基于约束拓扑变换的大规模复杂多刚体系统振动分析
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摘要
随着现代机械系统动态性能要求的日益提高,机械系统的结构复杂程度急剧增加,动力学分析和优化逐渐成为结构设计中至关重要的一环。为满足一定的精度要求,通常采用大规模复杂多刚体动力学模型来描述这些复杂机械系统。传统动力学分析方法解决这一类大规模复杂多刚体动力学模型的计算问题时面临精度和效率两方面的严峻挑战,这是现阶段机械系统结构设计中迫切需要解决的关键难题之一。特别地,振动计算作为此类系统动力学分析的核心和基础,其计算效率成为设计、优化和控制的瓶颈之一。本论文结合国家重大科研项目和重大工程的实际需求,从空间多刚体系统约束拓扑关系的角度入手,研究这一类系统振动方程的建立和求解问题,旨在针对大规模复杂多刚体系统建立一种精确和高效的振动求解新方法。
采用矩阵和向量描述多刚体系统中的物理参数,包括刚体的质量和惯性张量、刚体间弹簧—阻尼连接的系数、约束的数学表达,以及刚体的空间振动状态,由此以简化符号表示,并有助于形成关于系统的更深刻认识。基于导出的刚体空间振动位移传递和坐标系间变换的统一公式,提出了采用矩阵变换分三步建立一般多刚体系统振动微分方程的新方法。首先,不考虑任何约束,采用拉格朗日方法建立以绝对坐标描述的二阶线性常微分方程组;然后,忽略闭环约束链中的切断铰,构造开环约束矩阵,对无约束系统矩阵做线性变换得到开环约束系统二阶线性常微分方程组;最后,构造切断铰约束矩阵,对开环约束系统矩阵做线性变换得到闭环约束系统二阶线性常微分方程组。由于此方法无须矩阵求导和方程线性化,与传统方法相比可显著提高计算效率。
采用复模态分析求取特征值和特征向量,进而得到系统的模态参数。基于振动位移变换关系导出了任意两点之间不同坐标系下的一般传递函数公式,该公式包含了物理坐标与独立广义坐标之间的显式变换关系,因此较传统基于独立广义坐标的传递函数计算公式更为实用。在传统模态频率关于矩阵元素的灵敏度的基础上,导出了模态频率关于设计参数的灵敏度计算公式,使参数灵敏度分析和优化得以简捷、高效地实现。提出了一种递归算法求解多刚体系统在装配位置的无变形平衡问题,解决了多刚体系统动力学仿真中的初始状态模拟难题。
基于上述算法开发了多体动力学软件Simulith,提供了振动模态分析、传递函数分析、频域响应分析、灵敏度分析、动力学优化以及控制等功能。针对不同约束拓扑的多刚体系统进行数值实验,验证了本算法的正确性和效率。中国软件评测中心性能测试结果表明,该求解器较传统方法(如ADAMS)可以显著提高计算速度。而且,模型中刚体个数、刚体间作用力元个数或约束个数越多,该求解器的计算效率提高越明显。本文提出的方法已成功应用于100nm光刻机动力学分析与优化,有效缩短了光刻机设计周期,降低了研发成本,实验结果进一步验证了本文所述方法的正确性和有效性。本文提出的方法还可用于各种类型的结构和机构系统振动分析,以及参数灵敏度分析与优化。
本文研究工作是2007年度教育部自然科学奖一等奖“精密运动机构中若干关键动力学与控制问题研究”的主要成果之一。
As the increasement of requirements in dynamic performance of modern mechanical systems, the structural complexity of mechanical systems has significantly increased. Dynamic analysis and optimization has become the most critical issue in structural design. Since mechanical systems are usually modeled as large-scale complex multibody systems to acquire satisfied accuracy, it leads to two major problems for dynamic analysis of such kinds of large-scale complex multibody systems using conventional methods, i.e., accuracy and computational efficiency, which are one of the critical problems to be resolved in structural design at present. Particularly, vibration analysis is the core and basis of dynamic analysis of such kind of systems, and the computational efficiency becomes one of the bottlenecks for design, optimization and control. In order to fulfil the urgent requirements of state key scientific research and engineering projects, formulation and solution of vibrational equations for such kinds of systems are studied in this dissertation, by starting with investigation of constraint topologies for spatial multibody systems. A new method for vibration analysis of large-scale complex multibody systems with high accuracy and efficiency is finally presented.
