含单面约束的多体系统动力学
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摘要
随着多体系统动力学的发展,单面约束问题越来越引起人们的关注。因为绳索在船舶、航空航天等领域有着广泛应用,因此由绳索引起的单面约束问题的研究就显得至关重要。
用传统方法求解由绳索引起的单面约束问题时,频繁判断单面约束的接触条件给求解带来很多困难,更难进行建模仿真分析。因此,寻找一种比较简单的建模方法就显得尤为重要,本文旨在于用比较简单的建模方法来分析由绳索引起单面约束问题和绳索作为柔体的刚柔耦合系统。
主要内容:
(1)多刚体动力学模型能有效的处理强非线性问题,并在一定程度上反映系统的真实情况。采用多刚体一球铰模型对绳索进行离散化建模,将单面约束问题转化为双面约束问题求解,用多体软件和ADAMS软件进行建模分析。
(2)对于绳索弹性变形不可忽略的刚柔耦合系统,有限段方法与一般有限元方法用于多柔体系统相比具有无可比拟的优越性。采用有限段方法使很棘手的刚柔耦合问题转化为比较成熟的多刚体动力学问题。将动力学方程建立在段坐标系上,而非体坐标系上,通过段间的线性变形来表现整体的非线性变形,不但使问题简化,而且提高了精确度。
(3)最后分别以单摆系统,拖拽系统和碰撞系统为例在MATLAB中结合多刚体动力学的程序和ADAMS中进行建模分析,仿真结果证明了两种方法的正确性。
With the development of dynamics of the multibody systems the problem of unilateral constraint has been paid more attention by people.Beause the rope has been used in many fields such as the ship,the aerospace and so on,the unilateral constraint problem caused by the rope has become more and more important.
When the traditional method is used to solve the problem of unilateral constraint, frequent judgment of the unilateral constraint contact conditions will cause a lot of difficulties and it is impossible for analysis and modeling.So it is very improtant to find simple models for analysis and modeling.Using simple modeling methods to analyz the unilateral constraint problem and the complex rigid-flexible coupling multibody system which the rope is the flexible body is proposed to find in this thesis.
The main research work can be summarized as follows:
(1)The multi-rigid body dynamic model can efficiently deal with a strongly nonlinear problem.Discrete model of the rope is established by using multi-rigid body sphericla hinge model.So the problem of unilateral constraint will be changed into a bilateral constraint problem.Use the software of the multibody and ADAMS to model and analyz.
(2)Compared with the finite element method used in the flexible multibody system,the finite segment method has an unparalleled advantage,if the elastic deformation of the rope should not be neglected in the complex rigid-flexible coupling multibody system.The finite segment method has been used to make the complex rigid-flexible coupling system become to be a multi-rigid-body dynamics problem which is a more mature system in this thesis. Dynamic equations will be built on the above coordinate system,rather than the flexible body coordinate system.The overall deformation of the non-deformation will be descriped by inter-segment linear deformation.This will not only make the problem greatly simplified,but also make the accuracy futher improved.
(3)In the end pendulum system,drag-and-drop system and collision system are exampled for modeling and analysis using the former mentioned modeling methods with MATLAB in the multibody systems programs and ADAMS in this paper.The numerical simulation proves the validity of the modeling methods.
用传统方法求解由绳索引起的单面约束问题时,频繁判断单面约束的接触条件给求解带来很多困难,更难进行建模仿真分析。因此,寻找一种比较简单的建模方法就显得尤为重要,本文旨在于用比较简单的建模方法来分析由绳索引起单面约束问题和绳索作为柔体的刚柔耦合系统。
主要内容:
(1)多刚体动力学模型能有效的处理强非线性问题,并在一定程度上反映系统的真实情况。采用多刚体一球铰模型对绳索进行离散化建模,将单面约束问题转化为双面约束问题求解,用多体软件和ADAMS软件进行建模分析。
(2)对于绳索弹性变形不可忽略的刚柔耦合系统,有限段方法与一般有限元方法用于多柔体系统相比具有无可比拟的优越性。采用有限段方法使很棘手的刚柔耦合问题转化为比较成熟的多刚体动力学问题。将动力学方程建立在段坐标系上,而非体坐标系上,通过段间的线性变形来表现整体的非线性变形,不但使问题简化,而且提高了精确度。
(3)最后分别以单摆系统,拖拽系统和碰撞系统为例在MATLAB中结合多刚体动力学的程序和ADAMS中进行建模分析,仿真结果证明了两种方法的正确性。
With the development of dynamics of the multibody systems the problem of unilateral constraint has been paid more attention by people.Beause the rope has been used in many fields such as the ship,the aerospace and so on,the unilateral constraint problem caused by the rope has become more and more important.
When the traditional method is used to solve the problem of unilateral constraint, frequent judgment of the unilateral constraint contact conditions will cause a lot of difficulties and it is impossible for analysis and modeling.So it is very improtant to find simple models for analysis and modeling.Using simple modeling methods to analyz the unilateral constraint problem and the complex rigid-flexible coupling multibody system which the rope is the flexible body is proposed to find in this thesis.
The main research work can be summarized as follows:
(1)The multi-rigid body dynamic model can efficiently deal with a strongly nonlinear problem.Discrete model of the rope is established by using multi-rigid body sphericla hinge model.So the problem of unilateral constraint will be changed into a bilateral constraint problem.Use the software of the multibody and ADAMS to model and analyz.
(2)Compared with the finite element method used in the flexible multibody system,the finite segment method has an unparalleled advantage,if the elastic deformation of the rope should not be neglected in the complex rigid-flexible coupling multibody system.The finite segment method has been used to make the complex rigid-flexible coupling system become to be a multi-rigid-body dynamics problem which is a more mature system in this thesis. Dynamic equations will be built on the above coordinate system,rather than the flexible body coordinate system.The overall deformation of the non-deformation will be descriped by inter-segment linear deformation.This will not only make the problem greatly simplified,but also make the accuracy futher improved.
(3)In the end pendulum system,drag-and-drop system and collision system are exampled for modeling and analysis using the former mentioned modeling methods with MATLAB in the multibody systems programs and ADAMS in this paper.The numerical simulation proves the validity of the modeling methods.
引文
[1]Bezverkhii A 1,Kornienko V F,Shul'ga N A.The visco elastic effect of the cable on the dynamics of an underwatertowed system suspended from a buoy.International Applied Mechanics,2001,37(8):10551061
[2]Sun Y,Leonard J W.Dynamics of ocean cables with lo-cal low-tension regions.OceanEngineering,1998,25(6):443463
[3]Stump D M,Van der Heijden G H M.Matched asymptotic expansions for bent and twisted rods:applications for cable and pipeline laying.Journal of Engineering Mathematics,2000,38:1331
[4]Henderson J F,Potjewyd J,Ireland B.The dynamics of an airborne towed target system with active control.ProcInstn Mech Engrs,1999,213(Part G):305319
[5]Banerjee A K,Do Van N.Deployment control of a cable connecting a ship to an underwarter vehicle.Applied Math-ematics and Computation,1995,70:97116
[6]金栋平,胡海岩.行进绳索在横向流体激励下的运动.力学学报,2001,33(4):525530
[7]Matteo Luca Facchinetti,Emmanuel de Langre,Francis Biolley.Vortex-induced travelling waves along a cable.European Journal of Mechanics B1Fluids,2004,23:199208
[8]Catti C.Numerical simulation of large deformation cable dynamics:dissertation Michigan:University of Michigan,2002.1295
[9]Abdel-Rahman E M,Nayfeh A H.Pendulation reduction in boom cranes using cable length manipulation.Nonlinear Dynamics,2002,27(3):255269
[10]Kimiaghalam B,Homaifar A,Bikdash M.Feedforward control law for a shipboard crane with maryland rigging system.Joural of Vibration and Control,2002,8(2):159-188
[11]袁曾怀,金栋平,金世伟.环锭纺气圈动态方程的理论研究.合肥工业大学学报,1994,17(3):3438
[12]Fraser W B,Clark J D,Ghosh T K,Zeng(a.The effect of a control ring on the stability of the ring-spinning balloon.Proc R Soc Lond A,1996,452:4762
[13]Zhu F,Rahn C D.Stability analysis of a circularly rowed cable-body system.Joural of Sound and Vibration,1998,217(3):435452
[14]顾明,刘慈军,彭天波,宋锦忠.海口世纪大桥斜垃索风(雨)振动的初步分析.结构工程师.1999,1:1822
[15]Abdel-Rahman E M,Hasan M.Control by passive TMD of wind-induced nonlinear vibrations in cable stayed bridges.Joural of Vibration and Control,1996,2(2):251267
[16]Masaru Matsumoto,Tomomi Yagi,Yoshinori Shigemura,Daisuke Tsukhima.Vortex-induced cable vibration of cable stayed bridges at high reduced wind velocity.Joural of Wind Engineering and Industrial Aerodynamics,2001,89:633647
[17]Yu P,Desai Y M,Shah A H,Popplewell N.Theree-degree-of-freedom model for galloping.part 1:formulation.Journal of Engineering Mechanics,1993,119(12):24042425
[18]Pierre McComber,Alain Paradis.A cable galloping model for thin ice accretions.Atmospheric Research,1998,46:1325
[19]Ehud Netzer,Thomas R Kane.Estimation and control of tethered satellite systems.Journal of Guidance,Control,and Dynamics,1995,18(4):851858
[20]Irvine H M,Caughey T K.The linear theory of free vibrations of a suspended cable.Proc R Soc Lond A,1974,341:299315
[21]R.L.Huston.Multibody dynamics including the effects of flexibility and compliance.Computers and Structures.1981,14(56):443-451
[22]F.M.L.Amirouche et al.Dynamics of large constraint flexible structures.J.of Dyn.Sys.Mea.and Cont.1988,110:78-83
[23]Zhang Dajun,Liu Youwn,and R.L.Huston.Stiffness equations of finite segment method.Chinese J.of Mech.Eng.,1992,5
[24]闫绍泽、刘冰清、刘又午等.柔性多体系统动力学-有限段方法.河北工业大报.1997,Vol23.No.3
[25]闰绍泽.计及动力刚化的柔性机械系统动力学理论、仿真及实验研究.天津大学博士学文.1996,8
[26]金栋平、文浩、胡海岩.绳索系统的建模、动力学和控制.力学进展.Vol.34 No.3 Aug.25,2004
[27]伙艳琼、邹心勇、赵纪生.大型构件吊装最佳绳系方案研究
[28]程志军、孙炳楠、唐锦春.大垂度悬索结构的几何非线性分析.浙江建筑.No.2,2000
[29]李宾、李映辉、殷学纲在.大锤度柔索的动力学建模与仿真.应用数学和力学.Vol.21No.6,2000
[30]T.R.Kane,R.R.Ryan,A.K.Banerjee.Dynamics of a cantilever Beam Attached to a moving Base.J.GUIDANCE.VOL.10,NO.2,MARCH-APRIL 1987
[31]齐朝晖.多体系统动力学.科学出版社
[32]陈立平,张云清,任卫群等.机械系统动力学分析及ADAMS应用教程.北京:清华大学出版社2005.
[2]Sun Y,Leonard J W.Dynamics of ocean cables with lo-cal low-tension regions.OceanEngineering,1998,25(6):443463
[3]Stump D M,Van der Heijden G H M.Matched asymptotic expansions for bent and twisted rods:applications for cable and pipeline laying.Journal of Engineering Mathematics,2000,38:1331
[4]Henderson J F,Potjewyd J,Ireland B.The dynamics of an airborne towed target system with active control.ProcInstn Mech Engrs,1999,213(Part G):305319
[5]Banerjee A K,Do Van N.Deployment control of a cable connecting a ship to an underwarter vehicle.Applied Math-ematics and Computation,1995,70:97116
[6]金栋平,胡海岩.行进绳索在横向流体激励下的运动.力学学报,2001,33(4):525530
[7]Matteo Luca Facchinetti,Emmanuel de Langre,Francis Biolley.Vortex-induced travelling waves along a cable.European Journal of Mechanics B1Fluids,2004,23:199208
[8]Catti C.Numerical simulation of large deformation cable dynamics:dissertation Michigan:University of Michigan,2002.1295
[9]Abdel-Rahman E M,Nayfeh A H.Pendulation reduction in boom cranes using cable length manipulation.Nonlinear Dynamics,2002,27(3):255269
[10]Kimiaghalam B,Homaifar A,Bikdash M.Feedforward control law for a shipboard crane with maryland rigging system.Joural of Vibration and Control,2002,8(2):159-188
[11]袁曾怀,金栋平,金世伟.环锭纺气圈动态方程的理论研究.合肥工业大学学报,1994,17(3):3438
[12]Fraser W B,Clark J D,Ghosh T K,Zeng(a.The effect of a control ring on the stability of the ring-spinning balloon.Proc R Soc Lond A,1996,452:4762
[13]Zhu F,Rahn C D.Stability analysis of a circularly rowed cable-body system.Joural of Sound and Vibration,1998,217(3):435452
[14]顾明,刘慈军,彭天波,宋锦忠.海口世纪大桥斜垃索风(雨)振动的初步分析.结构工程师.1999,1:1822
[15]Abdel-Rahman E M,Hasan M.Control by passive TMD of wind-induced nonlinear vibrations in cable stayed bridges.Joural of Vibration and Control,1996,2(2):251267
[16]Masaru Matsumoto,Tomomi Yagi,Yoshinori Shigemura,Daisuke Tsukhima.Vortex-induced cable vibration of cable stayed bridges at high reduced wind velocity.Joural of Wind Engineering and Industrial Aerodynamics,2001,89:633647
[17]Yu P,Desai Y M,Shah A H,Popplewell N.Theree-degree-of-freedom model for galloping.part 1:formulation.Journal of Engineering Mechanics,1993,119(12):24042425
[18]Pierre McComber,Alain Paradis.A cable galloping model for thin ice accretions.Atmospheric Research,1998,46:1325
[19]Ehud Netzer,Thomas R Kane.Estimation and control of tethered satellite systems.Journal of Guidance,Control,and Dynamics,1995,18(4):851858
[20]Irvine H M,Caughey T K.The linear theory of free vibrations of a suspended cable.Proc R Soc Lond A,1974,341:299315
[21]R.L.Huston.Multibody dynamics including the effects of flexibility and compliance.Computers and Structures.1981,14(56):443-451
[22]F.M.L.Amirouche et al.Dynamics of large constraint flexible structures.J.of Dyn.Sys.Mea.and Cont.1988,110:78-83
[23]Zhang Dajun,Liu Youwn,and R.L.Huston.Stiffness equations of finite segment method.Chinese J.of Mech.Eng.,1992,5
[24]闫绍泽、刘冰清、刘又午等.柔性多体系统动力学-有限段方法.河北工业大报.1997,Vol23.No.3
[25]闰绍泽.计及动力刚化的柔性机械系统动力学理论、仿真及实验研究.天津大学博士学文.1996,8
[26]金栋平、文浩、胡海岩.绳索系统的建模、动力学和控制.力学进展.Vol.34 No.3 Aug.25,2004
[27]伙艳琼、邹心勇、赵纪生.大型构件吊装最佳绳系方案研究
[28]程志军、孙炳楠、唐锦春.大垂度悬索结构的几何非线性分析.浙江建筑.No.2,2000
[29]李宾、李映辉、殷学纲在.大锤度柔索的动力学建模与仿真.应用数学和力学.Vol.21No.6,2000
[30]T.R.Kane,R.R.Ryan,A.K.Banerjee.Dynamics of a cantilever Beam Attached to a moving Base.J.GUIDANCE.VOL.10,NO.2,MARCH-APRIL 1987
[31]齐朝晖.多体系统动力学.科学出版社
[32]陈立平,张云清,任卫群等.机械系统动力学分析及ADAMS应用教程.北京:清华大学出版社2005.