Quasi-variational principle and application of initial value problem for rigid-elastic coupling dynamics
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摘要:
刚弹耦合动力学在国防和民用经济建设中有着广阔的应用前景，但目前还没有完全成熟的理论研究成果。鉴于此，针对刚弹耦合特性，建立初值问题拟变分原理；应用变分方法，推导拟变分原理的拟驻值条件，即得到刚弹耦合动力学的控制方程；给出刚弹耦合动力学初值问题拟变分原理应用的2个算例，1个是应用控制方程求得自由梁的奇数阶振型的解析解，1个是应用变分直接方法Ritz方法求得自由梁的偶数阶振型的解析解。研究表明，刚弹耦合动力学初值问题拟变分原理为建立有限元计算模型提供了依据。
Abstract:The rigid-elastic coupling dynamics has been widely used in the national defense and civil economic construction, but there are still no mature theoretical research results. In this view, the quasi-variational principle of the initial value problem was established, according to rigid-elastic coupling characters, and the quasi-stationary condition of the quasi-variational principle was derived by the variational method. This condition is the governing equation of rigid-elastic coupling dynamics. Two examples were given to show the application of this condition. One was the analytical solution of the odd order vibration mode of free beam obtained by the governing equation. The other is the analytical solution of the even order vibration mode of the free beam obtained by the variational direct method Ritz method. The results show that the quasi-variational principle of the initial value problem of the rigid-elastic coupling dynamics provides the basis for the establishment of finite element model.
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图 1 无约束梁自由振动的三阶振型
Figure 1. Third-order vibration mode of unrestrained beam in a free vibration
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[1] 蒋建平, 李东旭.航天器挠性附件刚柔耦合动力学建模与仿真[J].宇航学报, 2015, 26(3):270-274. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200503006.htmJIANG J P, LI D X.Modeling and simulation for the rigid-flexible coupling[J].Journal of Astronautics, 2015, 26(3):270-274(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200503006.htm [2] 戈庆明, 郭军.作大范围运动刚柔混合体的动力学建模与仿真[J].北京航空航天大学学报, 2011, 37(9):1110-1114. http://bhxb.buaa.edu.cn/CN/abstract/abstract12071.shtmlGE Q M, GUO J.Dynamical modeing and simulaion of rigid-flexible hybrids in large overall motions[J].Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(9):1110-1114(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract12071.shtml [3] 陆毓颖, 刘铸永, 洪嘉振.挠性航天器系统动力学耦合特性研究[J].空间科学学报, 2012, 32(4):550-554. doi: 10.11728/cjss2012.04.550LU Y Y, LIU Z Y, HONG J Z.Study on dynamic coupling characteristic of flexible spacecraft[J].Chinese Journal of Space Science, 2012, 32(4):550-554(in Chinese). doi: 10.11728/cjss2012.04.550 [4] 游斌弟, 温建民, 张广玉, 等.航天器薄壳柔性附件展开耦合行为特性研究[J].宇航学报, 2015, 36(6):640-647. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201506004.htmYOU B D, WEN J M, ZHANG G Y, et al.Study on coupling behavior of spacecraft deployment with flexible appendages of shell structure[J].Journal of Astronautics, 2015, 36(6):640-647(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201506004.htm [5] 韩清鹏, 高培鑫.大范围运动条件下的刚柔混合机械臂动力学分析[J].机械设计, 2013, 30(2):27-31. http://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ201302007.htmHAN Q P, GAO P X.Dynamic analysis of rigid-flexible manipulators undergoing a large overall motion condition[J].Journal of Machine Design, 2013, 30(2):27-31(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ201302007.htm [6] 车仁炜, 陆念力, 薛渊.基于EFEM的5R机械臂刚柔耦合动力学分析[J].哈尔滨工程大学学报, 2015, 36(11):1504-1508. http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201511016.htmCHE R W, LU N L, XUE Y.Dynamic analysis on the rigid-flexible coupled multi-boby system of 5R manipulator based on EFEM[J].Journal of Harbin Engineering University, 2015, 36(11):1504-1508(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201511016.htm [7] 张清华, 张宪民.平面3-RRR柔性并联机器人动力学建模与分析[J].振动工程学报, 2013, 26(2):239-245. http://cdmd.cnki.com.cn/Article/CDMD-10561-1013320363.htmZHANG Q H, ZHANG X M.Dynamic modeling and analysis of planar 3-RRR flexible parallel robots[J].Journal of Vibration Engineering, 2013, 26(2):239-245(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10561-1013320363.htm [8] 凌云, 宋爱国, 卢伟.一种刚、柔机械臂组合的月壤取样器动力学分析[J].宇航学报, 2014, 35(7):770-776. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201407006.htmLING Y, SONG A G, LU W.Dynamics analysis of a rigid-flexible combined lunar sampler[J].Journal of Astronautics, 2014, 35(7):770-776(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201407006.htm [9] 梁立孚, 宋海燕, 郭庆勇.应用Lagrange方程研究刚弹耦合动力学[J].哈尔滨工程大学学报, 2015, 36(4):456-460. http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201504006.htmLIANG L F, SONG H Y, GUO Q Y.Research on rigid-flexible coupling dynamics using Lagrange equation[J].Journal of Harbin Engineering University, 2015, 36(4):456-460(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201504006.htm [10] WASFY T M, NOOR A K.Computational strategies for flexible multi-body systems[J].Applied Mechanics Review, 2003, 56(6): 553-613. doi: 10.1115/1.1590354 [11] 钟杭, 王耀南, 李玲, 等.旋翼飞行机械臂建模及动态重心补偿控制[J].控制理论与应用, 2016, 33(3):311-320. http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201603006.htmZHONG H, WANG Y N, LI L, et al.Rotor-flying manipulator modeling and control with dynamic compensation for gravity offset[J].Control Theory & Applications, 2016, 33(3):311-320(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201603006.htm [12] KOJIMA Y, TANIWAKI S, OKAMI Y.Dynamic simulation of stick-slip motion of a flexible solar array[J].Control Engineering Practice, 2008, 16(6):724-735. doi: 10.1016/j.conengprac.2006.11.014 [13] 李发宗, 童水光, 王相兵, 等.船用挖掘机机械臂刚柔耦合动力学及特性研究[J].振动与冲击, 2014, 33(20):157-163. http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201420031.htmLI F Z, TONG S G, WANG X B, et al.Rigid-flexible coupling dynamics and characteristics of marine excavator's mechanical arm[J].Journal of Vibration and Shock, 2014, 33(20):157-163(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201420031.htm [14] 朴明伟, 杨晶, 赵强, 等.高铁车辆刚柔耦合仿真奇异性及其处理对策[J].计算机集成制造系统, 2015, 21(9):2458-2466. http://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201509024.htmPIAO M W, YANG J, ZHAO Q, et al.Rigid-flexible coupling simulation singularity of high-speed rolling stocks and transaction strategy[J].Computer Integrated Manufacturing Systems, 2015, 21(9):2458-2466(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201509024.htm [15] 刘莉, 陈树霖, 周思达, 等.脉冲子结构与有限元刚-弹混合连接的子结构方法[J].航空学报, 2015, 36(8):2670-2680. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201508017.htmLIU L, CHEN S L, ZHOU S D, et al.A substructure method for coupling impulse response functions with finite element models via rigid-elastic joints[J].Acta Aeronautica et Astronautica Sinica, 2015, 36(8):2670-2680(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201508017.htm [16] 谢琴, 吴运新.液压挖掘机刚柔耦合动力学分析[J].机械传动, 2016, 40(5):101-104. http://cdmd.cnki.com.cn/Article/CDMD-10184-1013320775.htmXIE Q, WU Y X.Rigid-flexible coupling dynamics analysis of hydraulic excavator[J].Journal of Mechanical Transmission, 2016, 40(5):101-104(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10184-1013320775.htm [17] 杨丽, 孙志礼, 柴小冬, 等.供弹机虚拟样机刚柔耦合动力学特性[J].中国工程机械学报, 2014, 12(5):377-383. http://www.cnki.com.cn/Article/CJFDTOTAL-GCHE201405001.htmYANG L, SUN Z L, CHAI X D, et al.Feeder virtual prototyping on rigid-flexible coupling dynamical properties[J].Chinese Journal of Construction Machinery, 2014, 12(5):377-383(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GCHE201405001.htm [18] BASHER H A.Modeling and simulation of flexibe robot manipulator with a prismatic joint[C]//Proceedings of IEEE Southeast Conference.Piscataway, NJ:IEEE Press, 2007:255-260. [19] 马兴瑞, 王本利, 苟兴宇.航天器动力学——若干问题进展及应用[M].北京:科学出版社, 2001.MA X R, WANG B L, GOU X Y.Spacecraft dynamics—Development and application in a few problems[M].Beijing:Science Press, 2001(in Chinese). [20] 黄文虎, 曹登庆, 韩增尧.航天器动力学与控制的研究进展与展望[J].力学进展, 2012, 42(4):367-394. doi: 10.6052/1000-0992-11-171HUANG W H, CAO D Q, HAN Z Y.Advances and trends in dynamics and control of spacecrafts[J].Advances in Mechanics, 2012, 42(4):367-394(in Chinese). doi: 10.6052/1000-0992-11-171 [21] 岳宝增, 宋晓娟.具有刚-柔-液-控耦合的航天器动力学研究进展[J].力学进展, 2013, 43(1):162-172. http://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201301013.htmYUE B Z, SONG X J.Advances in rigid-flexible-liquid-control coupling dynamics of spacecraft[J].Advances in Mechanics, 2013, 43(1):162-172(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201301013.htm [22] 梁立孚, 宋海燕, 樊涛, 等.非保守系统的拟变分原理及其应用[M].北京:科学出版社, 2015:62-70, 137-138.LING L F, SONG H Y, FAN T, et al.Quasi-variational principles of non-conservative system and Their applications[M].Beijing:Science Press, 2015:62-70, 137-138(in Chinese). [23] GURTIN M E.Variationnal principles for elastodynamics[J].Archive for Rational Mechanics and Analysis, 1964, 16(1):34-50. [24] 罗恩.关于线弹性动力学中各种Gurtin型变分原理[J].中国科学:A辑, 1987(9):936-948. http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK198709004.htmLUO E.Gurtin-type variational principles in linear elastodynamics[J].Science in China(Series A), 1987(9):936-948(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK198709004.htm [25] 罗恩, 朱慧坚.有限变形弹性动力学的非传统Gurtin型变分原理[J].固体力学学报, 2003, 24(1):1-7. http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200301000.htmLOU E, ZHU H J.Unconventional Gurtin-type variational principles for finite deformation elastodynamics[J].Acta Mechanica Solida Sinica, 2003, 24(1):1-7(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200301000.htm [26] 梁立孚, 周平, 刘宗民.刚体动力学初值问题的拟变分原理及其应用[J].哈尔滨工程大学学报, 2009, 30(10):1091-1096. http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200910003.htmLING L F, ZHOU P, LIU Z M.Quasi-variational principles of the initial value problem in rigid-body dynamics and their applications[J].Journal of Harbin Engineering University, 2009, 30(10):1091-1096(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200910003.htm [27] 梁立孚, 宋海燕, 李海波.航天分析动力学[M].北京:科学出版社, 2016:125-128.LING L F, SONG H Y, LI H B.Analytical dynamics of aerospace systems[M].Beijing:Science Press, 2016:125-128 (in Chinese). [28] 克拉夫R W, 彭津J. 结构动力学[M]. 王光远, 等译. 北京: 高等教育出版社, 2006: 294-306.CLOUGH R W, PENZIEN J.Dynamics of structures[M].WANG G Y, et al, translated.Beijing:Higher Education Press, 2006:294-306(in Chinese). [29] 诸德超, 邢誉峰.工程振动基础[M].北京:北京航空航天大学出版社, 2004:168-277.ZHU D C, XING Y F.Engineering vibration foundation[M].Beijing:Beihang University Press, 2004:168-277(in Chinese). [30] 姚熊亮.舰船结构振动冲击与噪声[M].北京:国防工业出版社, 2007:168-178.YAO X L.Vibration ahock and noise of warship structure[M].Beijing:National Defend Industry Press, 2007:168-178(in Chinese). [31] 邱吉宝, 张正平, 李海波.航天器与运载火箭耦合分析相关技术研究进展[J].力学进展, 2012, 42(4):416-434. doi: 10.6052/1000-0992-11-203QIU J B, ZHANG Z P, LI H B.Progresses in research on coupled analysis technology for space vehicle and launch vehicles[J].Advances in Mechanics, 2012, 42(4):416-434(in Chinese). doi: 10.6052/1000-0992-11-203 [32] 李东旭.高等结构动力学[M].北京:科学出版社, 2010:319-329.LI D X.Advanced atructural dynamics[M].Beijing:Science Press, 2010:319-329(in Chinese). [33] 史密斯M S. 结构动力学[M]. 五〇四翻译小组, 译. 北京: 国防工业出版社, 1976: 71-75.SMITH M S.Structural dynamics[M].504 Translation Group, translated.Beijing:National Defend Industry Press, 1976:71-75(in Chinese). [34] 李海波, 宋海燕, 梁立孚.确定无约束梁耦合振型的一种途径[J].强度与环境, 2011, 38(2):6-12. http://www.cnki.com.cn/Article/CJFDTOTAL-QDHJ201102002.htmLI H B, SONG H Y, LING L F.An approach of coupled vibration mode determined of unrestrained beam[J].Structure & Environment Engineering, 2011, 38(2):6-12(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-QDHJ201102002.htm -
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