All the physical parameters are defined in matrix-vector form, including mass and inertia tensor of each body, coefficients of spatial spring-damper, mathematical representation of joint, and spatial motion status of rigid body, so as to get clear notation and provides clear insight into the system. Based on uniform transformation of vibrational displacements, a new method for formulating a minimal set of second-order linear ordinary differential equations (ODEs) in three steps is proposed. Firstly, a set of linearized ODEs are formulated in terms of absolute coordinates without considering any constraint in the system. Secondly, an open-loop constraint matrix is generated to formulate ODEs for open-loop mechanism system which is obtained by ignoring all cut-joints in the original system. Finally, a cut-joint constraint matrix is generated to formulate a minimal set of ODEs for the original closed-loop mechanism system. Since there is no need for derivation of matrices and linearization of equations, computational efficiency can be significantly improved by using the proposed method as compared with traditional approaches.
Complex modal analysis is then performed to calculate the eigenvalues and eigenvectors, and then modal parameters are obtained. General formulation of transfer function between two arbitrary points with respect to different reference frames is derived. The presented physical-coordinates-based formula consists of explicit transformation between physical coordinates and modal coordinates, and hence is more practical than traditional general-coordinates-based formulation. Transfer function in the vicinity of each natural frequency is always computed to improve numerical accuracy near the resonance frequencies. Sensitivity of natural frequency with respect to design parameters, instead of conventional elements of mass (stiffness, or damping) matrix, is derived with a simple expression. A recursive algorithm is proposed to solve inverse equilibrium problems, which computes inner forces to keep the system with nearly zero deformation.
Software named Simulith has been developed based on the proposed algorithm. Function such as normal mode analysis, transfer function analysis, sensitivity analysis, optimization and control are all included. The correctness and efficiency of the proposed method have been verified by numerical experiments on multibody systems with different kinds of constraint topologies. The results of performance test done by China Software Test Center (CSTC) show that, the computational efficiency of the presented approach has been significantly improved in compare with traditional methods such as ADAMS. Furthermore, the greater the number of bodies, joints, or spring-dampers is, the more the improvement in computational efficiency is obtained. The proposed method has been successfully applied in dynamic analysis and optimization of 100nm optical lithography equipment. The design period and the cost of development for the optical lithography equipment have been significantly reduced. Experimental results have further verified the correctness and effectiveness of the presented approach. The proposed method can also be used for vibration analysis of many other kinds of structures and mechanism systems.
The study work is one of the major achievements in A Study of the Key Issues on Dynamics and Control in the Ultra Precision Mechanisms, which has won the First Prize of Ministry of Education Natural Science Award in 2007.
采用矩阵和向量描述多刚体系统中的物理参数,包括刚体的质量和惯性张量、刚体间弹簧—阻尼连接的系数、约束的数学表达,以及刚体的空间振动状态,由此以简化符号表示,并有助于形成关于系统的更深刻认识。基于导出的刚体空间振动位移传递和坐标系间变换的统一公式,提出了采用矩阵变换分三步建立一般多刚体系统振动微分方程的新方法。首先,不考虑任何约束,采用拉格朗日方法建立以绝对坐标描述的二阶线性常微分方程组;然后,忽略闭环约束链中的切断铰,构造开环约束矩阵,对无约束系统矩阵做线性变换得到开环约束系统二阶线性常微分方程组;最后,构造切断铰约束矩阵,对开环约束系统矩阵做线性变换得到闭环约束系统二阶线性常微分方程组。由于此方法无须矩阵求导和方程线性化,与传统方法相比可显著提高计算效率。
采用复模态分析求取特征值和特征向量,进而得到系统的模态参数。基于振动位移变换关系导出了任意两点之间不同坐标系下的一般传递函数公式,该公式包含了物理坐标与独立广义坐标之间的显式变换关系,因此较传统基于独立广义坐标的传递函数计算公式更为实用。在传统模态频率关于矩阵元素的灵敏度的基础上,导出了模态频率关于设计参数的灵敏度计算公式,使参数灵敏度分析和优化得以简捷、高效地实现。提出了一种递归算法求解多刚体系统在装配位置的无变形平衡问题,解决了多刚体系统动力学仿真中的初始状态模拟难题。
基于上述算法开发了多体动力学软件Simulith,提供了振动模态分析、传递函数分析、频域响应分析、灵敏度分析、动力学优化以及控制等功能。针对不同约束拓扑的多刚体系统进行数值实验,验证了本算法的正确性和效率。中国软件评测中心性能测试结果表明,该求解器较传统方法(如ADAMS)可以显著提高计算速度。而且,模型中刚体个数、刚体间作用力元个数或约束个数越多,该求解器的计算效率提高越明显。本文提出的方法已成功应用于100nm光刻机动力学分析与优化,有效缩短了光刻机设计周期,降低了研发成本,实验结果进一步验证了本文所述方法的正确性和有效性。本文提出的方法还可用于各种类型的结构和机构系统振动分析,以及参数灵敏度分析与优化。
本文研究工作是2007年度教育部自然科学奖一等奖“精密运动机构中若干关键动力学与控制问题研究”的主要成果之一。
As the increasement of requirements in dynamic performance of modern mechanical systems, the structural complexity of mechanical systems has significantly increased. Dynamic analysis and optimization has become the most critical issue in structural design. Since mechanical systems are usually modeled as large-scale complex multibody systems to acquire satisfied accuracy, it leads to two major problems for dynamic analysis of such kinds of large-scale complex multibody systems using conventional methods, i.e., accuracy and computational efficiency, which are one of the critical problems to be resolved in structural design at present. Particularly, vibration analysis is the core and basis of dynamic analysis of such kind of systems, and the computational efficiency becomes one of the bottlenecks for design, optimization and control. In order to fulfil the urgent requirements of state key scientific research and engineering projects, formulation and solution of vibrational equations for such kinds of systems are studied in this dissertation, by starting with investigation of constraint topologies for spatial multibody systems. A new method for vibration analysis of large-scale complex multibody systems with high accuracy and efficiency is finally presented.
All the physical parameters are defined in matrix-vector form, including mass and inertia tensor of each body, coefficients of spatial spring-damper, mathematical representation of joint, and spatial motion status of rigid body, so as to get clear notation and provides clear insight into the system. Based on uniform transformation of vibrational displacements, a new method for formulating a minimal set of second-order linear ordinary differential equations (ODEs) in three steps is proposed. Firstly, a set of linearized ODEs are formulated in terms of absolute coordinates without considering any constraint in the system. Secondly, an open-loop constraint matrix is generated to formulate ODEs for open-loop mechanism system which is obtained by ignoring all cut-joints in the original system. Finally, a cut-joint constraint matrix is generated to formulate a minimal set of ODEs for the original closed-loop mechanism system. Since there is no need for derivation of matrices and linearization of equations, computational efficiency can be significantly improved by using the proposed method as compared with traditional approaches.
Complex modal analysis is then performed to calculate the eigenvalues and eigenvectors, and then modal parameters are obtained. General formulation of transfer function between two arbitrary points with respect to different reference frames is derived. The presented physical-coordinates-based formula consists of explicit transformation between physical coordinates and modal coordinates, and hence is more practical than traditional general-coordinates-based formulation. Transfer function in the vicinity of each natural frequency is always computed to improve numerical accuracy near the resonance frequencies. Sensitivity of natural frequency with respect to design parameters, instead of conventional elements of mass (stiffness, or damping) matrix, is derived with a simple expression. A recursive algorithm is proposed to solve inverse equilibrium problems, which computes inner forces to keep the system with nearly zero deformation.
Software named Simulith has been developed based on the proposed algorithm. Function such as normal mode analysis, transfer function analysis, sensitivity analysis, optimization and control are all included. The correctness and efficiency of the proposed method have been verified by numerical experiments on multibody systems with different kinds of constraint topologies. The results of performance test done by China Software Test Center (CSTC) show that, the computational efficiency of the presented approach has been significantly improved in compare with traditional methods such as ADAMS. Furthermore, the greater the number of bodies, joints, or spring-dampers is, the more the improvement in computational efficiency is obtained. The proposed method has been successfully applied in dynamic analysis and optimization of 100nm optical lithography equipment. The design period and the cost of development for the optical lithography equipment have been significantly reduced. Experimental results have further verified the correctness and effectiveness of the presented approach. The proposed method can also be used for vibration analysis of many other kinds of structures and mechanism systems.
The study work is one of the major achievements in A Study of the Key Issues on Dynamics and Control in the Ultra Precision Mechanisms, which has won the First Prize of Ministry of Education Natural Science Award in 2007.
引文
[1] Bremer H. Elastic Multibody Dynamic: A Direct Ritz Approach[M]. Springer, 2008.
[2] Cheung K Y, Zhou D. The Free Vibrations of Tapered Rectangular Plates Using a New Set of Beam Functions with the Rayleigh-Ritz Method[J]. