车载式火炮刚柔耦合发射动力学研究
|
摘要
本文基于多体动力学、有限元、接触／碰撞动力学和数值计算等理论对某车载式火炮刚柔耦合发射动力学问题进行了探索研究,为该类武器的总体设计和结构设计提供理论依据和决策参考。
使用NURBS造型理论对车载式火炮零部件进行实体建模,为接触／碰撞分析提供精确的三维几何模型；对LMS/Motion软件进行了底层开发,利用动态链接库将Lankarani和Nikravesh接触力模型嵌入到LMS/Motion软件中,通过典型构件接触／碰撞的计算与比较分析,提出了某车载式火炮主要零部件接触／碰撞问题的处理方式；以某车载式火炮方向回转轴承为对象,用VBScript编制了滚珠接触／碰撞批量建模的宏命令,建立了计及滚珠与内／外滚道、相邻滚珠间、齿弧与方向机主齿轮之间的接触／碰撞以及间隙的多刚体接触／碰撞模型,通过数值计算给出了方向回转轴承结构参数对炮口扰动和部件受力的影响规律。
利用柔体-柔体接触／碰撞的模型模拟身管与摇架衬套的相互作用,通过8节点等参六面体单元和主／从节点建立身管、摇架衬套的精细有限元模型,基于Craig-Bampton模态分析理论计算主模态和约束模态,利用模态截断的方法,获得LMS/Motion柔性动力学分析所需的模态信息；以某车载式火炮为例,通过柔体间接触／碰撞模型的计算分析,得到了身管柔性、接触间隙对炮口扰动的影响规律。
对土壤弹塑性变形的建模进行了探讨,使用实体单元、壳单元等单元形式对土壤、座钣和驻锄进行有限元离散,利用Drucker-Prager材料模型描述土壤的弹塑性,基于主控／从属接触搜索算法计算土壤载荷和变形之间的关系,应用最小二乘拟合法获得描述土壤弹塑性的非线性刚度曲线,对两种典型土壤的弹塑性模型进行了数值计算,给出了不同土壤对炮口扰动的影响规律。
建立了综合考虑方向回转轴承接触／碰撞、柔性身管-柔性摇架衬套接触／碰撞以及土壤弹塑性的车载式火炮发射过程刚柔耦合动力学模型,通过数值计算分析,研究了土壤弹塑性、方向回转轴承、柔性身管等因素对火炮炮口扰动及关键部件受力的影响规律,数值计算结果与实测数据取得了较好的一致性。
Based on multibody dynamics, finite element analysis, contact/impact theory and the correlational numerical methods, an approach toward the rigid-flexible couple launch dynamics was investigated for the trucked-mounted gun, which can provide theoretical foundation and design decision for overall design and structural design of such weapon systems.
The solution accuracy of the contact problem depends upon the precision of the 3D model, so the components were modeled based on the NURBS theory. A subroutine about the Lankarani and Nikravesh contact force model was linked to extend the LMS/Motion's contact force model using the method of dynamic link library. In light of summation on the results from dynamic responses of impact/contact between typical parts, a procedure for dealing with impact/contact problem was presented for the trucked-mounted gun. The macro edited by VBScript was used to automatically set numerous models of contact/impact between balls for the traverse bearing. By taking the contact between ball and raceway, ball and adjacent ball, gear arc and main gear of the traversing mechanism, and the clearance between ball and raceway into consideration, the dynamic model of rigid bodies system was set up for the trucked-mounted gun. The effects of structural parameters of traverse bearing on muzzle disturbance and forces acted on parts were examined by using numerical computation.
The flexible-body contact method is used to construct the coupling between the barrel and cradle bush. The barrel and the bush of cradle were meshed by CHEXA element manually and the master/slave nodes technique was used. Based on the Craig-Bampton method and the mode truncation technique, the main mode and the constraint mode of the barrel and bush were used to construct the flexible bodies by LMS/Motion. Via the model of contact between the flexible bodies, the effects of the barrel's flexibility and contact clearance on muzzle disturbance were analyzed for the trucked-mounted gun.
Modeling of elastic and plastic deformation is conducted for soil. Soil, base plate, and spade were discretisized by solid and shell element, respectively. Drucker-Prager model was utilized for describing elasticity and plasticity of soil. The master/slave searching technique was used to get the relation between load and deformation. The least square fitting method was applied to attain the nonlinear stiffness curve, which was used in representing elasticity and plasticity of soil, and providing the soil model for multi-body dynamics analysis of the trucked-mounted gun. The plasticity of the two typical soil materials were numerically simulated, and their effects on muzzle disturbance were figured out.
With comprehensive consideration on the multiple contacts in the traversing bearing, the contact between barrel and cradle bush, and the elasticity and plasticity of soil, a model of rigid-flexible couple launch dynamics was established for the trucked-mounted gun. The effects of the elasticity and plasticity of soil, the traversing bearing, and the flexibility of barrel on muzzle disturbance and forces acted on the key components were investigated by means of numerical method, and the simulated results were in excellent agreement with the test data.
使用NURBS造型理论对车载式火炮零部件进行实体建模,为接触／碰撞分析提供精确的三维几何模型；对LMS/Motion软件进行了底层开发,利用动态链接库将Lankarani和Nikravesh接触力模型嵌入到LMS/Motion软件中,通过典型构件接触／碰撞的计算与比较分析,提出了某车载式火炮主要零部件接触／碰撞问题的处理方式；以某车载式火炮方向回转轴承为对象,用VBScript编制了滚珠接触／碰撞批量建模的宏命令,建立了计及滚珠与内／外滚道、相邻滚珠间、齿弧与方向机主齿轮之间的接触／碰撞以及间隙的多刚体接触／碰撞模型,通过数值计算给出了方向回转轴承结构参数对炮口扰动和部件受力的影响规律。
利用柔体-柔体接触／碰撞的模型模拟身管与摇架衬套的相互作用,通过8节点等参六面体单元和主／从节点建立身管、摇架衬套的精细有限元模型,基于Craig-Bampton模态分析理论计算主模态和约束模态,利用模态截断的方法,获得LMS/Motion柔性动力学分析所需的模态信息；以某车载式火炮为例,通过柔体间接触／碰撞模型的计算分析,得到了身管柔性、接触间隙对炮口扰动的影响规律。
对土壤弹塑性变形的建模进行了探讨,使用实体单元、壳单元等单元形式对土壤、座钣和驻锄进行有限元离散,利用Drucker-Prager材料模型描述土壤的弹塑性,基于主控／从属接触搜索算法计算土壤载荷和变形之间的关系,应用最小二乘拟合法获得描述土壤弹塑性的非线性刚度曲线,对两种典型土壤的弹塑性模型进行了数值计算,给出了不同土壤对炮口扰动的影响规律。
建立了综合考虑方向回转轴承接触／碰撞、柔性身管-柔性摇架衬套接触／碰撞以及土壤弹塑性的车载式火炮发射过程刚柔耦合动力学模型,通过数值计算分析,研究了土壤弹塑性、方向回转轴承、柔性身管等因素对火炮炮口扰动及关键部件受力的影响规律,数值计算结果与实测数据取得了较好的一致性。
Based on multibody dynamics, finite element analysis, contact/impact theory and the correlational numerical methods, an approach toward the rigid-flexible couple launch dynamics was investigated for the trucked-mounted gun, which can provide theoretical foundation and design decision for overall design and structural design of such weapon systems.
The solution accuracy of the contact problem depends upon the precision of the 3D model, so the components were modeled based on the NURBS theory. A subroutine about the Lankarani and Nikravesh contact force model was linked to extend the LMS/Motion's contact force model using the method of dynamic link library. In light of summation on the results from dynamic responses of impact/contact between typical parts, a procedure for dealing with impact/contact problem was presented for the trucked-mounted gun. The macro edited by VBScript was used to automatically set numerous models of contact/impact between balls for the traverse bearing. By taking the contact between ball and raceway, ball and adjacent ball, gear arc and main gear of the traversing mechanism, and the clearance between ball and raceway into consideration, the dynamic model of rigid bodies system was set up for the trucked-mounted gun. The effects of structural parameters of traverse bearing on muzzle disturbance and forces acted on parts were examined by using numerical computation.
