(1):163-173 (in Chinese))
[3]	Wu WJ, Yue BZ, Huang H. Coupling dynamic analysis of spacecraft with multiple cylindrical tanks and flexible appendages. Acta Mechanica Sinica, 2016,32(1):144-155
[4]	Yue BZ, Wu WJ, Yan YL. Modeling and coupling dynamics of the spacecraft with multiple propellant tanks. AIAA Journal, 2016,54(11):3608-3618
[5]	Yan YL, Yue BZ. Analytical method for the attitude stability of partially liquid filled spacecraft with flexible appendage. Acta Mechanica Sinica, 2017,33(1):208-218
[6]	Tang Y, Yue BZ. Simulation of large-amplitude three-dimensional liquid sloshing in spherical tanks. AIAA Journal, 2017,55(6):1-8
[7]	Tang Y, Yue BZ, Yan YL. Improved method for implementing contact angle condition in simulation of liquid sloshing under microgravity. International Journal for Numerical Methods in Fluids, 2019,89(4-5):123-142
[8]	Yan YL, Yue BZ. Dynamic analysis of the flexible spacecraft with liquid sloshing in axisymmetrical container. Journal of Spacecraft and Rocket, 2018,55:282-291
[9]	Liu F, Yue BZ, Zhao LY. Attitude dynamics and control of spacecraft with a partially filled liquid tank and flexible panels. Acta Astronautica, 2018,143:327-336
[10]	李晓玉, 岳宝增. 基于多尺度方法的平动圆柱贮箱航天器刚-液耦合动力学研究. 力学学报, 2019,51(5):1448-1454
[10]	( Li Xiaoyu, Yue Baozeng. Study on the rigid-liquid coupling dynamics of a cylindrical-tank spacecraft in translation based on muti-scale method. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1448-1454 (in Chinese))
[11]	孙家亮, 田强, 胡海岩. 多柔体系统动力学建模与优化研究进展. 力学学报, 2019,51(6):1565-1586
[11]	( Sun Jialiang, Tian Qiang, Hu Haiyan. Advances in dynamic modeling and optimization of flexible multibody systems. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1565-1586 (in Chinese)).
[12]	曹登庆, 白坤朝, 丁虎等. 大型柔性航天器动力学与振动控制研究进展. 力学学报, 2019,51(1):1-13
[12]	( Cao Dengqing, Bai Kunchao, Ding Hu, et al. Advances in dynamics and vibration control of large-scale flexible spacecraft. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):1-13 (in Chinese))
[13]	王照林, 刘延柱. 充液系统动力学. 北京: 科学出版社, 2002
[13]	( Wang Zhaolin, Liu Yanzhu. Dynamics of Liquid Filled System. Beijing: Science Press, 2002 (in Chinese))
[14]	陈滨. 分析动力学(第2版). 北京: 北京大学出版社, 2012
[14]	( Chen Bin. Analytical Dynamics (2nd Edn). Beijing: Peking University Press, 2012 (in Chinese))
[15]	梅凤翔. 分析力学(下卷). 北京: 北京理工大学出版社, 2013
[15]	( Mei Fengxiang. Analytical Mechanics (Vol II). Beijing: Beijing University of Technology Press, 2013 (in Chinese))
[16]	钱学森, 工程控制论(新世纪版). 上海: 上海交通大学出版社, 2007
[16]	( Qian Xueshen. Engineering Cybernetics (New Century Edition). Shanghai: Shanghai Jiaotong University Press, 2007 (in Chinese))
[17]	刘豹, 唐万生. 现代控制理论(第3版). 北京: 机械工业出版社, 2007
[17]	( Liu Bao, Tang Wansheng. Modern Control Theory (Third Edn). Beijing: China Machine Press, 2007 (in Chinese))
[18]	王孝武, 张小红, 现代控制理论基础(第2版). 北京: 机械工业出版社, 2006
[18]	( Wang Xiaowu, Zhang Xiaohong. Fundamentals of Modern Control Theory (Second Edn). Beijing: China Machine Press, 2006 (in Chinese))
[19]	胡寿松. 自动控制原理(第5版). 北京: 科学出版社, 2007
[19]	( Hu Shousong. Principles of Automatic Control (Fifth Edn). Beijing: Science Press, 2007 (in Chinese))
[20]	马兴瑞, 王本利, 苟兴宇. 航天器动力学——若干问题进展及应用. 北京: 科学出版社, 2001
[20]	( Ma Xingrui, Wang Benli, Gou Xingyu. Spacecraft Dynamics-Progress and Application of Some Problems. Beijing: Science Press, 2001 (in Chinese))
[21]	Liang LF, Hu HC. Generalized variational principle of three kinds of variables in general mechanics. Science in China $($Ser.A$)$, 2001,44(6):770-776
[22]	Liang LF, Hu HC, Liu SQ. Non-contemporaneous variations and Holder's principle. Science in China $($G$)$, 2003,46(5):450-459
[23]	梁立孚. 变分原理及其应用. 哈尔滨: 哈尔滨工程大学出版社等五社联合出版, 2005
[23]	( Liang Lifu. Principles of Variation and Its Application. Harbin: Joint Publishing House of Harbin University of Engineering Press, etc, 2005 (in Chinese))
[24]	Liang LF, Liu DK, Song HY. The generalized quasi-variational principles of non-conservative systems with two kinds of variables. Science in China $($Ser.G$)$, 2005,48(5):600-613
[25]	罗恩, 梁立孚, 李纬华. 分析力学的非传统Hamilton型变分原理. 中国科学(G), 2006,36(6):633-643
[25]	( Luo En, Liang Lifu, Li Weihua. Unconventional Hamiltonian variational principles in analytical mechanics. Science in China $($Ser.G$)$, 2006,36(6):633-643 (in Chinese))
[26]	梁立孚, 罗恩, 冯晓九. 分析力学初值问题的一种变分原理形式. 力学学报, 2007,39(1):106-111
[26]	( Liang Lifu, Luo En, Feng Xiaojiu. A variational principle form for initial value problems in analytical mechanics. Chinese Journal of Theoretical and Applied Mechanics, 2007,39(1):106-111 (in Chinese))
[27]	梁立孚, 刘宗民, 刘殿魁. 非保守薄壁结构系统的广义拟余Hamilton原理及其应用. 工程力学, 2008,25(10):60-65
[27]	( Liang Lifu, Liu Zongmin, Liu Diankui. Generalized Hamilton-type quasi-complementary energy principle of non-conservative thin-wall structural system and its application. Engineering Mechanics, 2008,25(10):60-65 (in Chinese))
[28]	赵淑红, 梁立孚, 周平. 带有平动附件多柔体簇系统动力学拟变分原理及其应用. 工程力学, 2011,28(6):29-39
[28]	( Zhao Shuhong, Liang Lifu, Zhou Ping. Quasi-variational principles of flexible multi-body cluster system dynamics with annex of extendable translation and their applications. Engineering Mechanics, 2011,28(6):29-39 (in Chinese))
[29]	Liang LF, Liu SQ, Zhou JS. Quasi-variational principles of single flexible body dynamics and their applications. Science in China $($Ser.G$)$, 2009,52(5):775-787
[30]	梁立孚, 郭庆勇. 刚体动力学的拟变分原理及其应用. 力学学报, 2010,42(2):300-305
[30]	( Liang Lifu, Guo Qingyong. The quasi-variational principles of rigid-body dynamics and their applications. Journal of Theoretical and Applied Mechanics, 2010,42(2):300-305 (in Chinese))
[31]	李海波, 宋海燕, 梁立孚. 确定无约束梁耦合振型的一种途径. 强度与环境, 2011,38(2):6-12
[31]	( Li Haibo, Haiyan Song, Lifu Liang. An approach of coupled vibration mode determined of unrestrained beam. Structure & Environment Engineering, 2011,38(2):6-12 (in Chinese))
[32]	Liang LF, Song HY. Non-linear and non-conservative quasi- variational principle of flexible body dynamics and application in spacecraft dynamics. Science China Physics, Mechanics & Astronomy, 2013,56(11):2192-2199
[33]	Ma CY, Feng XJ, Liang LF. Variational principles of optimal control in holonomic and nonholonomic systems// International Conference on Mechanics and Control Engineering, Nanjing, Jiangsu, China, Apr. 11-12, 2015
[34]	梁立孚, 宋海燕, 樊涛等. 非保守系统的拟变分原理及其应用. 北京: 科学出版社, 2015
[34]	( Liang Lifu, Song Haiyan, Fan Tao, et al. Quasi Variational Principles of Nonconservative Systems and Their Applications. Beijing: Science Press, 2015 (in Chinese))
[35]	Song HY, Liang LF. Investigation of power-type variational principles in liquid-filled system. Applied Mathematics and Mechanics $($English Edition$)$, 2015,36(12):1651-1662
[36]	冯晓九, 梁立孚, 宋海燕. 刚-弹-液耦合动力学的功能型拟变分原理. 中国科学-技术科学, 2016,46(2):195-203
[36]	( Feng Xiaojiu, Liang Lifu, Song Haiyan. Quasi variational principle of the rigid-elastic-liquid coupling dynamics. Scientia Sinica: Technologica, 2016,46(2):195-203 (in Chinese))
[37]	梁立孚, 宋海燕, 李海波. 航天分析动力学. 北京: 科学出版社, 2016
[37]	( Liang Lifu, Song Haiyan, Li Haibo. Aerospace Analytical Dynamics Beijing: Science Press, 2016 (in Chinese))
[38]	周平, 李海波, 梁立孚. 刚弹耦合动力学初值问题拟变分原理及其应用. 北京航空航天大学学报, 2017,43(7):1321-1329
[38]	( Zhou Ping, Li Haibo, Liang Lifu. Quasi-variational principle and application of initial value problem for rigid-elastic coupling dynamics. Beijing University of Aeronautics and Astronautics, 2017,43(7):1321-1329 (in Chinese))
[39]	Feng XJ, Liang LF, Song HY. Application of Lagrange's equation to rigid-elastic coupling dynamics. Science China Technological Sciences, 2017,60(8):1263-1277
[40]	梁立孚, 周平. Lagrange方程应用于流体动力学. 哈尔滨工程大学学报, 2018,39(1):33-39
[40]	( Liang Lifu, Zhou Ping. Application of Lagrange equation in fluid mechanics. Journal of Harbin Engineering University, 2018,39(1):33-39 (in Chinese))
[41]	梁立孚, 郭庆勇. 航天刚-弹-液耦合系统的弹-液耦合研究. 北京航空航天大学学报, 2019,45(2):243-251
[41]	( Liang Lifu, Guo Qingyong. Elastic-liquid coupling in aerospace rigid-elastic-liquid coupling system. Journal of Beijing University of Aeronautics and Astronautics, 2019,45(2):243-251 (in Chinese))
[42]	梁立孚, 郭庆勇, 宋海燕. 连续介质分析动力学及其应用. 力学进展, 2019,49:201908
[42]	( Liang Lifu, Guo Qingyong, Song Haiyan. Analytical dynamics of continuous medium and its application. Advances in Mechanics, 2019,49:201908 (in Chinese))
[43]	邢景棠, 周盛, 崔尔杰. 流固耦合力学概述. 力学进展, 1997,27(1):19-38
[43]	( Xing Jingtang, Zhou Sheng, Cui Erjie. A survey on the fluid-solid interaction mechnics. Advances in Mechanics, 1997,27(1):19-38 (in Chinese))
[44]	Xing JT. Developments of numerical method for linear and nonlinear fluid-solid interaction dynamics with applications. Advances in Mechanics, 2016,46(2):95-139
[45]	岳宝增. 液体大幅晃动动力学. 北京: 科学出版社, 2012
[45]	( Yue Baozeng. Dynamics of Large Liquid Sloshing. Beijing: Science Press, 2012 (in Chinese))