The flexible-body contact method is used to construct the coupling between the barrel and cradle bush. The barrel and the bush of cradle were meshed by CHEXA element manually and the master/slave nodes technique was used. Based on the Craig-Bampton method and the mode truncation technique, the main mode and the constraint mode of the barrel and bush were used to construct the flexible bodies by LMS/Motion. Via the model of contact between the flexible bodies, the effects of the barrel's flexibility and contact clearance on muzzle disturbance were analyzed for the trucked-mounted gun.
Modeling of elastic and plastic deformation is conducted for soil. Soil, base plate, and spade were discretisized by solid and shell element, respectively. Drucker-Prager model was utilized for describing elasticity and plasticity of soil. The master/slave searching technique was used to get the relation between load and deformation. The least square fitting method was applied to attain the nonlinear stiffness curve, which was used in representing elasticity and plasticity of soil, and providing the soil model for multi-body dynamics analysis of the trucked-mounted gun. The plasticity of the two typical soil materials were numerically simulated, and their effects on muzzle disturbance were figured out.
With comprehensive consideration on the multiple contacts in the traversing bearing, the contact between barrel and cradle bush, and the elasticity and plasticity of soil, a model of rigid-flexible couple launch dynamics was established for the trucked-mounted gun. The effects of the elasticity and plasticity of soil, the traversing bearing, and the flexibility of barrel on muzzle disturbance and forces acted on the key components were investigated by means of numerical method, and the simulated results were in excellent agreement with the test data.
引文
[1]徐稼轩,郑铁生.结构动力学分析的数值方法[M].西安：西安交通大学出版社,1993：5～270.
[2]郭齐胜,董志明,单家元,等.系统仿真[M].北京：国防工业出版社,2006：5-45.
[3]陈家庆,周海,徐琳琳.滚动轴承载荷分布问题的理论研究进展[J].北京石油化工学院学报,8(1)：47～52.
[4]谢定义.土动力学[M].西安：西安交通大学出版社,1988：2-255.
[5]Henry J. Sneck. Main battle tank flexinble gun disturbance model three-segment model [J],ADA408136.
[6](苏)奥尔洛夫(B.B.OpπoB).炮身构造与设计[M].王天槐,刘淑华译.北京：国防工业出版社,1982：5-125.
[7]Boresi, Arthur P., Langhaar, Henry L. Dynamics of rigid guns with straight tubes[J], Recent advances in engineering mechanics and their impact on civil engineering practice, 1983:226～229.
[8]Jones, Donald E. Analysis of a controller for the M61 movable gun[J]. ADA081893.
[9]P.A. Cox, J.C. Hokanson. Muzzle motions of the M68 105mm tank gun, Final Technical Report, Contact DAAD05-75-C-0739, U.S. Army ARADCOM, Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland.
[10]D. J. Purdy, Modeling and simulation of a weapon control system for a main battle tank[J], Proceedings of the Eighth U.S. Army Symposium on Gun Dynamics.
[11]万长森.滚动轴承的分析方法[M].北京：机械工业出版社,1985：2-300.
[12]Martin T. Soifer, Robert S. Becker. Dynamic analysis of the 75mm ADMAG gun system[J],AD-A123867.
[13]Thomas F. Erline. Deviation effect of an in-bore centerline on a 5-inch naval gun[J]. AD-A193383.
[14]Stephen A. Wilkerson, David H. Lyon, Larry Rusch. Comparison between simulated and experimental results for a balanced-breeched M256 cannon system[J]. AD-A396625, 2000.
[15]P. C. T Chen, M Leach. Modeling of barrel/projectile interaction in a rotating band[J].AD-A392148,2001.
[16]火炮发射时的动力学分析研究.南京理工大学科研报告,1992,11.
[17]张振友.火炮发射时的动力学方程的建立与计算[D].南京：南京理工大学, 1992.
[18]杨国来.多柔体系统参数化模型及其在火炮中的应用研究[D].南京：南京理工大学,1999.
[19]王晓锋,姜兴渭.有限段法在高炮发射多体系统动力学分析中的应用[J].南京理工大学学报,2001,25(1)：25～27.
[20]敖勇.柔性多体系统动力学和动态子结构方法及其在自行火炮动力学仿真中的的应用[D].南京：南京理工大学,1997.
[21]毛保全.动力学优化设计及其在火炮中的应用研究[D].南京：南京理工大学,1997.
[22]楚志远.自行火炮非线性有限元动力学仿真[D].南京：南京理工大学,2001.
[23]王长武.自行火炮非线性有限元模型及仿真可视化技术研究[D].南京：南京理工大学,2002.
[24]石明全.某火炮自动供输弹系统和全炮耦合的发射动力学研究[D].南京：南京理-工大学,2003.
[25]刘雷.自行火炮刚弹耦合发射动力学研究[D].南京：南京理工大学,2005.
[26]管红根,陈常顺,高树滋.基于系统响应的模态截断方法的研究[J].南京理工大学学报,2000,24(6)：532～534.
[27]袁兆鼎,费景高,刘德贵等.刚性常微分方程初值问题的数值解法[M].北京：科学出版社,1987,11,5～200.
[28]芮筱亭,陆毓琪,陆文广,钱剑飞,王国平.自行炮发射动力学研究[J].兵工学报,2000,S1,38-21.
[29]张培林,王成,任国全.冲击作用下火炮复进机的实际效能分析[J].振动与冲击.2009,28(4)：142-148.
[30]万晓峰,刘根,杨树森.航炮系统的虚拟样机仿真与分析[J].系统仿真学报,2005,17(10)：2392～2394.
[31]王钢,王立权,孟祥伟,胡海胜.某火炮供弹系统的设计研究[J].兵工学报,2009,30(5)：518～524.
[32]葛建立.车载炮非线性有限元仿真分析[D].南京：南京理工大学,2007.
[33]刘延柱.多刚体系统动力学[M].北京：高等教育出版社,1989,3：7～300.
[34]洪嘉振.计算多体系统动力学[M].北京：高等教育出版社,1999,7：207～300.
[35]丁遂亮,洪嘉振.柔性多体系统接触/碰撞动力学研究[J].上海交通大学学报,2003,12,37(12)：1927～1930.
[36]陈立平,张云清,任为群,覃刚.机械系统动力学分析及ADAMS应用教程[M].北京：清华大学出版社,2005,1：2～300.
[37]Roberson R E, Wittenburg J. A dynamics for an formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite control [J].3rd IFAC Congr.1966, Proc London,1968:46D.2～46D.9.
[38]Fletcher H.J., Rongved L. Yu E Y. Dynamics analysis of a two-body gravitationally oriented satellite[J]. Bell System Tech J,1963,42(5):2239～2266.
[39](美)E.J.豪格.机械系统的计算机辅助运动学和动力学,第Ⅰ卷,基本方法[M].刘兴祥等译.北京：高等教育出版社,1996.4：4～300.
[40]于霖冲.柔性机构动态可靠性分析、设计与仿真[D].北京：北京航空航天大学,2006.
[41]李彬,刘锦阳.大变形柔性梁系统的绝对坐标方法[J].上海交通大学学报,39(5).2005.827～831.
[42]宋轶民,余跃庆,张策,马金盛.柔性机器人动力学分析与振动控制研究综述[J].机械设计,20(4),2003：1-5.
[43]Avello A, Jalon J. Dynamics of flexible multibody systems using cartesians coordinates and large displacement theory [J]. International Journal for Numerical Methods in Engineering,1991,32(1):543～563.
[44]Leonard Meirovitch, H. D. Nelson. High spin motion of satellite containing elastic parts[J]. J. Spacecraft and Rocked.13,1966,1597～1602.
[45]梁立孚,刘石泉,周健生.单柔体动力学的拟变分原理及其应用[J].中国科学,39(2),2009,293～304.
[46]H. B. Hablani. Constrained and unconstrained mode:some modeling aspects of flexible Spacecraf[J]. J. Guidance, Control and Dynamics,1982,5(2):164～198.
[47]W. S. Yoo, E. J. Haug. Dynamics of flexible mechanical system using vibration and static correction[J]. ASME J. of Mechanics, Transmission and Automation in Design,1986, 108:315～322.
[48]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,29(2)1999：145～154.
[49]Huston R L.多体系统动力学(上/下册)[M].刘又午译.天津：天津人学出版社,1987/1991.
[50]Huston R L, Passerello C E, Harlow M W. Dynamics of multi-rigid-body system[J]. ASME Journal of Applied Mechanics,1978,45(4):889～894.
[51]Huston R L., Passerello C E. Multibody structural dynamics including translation between the bodies[J]. Computers and Structures,1980,11:713～720.
[52]张人钧,刘又午.柔性多体系统动力学[J].机械工程学报(英文版),1994, 7(2)：156～162.
[53]张人钧,刘又午.有限段方法的刚度方程[J].机械工程学报(英文版),1992,5(1)：23～30.
[54]闫绍泽,刘冰清,刘又午,黄铁球.柔性多体系统动力学-有限段方法[J].河北工业大学学报,1997,3(26),1-9.
[55]Konno A, Uchiyama M. Modeling of a flexible manipulator dynamics based on the Holzer's method[J]. Journal of Japan Robot Institute,1994,12 (7):1021～1028.
[56]张铁民.柔性机械臂振动控制理论与实验研究[D].天津：天津大学,1996.
[57]阎绍泽.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[D].天津：天津大学,1996.
[58]许宏伟,马兴瑞,黄文虎,邵成勋,邹振祝.双臂协调约束系统动力学问题探讨[J],振动工程学报,7(1),1994：1-8.
[59]王琪.多体系统动力学的Lagrange算法研究[D].北京：北京航空航天大学,1996.
[60]林宝玖,谢传锋.挠性多体系统动力学[J].力学学报,21(4),1989,469～478
[61](德)维腾伯格,J.多刚体系统动力学[M].谢传锋译.北京：北京航空学院出版社,1988,1～205.
[62]洪嘉振,粱敏.多刚体碰撞动力学方程及可解性判别准则[J].应用力学学报,1991,8(1)：10～17.
[63]洪嘉振,粱敏.多刚体内碰撞数学模型与计算程序[J].力学学报,1989.21(4)：35-42.
[64]E. K., Rooth. Dynamics of a system of rigid bodies[M]. New York:Dover Publications Inc.1960.
[65]Wehage R A, Haug E J. Dynamic analysis of mechanical systems with intermittent motions[J]. ASME J of Mechanical Design.1982,104(4):778～785.
[66]刘才山,陈滨.多柔体系统碰撞动力学研究综述[J].力学进展,2000,30(1)：7-14.
[67]Rismantab-Sang J, Shabana A A. On the use of the momentum balance in the impact analysis of constrained elastic systems[J]. Journal of Vibration and Acoustics,1990,112: 119～126.
[68]Yigit A S, Ulsoy A G, Scott R A. Dynamic analysis of a radically rotating beam with impact. Part 1:theoretical and computational model[J]. Journal of Vibration and Acoustics, 1990,112:65～70.
[69]S. Wu, E. Haug. Geometric non-linear substructuring for dynamics of flexible mechanical systems [J], International Journal for Numerical Methods in Engineering,1988, 26:2211～2226.
[70]刘锦阳,洪嘉振.闭环柔性多体系统的多点撞击问题[J].中国机械工程,2000,11(6)：619～623.
[71]郭吉丰,升古保博,宫崎文夫.具有摩擦的刚体碰撞[J].应用力学学报,21(2),2004：77～83.
[72]Thornton C. Coefficient of Restitution for collinear collisions of elastic-perfectly plastic spheres[J]. J of Applied Mechanics,1997,64(2):383～886.
[73]A. P. Ivanov. On multiple impact[J]. J. App￡ Maths Mechs,59(6),1995:887-902.
[74]Dubowsky, F. Freudenstein, Dynamic analysis of mechanical systems with clearances. Part 1:formulation of dynamic model[J], Journal of Engineering for Industry Series B,93(1),1971:305～309.
[75]Hertz, H.. Gesammelte Werke(Volume.1), Leipzig, Germany,1985:2～200.
[76]Cookie, A. W.. Study of some impacts between metallic bodies by a piezoelectric method[J], Proceedings of the Royal Society London A212,1952:377～390.
[77]Johnson, K. L. Contact mechanics[M]. Cambridge:Cambridge University Press, 1992:5～206.
[78]Hunt, K. H., Crosslye, F. R. E.. Coefficient of restitution interpreted as damping in vibroimpact[J]. ASME J of Appl Mech,1975,42E:440～456.
[79]Lee, Ting W., Wang, A.C. On the dynamics of intermittent-motion mechanisms, part 1:dynamic model and response. Part 2:geneva mechanisms, ratchets, and escapetments [J]. Journal of Mechanisms, Transmissions, and Automation in Design,105(3),1982:534～551.
[80]Yigit, A. S., Usloy A. G. Spring dashpot models for the dynamics of a radically rotating beam with impact[J]. Journal of Sound and Vibration,1990,143(3),515～525.
[81]Yigit A S. The effect of flexibility on the impact response of a two-link rigid-flexible manipulator[J]. Journal of Sound and Vibration,1994,177(3):349～361.
[82]Lin FH, Tseng AA. A finite element analysis of elasto-plastic contact problems in metal forming[J]. Materials and Design,1998,19:99～108.
[83]Vasudevan S. Okada H and Atluri SN. Development of a new frame finite element. for crash analysis using a mixed variational principle and rotations as independent variables[J]. Finite Elements in Analysis and Design,1996,23:155～171.
[84]Hallquist, J. O, Goudreau, G. L., Benson, D. J.. Sliding interfaces with contact-impact in large scale Lagrangian computations[J]. Computer Methods in Applied Mechanics and Engineering,1985,751(1):107～137.
[85]S.W. Kim, A. K. Misra, V. J. Modix, Cyril. Simulation of contact dynamics of flexible multibody systems, AIAA-98-4552.
[86]Marco Anghileri, Luigi-M. L. Castelletti, Fabio Invernizzi, Marco Mascheroni. A survey of numerical models for hail impact analysis using explicit finite element codes[J]. International Journal of Impact Engineering,2005,31:929～944.
[87]R. W. Cottle, J. P. Pang, R. E. Stone. The Linear Complimentarily Problem[M]. Academic Press, London,1992.
[88]Pfeiffer, F., Glocker, Ch.. Contacts in multi-body systems[J]. J. Applied Mathematics Mechanics,2000,5:773～782.
[89]Moreau J. J. Evolution problem associated with a moving convex set in a Hilbert space[J]. J. Diff. Equations 1977,26:347～374.
[90]Bauchau, O, A,. Analysis of flexible multibody systems with intermittent contacts[J]. Multibody System Dynamics,2000,4:23～54.
[91]Wang, Hui-Ping. Meshfree smooth contact formulation and boundary condition treatments in multi-body contact[D]. The University of Iowa,2000:25～110.
[92]Nam H. Kim, Ki-Young Yi, Kyung K. Choi. Meshfree analysis and die shape design of extrusion process[J].9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA 2002-5563.
[93]Seifried, R., Eberhard P.. Impact analysis using modal reduction[J]. PAMM Proceedings in Applied Mathematics and Mechanics,2005,5:129～130.
[94]刘锦阳,洪嘉振.多点接触／碰撞的数值计算[J].上海交通大学学报,1997,31(7)：45～53.
[95]Ting-Nung Shiau, Yi-Jeng Tsai, Meng-Shiun Tsai. Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects[J]. J. of Mechanism and Machine Theory,43,2008:491～508.
[96]姚文莉,王育平,边力,赵振.多刚体系统接触／碰撞动力学研究进展[J].力学与实践,2007,29(6)：9-12.
[97]G. Gilardi, I. Sharf. Literature survey of contact dynamics modeling[J]. Mechanism and Machine Theory.2002,37:1213～1239.
[98]蔡建乐.多刚体系统动力学分析方法(Ⅰ)[J].益阳师专学报,1994,11(6)：40～46.
[99]蔡建乐.多刚体系统动力学分析方法(Ⅱ)[J].益阳师专学报,1995,12(5)：50～54.
[100]刘延柱.多刚体系统动力学的研究现状和展望[J].上海力学,1989.10(3)：58-62.
[101]陆佑方.柔性多体系统：理论和应用力学的一个活跃领域[J].力学与实践, 1994,16(2)：1-9.
[102]刘铸永,洪嘉振.柔性多体系统动力学研究现状与展望[J].计算力学学报,2008,25(4)：411～416.
[103]Wehage, R.A., Haug, E.J., Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems[J], ASME Paper 80-DET-106,1980.
[104]Shampine, L.F., Gordon, M.K.. Computer solution of ordinary differential equations:the initial value problem[M]. J. Freeman, San Francisco, CA,1975.
[105]Greenwood, D. T., Principles of dynamics[M], Prentice-Hall,1965.
[106]Soo Chung, Chia-Ou Chang, Edward J. Haug, Roger A. Wehage, Ronald R. Beck, TACOM, Dynamic analysis of three dimensional constrained mechanical systems using euler parameter s[J]. ADA 124100.
[107]王琪,陆启韶.多体系统Lagrange方程数值算法的研究进展[J].力学进展,2001,31(1)：9-17.
[108]潘振宽,赵维加,洪嘉振,刘延柱.多体系统动力学微分／代数方程组数值方法[J].力学进展,1996,26(1)：28～40.
[109]Nikravesh P E., Haug E J. Generalized coordinates partitioning for analysis of mechanical systems with homological constraints [J]. ASME 1983(105):384～397.
[110]李庆扬.常微分方程数值解法(刚性问题与边值问题)[M].北京：高等教育出版社,1991.9：5～160.
[111]凌复华,殷学纲,何治奇.常微分方程数值方法及其在力学中的应用[M].重庆：重庆大学出版社,1990：2-300.
[112]Lankarani, H. M. and Nikravesh, P. E. A contact force model with hysteresis damping for impact analysis of multi-body systems[J]. J. Mech. Des.,1990,112,369～376.
[113]Pfeiffer, F., Glocker, C. Multi-body dynamics with unilateral constraints[M], John Wiley and Sons, New York.1996.
[114]唐云冰.航空发动机高速滚动轴承力学特性研究[D].南京：南京航空航天大学,2005：2～100.
[115]Harris, T. A., Mindel, M. H. Rolling bearing dynamics[M]. Wear.1973,23.
[116]Gupta,P. K. Advanced Dynamics of Rolling Elements[M]. Springer-Verlag, New York Inc.,1984.
[117]罗继伟.滚动轴承中的弹性接触问题及其数值求解[D].北京：清华大学,1989.
[118]罗继伟.滚动轴承受力分析及其发展[J].轴承,2001,(9)：28～31.
[119](日)冈本纯三.球轴承的设计计算[M].黄志强,罗继伟译.北京：机械工业出版社,2000,4：6～200.
[120]Haug, E. J., Wu, S. C, Yang, S. M. Dynamics of mechanical systems with coulomb friction, suction, impact and constraint addition-deletion-I theory [J]. Mech. Mach. Theory, 1986,21(5),401～406.
[121]LMS/Motion online help.
[122]CH. Glocker, F. Pfeiffer. Multiple impacts with friction in rigid multi-body systems [J]. Nonlinear Dynamics,1995:471～497.
[123]王勖成.有限单元法[M].北京：清华大学出版社,2003：2～300.
[124]Moore M, Wilhelms J. Collision detection and response for computer animation[J]. Computer Graphics,1988,22(4):289～298.
[125]Rogers D F. Procedural elements for computer graphics[M]. New York:McGraw Hill Book Company,1985.
[126]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001：2～320.
[127]徐瑾,张瑞秋,陈亮.NURBS曲面造型方法[J].信阳师范学院学报(自然科学版),2003,16(3)：353～356.
[128]范劲松,徐宗俊.利用NURBS进行复杂形体的设计[J].重庆大学学报,自然科学版,1996,19(1)：18～25
[129]李雪飞,张阗.基于AutoCAD的滚动轴承三维建模系统[J].轴承,2008,2：45～47.
[130]赵玉伦等.I-DEAS在齿轮造型中的应用[J].机械工程师,2000,2：49-50.
[131]胡赤兵等.Solid works环境下的齿轮精确三维造型设计[J].组合机床与自动化加工技术,2006,1：92～95.
[132]陈雄.角接触球轴承静力学与动力学分析[D].南京：南京航空航天大学,2007,2-70.
[133]T.A. Harris. Rolling Bearing Analysis[M]. New York:Willey,1991:50～200.
[134]王靖君,郝信鹏.火炮概论[M].北京：国防工业出版社,1990：3～313.
[135]陈运生,杨国来.自行火炮动力学的Kane方程方法建模研究[J].火炮发射与控制学报,1996,1：1-4.
[136]何永.火炮总体设计方法研究[D].南京：南京理工大学,1995.
[137]马吉胜.高炮发射动力学研究与高炮动力学优化设计[D].南京：南京理工大学,1997.
[138](Anil) K. Chopra.结构动力学：理论及其在地震工程中的应用(第2版)[M].谢礼立,吕大刚等译.北京：高等教育出版社,2007：201-500.
[139]刘又午.多体动力学在机械工程领域的应用[J].中国机械工程,2000,2,11(2)： 144～150.
[140]殷学纲,陈淮,蹇开林.结构振动分析的子结构方法[M].北京：中国铁道出版社,1991：2～400.
[141]陈运生,敖勇.自行火炮动力学分析的一种广义模态综合法[J].弹道学报,1997,9(1)：3 1～33.
[142]王文亮,杜作润.结构振动与动态子结构方法[M].上海：复旦大学出版社,1985：2～400.
[143]黄欢.柔细机械臂的模态综合建模及其动力学分析[D].杭州：浙江工业大学,2005.
[144]张永昌.MSC. Nastran有限元分析理论基础与应用[M].北京科学出版社,2004，11：386～408.
[145]于旭东,赵育善.飞行器结构动力学[M].西安：西北工业大学出版社,1998.
[146]张汝清等.计算结构动力学[M].重庆：重庆大学出版社,1987.
[147]缪炳棋,曲广吉等.关于柔性航天器动力学模型降阶问题[J].中国工程科学,2001,11(3)：60～64.
[148]David C. Hyland, et al. The optimal projection equations for model reduction and the relationship among the methods of Wilson, Skelton, and Moore[J]. IEEE Transactions on Automatic Control, AC-30, NO.12,1985,12,1201～1211.
[149]黄文虎,邵成勋等.多柔体系统动力学[M].北京：科学出版社,1996.
[150]邓楚键,何国杰,郑颖人.基于M-C准则的D-P系列准则在岩土工程中的应用研究[J].岩土工程学报,2006,28(6)：735～738.
[151]GB/T3487-1996：汽车轮辋规格系列.
[152]GB/T2933-1995：充气用轮胎和轮辋的术语\规格代号和标志.
[153]刘雷,陈运生.火炮虚拟样机仿真研究[J].系统仿真学报,2005,1：111～113.
[154]庄茁等译.ABAQUS/Explicit有限元软件入门指南[M].北京：清华大学出版社,1999：2～300.
[155](美)Ted Belytschko, Wing Kam Liu, Brian Moran.连续体和结构的非线性有限元[M].庄茁译.北京：清华大学出版社,2002：18-325.
[156]Simo J C, Laursen T A. An augment Lagrangian treatment of contact problems involving friction[J]. Computers and Structures.1992,42(1):97～116.
[157]Heegaard J H, Curnier A. An augmented Lagrangian method for discrete large-slip contact problems[J]. Int. J. Numer. Meth. Engine.1993,36:569～593.
[158]Pietrzak G, Curnier A. Large deformation frictional contact mechanics:continuum formulation and augmented Lagrangian treatment[J]. Computer Methods in Applied Mechanics and Engineering,1999,177(3-4):351-381.
[159]Simo J C, Wriggers P. A perturbed Langrangian formulation for the finite element solutions of contact problems [J]. Computer Methods in Applied Mechanics and Engineering,1985,50:163-180.
[160]张学言,闫澍旺.岩土塑性力学基础[M].天津：天津大学出版社,2004：20～100.
[161]王金昌,陈页开.ABAQUS在土木工程中的应用[M].杭州：浙江大学出版社,2006：5～200.
[162]乔立山,王玉兰,曾锦光.实验数据处理中曲线拟合方法探讨[J].成都理工大学学报(自然科学版),2004,31(1)：91～95.
[163]钟穗生,刘旭光.实验数据的计算机处理[M].北京：海洋出版社,1994,3：30～300.
[164](德)P.R.贝文顿.数据处理和误差分析[M].仇维礼,徐根兴译.北京：知识出版社，1986：50～300.
[165]胡宁杰.多项式拟合在实际应用中的优势[J].中国水运，2008,12,8(12)：120～121.
[166]李庆扬,关治,白峰彬.数值计算原理[M].北京：清华大学出版社,2000,30～300.
[167]王正林,龚纯,何倩.精通MATLAB科学计算[M].北京：电子工业出版社,2007,20-200.
[168]石亦平,周玉蓉.ABAQUS有限元分析实例详解[M].北京：机械工业出版社,2006.
[169]胡庆红.大直径扩底桩试验研究与数值分析[D].杭州：浙江大学,2007,10.
[170]贺嘉,陈国兴.基于ABAQUS软件的大直径桩承载力-变形分析[J],地下空间与工程学报,2007,4,3(2)：306～310.
[171]曾晋春,杨国来,王晓锋.某火炮自动机虚拟样机建模与仿真[J].火炮发射与控制学报,2008,1：42～45.
[172]王放明.随机动力学及其在兵器中的应用[M].北京：国防工业出版社,2000：2～140.
[173]Randolph M F. Science and empiricism in pile foundation design[J]. Geotechnique, 2003,53(10):847-875.
[174]Hung H M. Dynamics Response of weapon system with stochastic excitations [J], AD706837.
[175]田四朋,唐国金,雷勇军,李道奎.固体火箭发动机随机药柱结构分析参数的 灵敏度研究[J].固体火箭技术,2008,21(1)：28～32.
[176]Martin T. Soifer, Robert S. Becker. Stochastic gun dynamics[J]. AD-A180866.
[177]王国平,芮筱亭.随机动力学的数值解法[J].弹箭与制导学报,2003,23(2)：357～360.
[178]朱位秋.非线性随机动力学与控制[M].北京：科学出版社,2003：100-305.
[179]徐钟济.蒙特卡洛方法[M].上海：上海科学技术出版社,1985：5-130.
[180]杨国来,陈运生.火炮密集度的计算机模拟研究[J].火炮发射与控制学报,1999(3)：1-4.
[181]杭燚.火炮虚拟现实技术研究[D].南京：南京理工大学,2007.
[182]C Horsken, M Hiller. Statistical methods for tolerance analysis in multibody systems and computer aided design[J]. Advances in Computational Multibody Dynamics, 1999:1～19.
[183]曾晋春,杨国来,王晓锋.计及齿轮-齿弧接触的火炮动力学仿真分析[J].弹道学报,2008,20(2)：81～84.
[184]曾晋春,杨国来,王晓锋.考虑轴承接触／碰撞的某火炮动力学数值仿真[J].火炮发射与控制学报,2010(1)：30～33..
[185]龙凯,程颖.齿轮啮合力仿真计算的参数选取研究[J].计算机仿真,2002,19(6)：87～89.
[186]Bekker, M.G. Off-the-road locomotion[M]. Ann Arbor,MI:University of Michigan Press,1966:1～100.
[187]Wong, J. Y. On the characterization of shear stress displacement relationship of terrain[J]. Journal of Terramechanics,19,1983:107～127.
[2]郭齐胜,董志明,单家元,等.系统仿真[M].北京：国防工业出版社,2006：5-45.
[3]陈家庆,周海,徐琳琳.滚动轴承载荷分布问题的理论研究进展[J].北京石油化工学院学报,8(1)：47～52.
[4]谢定义.土动力学[M].西安：西安交通大学出版社,1988：2-255.
[5]Henry J. Sneck. Main battle tank flexinble gun disturbance model three-segment model [J],ADA408136.
[6](苏)奥尔洛夫(B.B.OpπoB).炮身构造与设计[M].王天槐,刘淑华译.北京：国防工业出版社,1982：5-125.
[7]Boresi, Arthur P., Langhaar, Henry L. Dynamics of rigid guns with straight tubes[J], Recent advances in engineering mechanics and their impact on civil engineering practice, 1983:226～229.
[8]Jones, Donald E. Analysis of a controller for the M61 movable gun[J]. ADA081893.
[9]P.A. Cox, J.C. Hokanson. Muzzle motions of the M68 105mm tank gun, Final Technical Report, Contact DAAD05-75-C-0739, U.S. Army ARADCOM, Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland.
[10]D. J. Purdy, Modeling and simulation of a weapon control system for a main battle tank[J], Proceedings of the Eighth U.S. Army Symposium on Gun Dynamics.
[11]万长森.滚动轴承的分析方法[M].北京：机械工业出版社,1985：2-300.
[12]Martin T. Soifer, Robert S. Becker. Dynamic analysis of the 75mm ADMAG gun system[J],AD-A123867.
[13]Thomas F. Erline. Deviation effect of an in-bore centerline on a 5-inch naval gun[J]. AD-A193383.
[14]Stephen A. Wilkerson, David H. Lyon, Larry Rusch. Comparison between simulated and experimental results for a balanced-breeched M256 cannon system[J]. AD-A396625, 2000.
[15]P. C. T Chen, M Leach. Modeling of barrel/projectile interaction in a rotating band[J].AD-A392148,2001.
[16]火炮发射时的动力学分析研究.南京理工大学科研报告,1992,11.
[17]张振友.火炮发射时的动力学方程的建立与计算[D].南京：南京理工大学, 1992.
[18]杨国来.多柔体系统参数化模型及其在火炮中的应用研究[D].南京：南京理工大学,1999.
[19]王晓锋,姜兴渭.有限段法在高炮发射多体系统动力学分析中的应用[J].南京理工大学学报,2001,25(1)：25～27.
[20]敖勇.柔性多体系统动力学和动态子结构方法及其在自行火炮动力学仿真中的的应用[D].南京：南京理工大学,1997.
[21]毛保全.动力学优化设计及其在火炮中的应用研究[D].南京：南京理工大学,1997.
[22]楚志远.自行火炮非线性有限元动力学仿真[D].南京：南京理工大学,2001.
[23]王长武.自行火炮非线性有限元模型及仿真可视化技术研究[D].南京：南京理工大学,2002.
[24]石明全.某火炮自动供输弹系统和全炮耦合的发射动力学研究[D].南京：南京理-工大学,2003.
[25]刘雷.自行火炮刚弹耦合发射动力学研究[D].南京：南京理工大学,2005.
[26]管红根,陈常顺,高树滋.基于系统响应的模态截断方法的研究[J].南京理工大学学报,2000,24(6)：532～534.
[27]袁兆鼎,费景高,刘德贵等.刚性常微分方程初值问题的数值解法[M].北京：科学出版社,1987,11,5～200.
[28]芮筱亭,陆毓琪,陆文广,钱剑飞,王国平.自行炮发射动力学研究[J].兵工学报,2000,S1,38-21.
[29]张培林,王成,任国全.冲击作用下火炮复进机的实际效能分析[J].振动与冲击.2009,28(4)：142-148.
[30]万晓峰,刘根,杨树森.航炮系统的虚拟样机仿真与分析[J].系统仿真学报,2005,17(10)：2392～2394.
[31]王钢,王立权,孟祥伟,胡海胜.某火炮供弹系统的设计研究[J].兵工学报,2009,30(5)：518～524.
[32]葛建立.车载炮非线性有限元仿真分析[D].南京：南京理工大学,2007.
[33]刘延柱.多刚体系统动力学[M].北京：高等教育出版社,1989,3：7～300.
[34]洪嘉振.计算多体系统动力学[M].北京：高等教育出版社,1999,7：207～300.
[35]丁遂亮,洪嘉振.柔性多体系统接触/碰撞动力学研究[J].上海交通大学学报,2003,12,37(12)：1927～1930.
[36]陈立平,张云清,任为群,覃刚.机械系统动力学分析及ADAMS应用教程[M].北京：清华大学出版社,2005,1：2～300.
[37]Roberson R E, Wittenburg J. A dynamics for an formalism for an arbitrary number of interconnected rigid bodies, with reference to the problem of satellite control [J].3rd IFAC Congr.1966, Proc London,1968:46D.2～46D.9.
[38]Fletcher H.J., Rongved L. Yu E Y. Dynamics analysis of a two-body gravitationally oriented satellite[J]. Bell System Tech J,1963,42(5):2239～2266.
[39](美)E.J.豪格.机械系统的计算机辅助运动学和动力学,第Ⅰ卷,基本方法[M].刘兴祥等译.北京：高等教育出版社,1996.4：4～300.
[40]于霖冲.柔性机构动态可靠性分析、设计与仿真[D].北京：北京航空航天大学,2006.
[41]李彬,刘锦阳.大变形柔性梁系统的绝对坐标方法[J].上海交通大学学报,39(5).2005.827～831.
[42]宋轶民,余跃庆,张策,马金盛.柔性机器人动力学分析与振动控制研究综述[J].机械设计,20(4),2003：1-5.
[43]Avello A, Jalon J. Dynamics of flexible multibody systems using cartesians coordinates and large displacement theory [J]. International Journal for Numerical Methods in Engineering,1991,32(1):543～563.
[44]Leonard Meirovitch, H. D. Nelson. High spin motion of satellite containing elastic parts[J]. J. Spacecraft and Rocked.13,1966,1597～1602.
[45]梁立孚,刘石泉,周健生.单柔体动力学的拟变分原理及其应用[J].中国科学,39(2),2009,293～304.
[46]H. B. Hablani. Constrained and unconstrained mode:some modeling aspects of flexible Spacecraf[J]. J. Guidance, Control and Dynamics,1982,5(2):164～198.
[47]W. S. Yoo, E. J. Haug. Dynamics of flexible mechanical system using vibration and static correction[J]. ASME J. of Mechanics, Transmission and Automation in Design,1986, 108:315～322.
[48]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,29(2)1999：145～154.
[49]Huston R L.多体系统动力学(上/下册)[M].刘又午译.天津：天津人学出版社,1987/1991.
[50]Huston R L, Passerello C E, Harlow M W. Dynamics of multi-rigid-body system[J]. ASME Journal of Applied Mechanics,1978,45(4):889～894.
[51]Huston R L., Passerello C E. Multibody structural dynamics including translation between the bodies[J]. Computers and Structures,1980,11:713～720.
[52]张人钧,刘又午.柔性多体系统动力学[J].机械工程学报(英文版),1994, 7(2)：156～162.
[53]张人钧,刘又午.有限段方法的刚度方程[J].机械工程学报(英文版),1992,5(1)：23～30.
[54]闫绍泽,刘冰清,刘又午,黄铁球.柔性多体系统动力学-有限段方法[J].河北工业大学学报,1997,3(26),1-9.
[55]Konno A, Uchiyama M. Modeling of a flexible manipulator dynamics based on the Holzer's method[J]. Journal of Japan Robot Institute,1994,12 (7):1021～1028.
[56]张铁民.柔性机械臂振动控制理论与实验研究[D].天津：天津大学,1996.
[57]阎绍泽.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[D].天津：天津大学,1996.
[58]许宏伟,马兴瑞,黄文虎,邵成勋,邹振祝.双臂协调约束系统动力学问题探讨[J],振动工程学报,7(1),1994：1-8.
[59]王琪.多体系统动力学的Lagrange算法研究[D].北京：北京航空航天大学,1996.
[60]林宝玖,谢传锋.挠性多体系统动力学[J].力学学报,21(4),1989,469～478
[61](德)维腾伯格,J.多刚体系统动力学[M].谢传锋译.北京：北京航空学院出版社,1988,1～205.
[62]洪嘉振,粱敏.多刚体碰撞动力学方程及可解性判别准则[J].应用力学学报,1991,8(1)：10～17.
[63]洪嘉振,粱敏.多刚体内碰撞数学模型与计算程序[J].力学学报,1989.21(4)：35-42.
[64]E. K., Rooth. Dynamics of a system of rigid bodies[M]. New York:Dover Publications Inc.1960.
[65]Wehage R A, Haug E J. Dynamic analysis of mechanical systems with intermittent motions[J]. ASME J of Mechanical Design.1982,104(4):778～785.
[66]刘才山,陈滨.多柔体系统碰撞动力学研究综述[J].力学进展,2000,30(1)：7-14.
[67]Rismantab-Sang J, Shabana A A. On the use of the momentum balance in the impact analysis of constrained elastic systems[J]. Journal of Vibration and Acoustics,1990,112: 119～126.
[68]Yigit A S, Ulsoy A G, Scott R A. Dynamic analysis of a radically rotating beam with impact. Part 1:theoretical and computational model[J]. Journal of Vibration and Acoustics, 1990,112:65～70.
[69]S. Wu, E. Haug. Geometric non-linear substructuring for dynamics of flexible mechanical systems [J], International Journal for Numerical Methods in Engineering,1988, 26:2211～2226.
[70]刘锦阳,洪嘉振.闭环柔性多体系统的多点撞击问题[J].中国机械工程,2000,11(6)：619～623.
[71]郭吉丰,升古保博,宫崎文夫.具有摩擦的刚体碰撞[J].应用力学学报,21(2),2004：77～83.
[72]Thornton C. Coefficient of Restitution for collinear collisions of elastic-perfectly plastic spheres[J]. J of Applied Mechanics,1997,64(2):383～886.
[73]A. P. Ivanov. On multiple impact[J]. J. App￡ Maths Mechs,59(6),1995:887-902.
[74]Dubowsky, F. Freudenstein, Dynamic analysis of mechanical systems with clearances. Part 1:formulation of dynamic model[J], Journal of Engineering for Industry Series B,93(1),1971:305～309.
[75]Hertz, H.. Gesammelte Werke(Volume.1), Leipzig, Germany,1985:2～200.
[76]Cookie, A. W.. Study of some impacts between metallic bodies by a piezoelectric method[J], Proceedings of the Royal Society London A212,1952:377～390.
[77]Johnson, K. L. Contact mechanics[M]. Cambridge:Cambridge University Press, 1992:5～206.
[78]Hunt, K. H., Crosslye, F. R. E.. Coefficient of restitution interpreted as damping in vibroimpact[J]. ASME J of Appl Mech,1975,42E:440～456.
[79]Lee, Ting W., Wang, A.C. On the dynamics of intermittent-motion mechanisms, part 1:dynamic model and response. Part 2:geneva mechanisms, ratchets, and escapetments [J]. Journal of Mechanisms, Transmissions, and Automation in Design,105(3),1982:534～551.
[80]Yigit, A. S., Usloy A. G. Spring dashpot models for the dynamics of a radically rotating beam with impact[J]. Journal of Sound and Vibration,1990,143(3),515～525.
[81]Yigit A S. The effect of flexibility on the impact response of a two-link rigid-flexible manipulator[J]. Journal of Sound and Vibration,1994,177(3):349～361.
[82]Lin FH, Tseng AA. A finite element analysis of elasto-plastic contact problems in metal forming[J]. Materials and Design,1998,19:99～108.
[83]Vasudevan S. Okada H and Atluri SN. Development of a new frame finite element. for crash analysis using a mixed variational principle and rotations as independent variables[J]. Finite Elements in Analysis and Design,1996,23:155～171.
[84]Hallquist, J. O, Goudreau, G. L., Benson, D. J.. Sliding interfaces with contact-impact in large scale Lagrangian computations[J]. Computer Methods in Applied Mechanics and Engineering,1985,751(1):107～137.
[85]S.W. Kim, A. K. Misra, V. J. Modix, Cyril. Simulation of contact dynamics of flexible multibody systems, AIAA-98-4552.
[86]Marco Anghileri, Luigi-M. L. Castelletti, Fabio Invernizzi, Marco Mascheroni. A survey of numerical models for hail impact analysis using explicit finite element codes[J]. International Journal of Impact Engineering,2005,31:929～944.
[87]R. W. Cottle, J. P. Pang, R. E. Stone. The Linear Complimentarily Problem[M]. Academic Press, London,1992.
[88]Pfeiffer, F., Glocker, Ch.. Contacts in multi-body systems[J]. J. Applied Mathematics Mechanics,2000,5:773～782.
[89]Moreau J. J. Evolution problem associated with a moving convex set in a Hilbert space[J]. J. Diff. Equations 1977,26:347～374.
[90]Bauchau, O, A,. Analysis of flexible multibody systems with intermittent contacts[J]. Multibody System Dynamics,2000,4:23～54.
[91]Wang, Hui-Ping. Meshfree smooth contact formulation and boundary condition treatments in multi-body contact[D]. The University of Iowa,2000:25～110.
[92]Nam H. Kim, Ki-Young Yi, Kyung K. Choi. Meshfree analysis and die shape design of extrusion process[J].9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA 2002-5563.
[93]Seifried, R., Eberhard P.. Impact analysis using modal reduction[J]. PAMM Proceedings in Applied Mathematics and Mechanics,2005,5:129～130.
[94]刘锦阳,洪嘉振.多点接触／碰撞的数值计算[J].上海交通大学学报,1997,31(7)：45～53.
[95]Ting-Nung Shiau, Yi-Jeng Tsai, Meng-Shiun Tsai. Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects[J]. J. of Mechanism and Machine Theory,43,2008:491～508.
[96]姚文莉,王育平,边力,赵振.多刚体系统接触／碰撞动力学研究进展[J].力学与实践,2007,29(6)：9-12.
[97]G. Gilardi, I. Sharf. Literature survey of contact dynamics modeling[J]. Mechanism and Machine Theory.2002,37:1213～1239.
[98]蔡建乐.多刚体系统动力学分析方法(Ⅰ)[J].益阳师专学报,1994,11(6)：40～46.
[99]蔡建乐.多刚体系统动力学分析方法(Ⅱ)[J].益阳师专学报,1995,12(5)：50～54.
[100]刘延柱.多刚体系统动力学的研究现状和展望[J].上海力学,1989.10(3)：58-62.
[101]陆佑方.柔性多体系统：理论和应用力学的一个活跃领域[J].力学与实践, 1994,16(2)：1-9.
[102]刘铸永,洪嘉振.柔性多体系统动力学研究现状与展望[J].计算力学学报,2008,25(4)：411～416.
[103]Wehage, R.A., Haug, E.J., Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems[J], ASME Paper 80-DET-106,1980.
[104]Shampine, L.F., Gordon, M.K.. Computer solution of ordinary differential equations:the initial value problem[M]. J. Freeman, San Francisco, CA,1975.
[105]Greenwood, D. T., Principles of dynamics[M], Prentice-Hall,1965.
[106]Soo Chung, Chia-Ou Chang, Edward J. Haug, Roger A. Wehage, Ronald R. Beck, TACOM, Dynamic analysis of three dimensional constrained mechanical systems using euler parameter s[J]. ADA 124100.
[107]王琪,陆启韶.多体系统Lagrange方程数值算法的研究进展[J].力学进展,2001,31(1)：9-17.
[108]潘振宽,赵维加,洪嘉振,刘延柱.多体系统动力学微分／代数方程组数值方法[J].力学进展,1996,26(1)：28～40.
[109]Nikravesh P E., Haug E J. Generalized coordinates partitioning for analysis of mechanical systems with homological constraints [J]. ASME 1983(105):384～397.
[110]李庆扬.常微分方程数值解法(刚性问题与边值问题)[M].北京：高等教育出版社,1991.9：5～160.
[111]凌复华,殷学纲,何治奇.常微分方程数值方法及其在力学中的应用[M].重庆：重庆大学出版社,1990：2-300.
[112]Lankarani, H. M. and Nikravesh, P. E. A contact force model with hysteresis damping for impact analysis of multi-body systems[J]. J. Mech. Des.,1990,112,369～376.
[113]Pfeiffer, F., Glocker, C. Multi-body dynamics with unilateral constraints[M], John Wiley and Sons, New York.1996.
[114]唐云冰.航空发动机高速滚动轴承力学特性研究[D].南京：南京航空航天大学,2005：2～100.
[115]Harris, T. A., Mindel, M. H. Rolling bearing dynamics[M]. Wear.1973,23.
[116]Gupta,P. K. Advanced Dynamics of Rolling Elements[M]. Springer-Verlag, New York Inc.,1984.
[117]罗继伟.滚动轴承中的弹性接触问题及其数值求解[D].北京：清华大学,1989.
[118]罗继伟.滚动轴承受力分析及其发展[J].轴承,2001,(9)：28～31.
[119](日)冈本纯三.球轴承的设计计算[M].黄志强,罗继伟译.北京：机械工业出版社,2000,4：6～200.
[120]Haug, E. J., Wu, S. C, Yang, S. M. Dynamics of mechanical systems with coulomb friction, suction, impact and constraint addition-deletion-I theory [J]. Mech. Mach. Theory, 1986,21(5),401～406.
[121]LMS/Motion online help.
[122]CH. Glocker, F. Pfeiffer. Multiple impacts with friction in rigid multi-body systems [J]. Nonlinear Dynamics,1995:471～497.
[123]王勖成.有限单元法[M].北京：清华大学出版社,2003：2～300.
[124]Moore M, Wilhelms J. Collision detection and response for computer animation[J]. Computer Graphics,1988,22(4):289～298.
[125]Rogers D F. Procedural elements for computer graphics[M]. New York:McGraw Hill Book Company,1985.
[126]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京：高等教育出版社,2001：2～320.
[127]徐瑾,张瑞秋,陈亮.NURBS曲面造型方法[J].信阳师范学院学报(自然科学版),2003,16(3)：353～356.
[128]范劲松,徐宗俊.利用NURBS进行复杂形体的设计[J].重庆大学学报,自然科学版,1996,19(1)：18～25
[129]李雪飞,张阗.基于AutoCAD的滚动轴承三维建模系统[J].轴承,2008,2：45～47.
[130]赵玉伦等.I-DEAS在齿轮造型中的应用[J].机械工程师,2000,2：49-50.
[131]胡赤兵等.Solid works环境下的齿轮精确三维造型设计[J].组合机床与自动化加工技术,2006,1：92～95.
[132]陈雄.角接触球轴承静力学与动力学分析[D].南京：南京航空航天大学,2007,2-70.
[133]T.A. Harris. Rolling Bearing Analysis[M]. New York:Willey,1991:50～200.
[134]王靖君,郝信鹏.火炮概论[M].北京：国防工业出版社,1990：3～313.
[135]陈运生,杨国来.自行火炮动力学的Kane方程方法建模研究[J].火炮发射与控制学报,1996,1：1-4.
[136]何永.火炮总体设计方法研究[D].南京：南京理工大学,1995.
[137]马吉胜.高炮发射动力学研究与高炮动力学优化设计[D].南京：南京理工大学,1997.
[138](Anil) K. Chopra.结构动力学：理论及其在地震工程中的应用(第2版)[M].谢礼立,吕大刚等译.北京：高等教育出版社,2007：201-500.
[139]刘又午.多体动力学在机械工程领域的应用[J].中国机械工程,2000,2,11(2)： 144～150.
[140]殷学纲,陈淮,蹇开林.结构振动分析的子结构方法[M].北京：中国铁道出版社,1991：2～400.
[141]陈运生,敖勇.自行火炮动力学分析的一种广义模态综合法[J].弹道学报,1997,9(1)：3 1～33.
[142]王文亮,杜作润.结构振动与动态子结构方法[M].上海：复旦大学出版社,1985：2～400.
[143]黄欢.柔细机械臂的模态综合建模及其动力学分析[D].杭州：浙江工业大学,2005.
[144]张永昌.MSC. Nastran有限元分析理论基础与应用[M].北京科学出版社,2004，11：386～408.
[145]于旭东,赵育善.飞行器结构动力学[M].西安：西北工业大学出版社,1998.
[146]张汝清等.计算结构动力学[M].重庆：重庆大学出版社,1987.
[147]缪炳棋,曲广吉等.关于柔性航天器动力学模型降阶问题[J].中国工程科学,2001,11(3)：60～64.
[148]David C. Hyland, et al. The optimal projection equations for model reduction and the relationship among the methods of Wilson, Skelton, and Moore[J]. IEEE Transactions on Automatic Control, AC-30, NO.12,1985,12,1201～1211.
[149]黄文虎,邵成勋等.多柔体系统动力学[M].北京：科学出版社,1996.
[150]邓楚键,何国杰,郑颖人.基于M-C准则的D-P系列准则在岩土工程中的应用研究[J].岩土工程学报,2006,28(6)：735～738.
[151]GB/T3487-1996：汽车轮辋规格系列.
[152]GB/T2933-1995：充气用轮胎和轮辋的术语\规格代号和标志.
[153]刘雷,陈运生.火炮虚拟样机仿真研究[J].系统仿真学报,2005,1：111～113.
[154]庄茁等译.ABAQUS/Explicit有限元软件入门指南[M].北京：清华大学出版社,1999：2～300.
[155](美)Ted Belytschko, Wing Kam Liu, Brian Moran.连续体和结构的非线性有限元[M].庄茁译.北京：清华大学出版社,2002：18-325.
[156]Simo J C, Laursen T A. An augment Lagrangian treatment of contact problems involving friction[J]. Computers and Structures.1992,42(1):97～116.
[157]Heegaard J H, Curnier A. An augmented Lagrangian method for discrete large-slip contact problems[J]. Int. J. Numer. Meth. Engine.1993,36:569～593.
[158]Pietrzak G, Curnier A. Large deformation frictional contact mechanics:continuum formulation and augmented Lagrangian treatment[J]. Computer Methods in Applied Mechanics and Engineering,1999,177(3-4):351-381.
[159]Simo J C, Wriggers P. A perturbed Langrangian formulation for the finite element solutions of contact problems [J]. Computer Methods in Applied Mechanics and Engineering,1985,50:163-180.
[160]张学言,闫澍旺.岩土塑性力学基础[M].天津：天津大学出版社,2004：20～100.
[161]王金昌,陈页开.ABAQUS在土木工程中的应用[M].杭州：浙江大学出版社,2006：5～200.
[162]乔立山,王玉兰,曾锦光.实验数据处理中曲线拟合方法探讨[J].成都理工大学学报(自然科学版),2004,31(1)：91～95.
[163]钟穗生,刘旭光.实验数据的计算机处理[M].北京：海洋出版社,1994,3：30～300.
[164](德)P.R.贝文顿.数据处理和误差分析[M].仇维礼,徐根兴译.北京：知识出版社，1986：50～300.
[165]胡宁杰.多项式拟合在实际应用中的优势[J].中国水运，2008,12,8(12)：120～121.
[166]李庆扬,关治,白峰彬.数值计算原理[M].北京：清华大学出版社,2000,30～300.
[167]王正林,龚纯,何倩.精通MATLAB科学计算[M].北京：电子工业出版社,2007,20-200.
[168]石亦平,周玉蓉.ABAQUS有限元分析实例详解[M].北京：机械工业出版社,2006.
[169]胡庆红.大直径扩底桩试验研究与数值分析[D].杭州：浙江大学,2007,10.
[170]贺嘉,陈国兴.基于ABAQUS软件的大直径桩承载力-变形分析[J],地下空间与工程学报,2007,4,3(2)：306～310.
[171]曾晋春,杨国来,王晓锋.某火炮自动机虚拟样机建模与仿真[J].火炮发射与控制学报,2008,1：42～45.
[172]王放明.随机动力学及其在兵器中的应用[M].北京：国防工业出版社,2000：2～140.
[173]Randolph M F. Science and empiricism in pile foundation design[J]. Geotechnique, 2003,53(10):847-875.
[174]Hung H M. Dynamics Response of weapon system with stochastic excitations [J], AD706837.
[175]田四朋,唐国金,雷勇军,李道奎.固体火箭发动机随机药柱结构分析参数的 灵敏度研究[J].固体火箭技术,2008,21(1)：28～32.
[176]Martin T. Soifer, Robert S. Becker. Stochastic gun dynamics[J]. AD-A180866.
[177]王国平,芮筱亭.随机动力学的数值解法[J].弹箭与制导学报,2003,23(2)：357～360.
[178]朱位秋.非线性随机动力学与控制[M].北京：科学出版社,2003：100-305.
[179]徐钟济.蒙特卡洛方法[M].上海：上海科学技术出版社,1985：5-130.
[180]杨国来,陈运生.火炮密集度的计算机模拟研究[J].火炮发射与控制学报,1999(3)：1-4.
[181]杭燚.火炮虚拟现实技术研究[D].南京：南京理工大学,2007.
[182]C Horsken, M Hiller. Statistical methods for tolerance analysis in multibody systems and computer aided design[J]. Advances in Computational Multibody Dynamics, 1999:1～19.
[183]曾晋春,杨国来,王晓锋.计及齿轮-齿弧接触的火炮动力学仿真分析[J].弹道学报,2008,20(2)：81～84.
[184]曾晋春,杨国来,王晓锋.考虑轴承接触／碰撞的某火炮动力学数值仿真[J].火炮发射与控制学报,2010(1)：30～33..
[185]龙凯,程颖.齿轮啮合力仿真计算的参数选取研究[J].计算机仿真,2002,19(6)：87～89.
[186]Bekker, M.G. Off-the-road locomotion[M]. Ann Arbor,MI:University of Michigan Press,1966:1～100.
[187]Wong, J. Y. On the characterization of shear stress displacement relationship of terrain[J]. Journal of Terramechanics,19,1983:107～127.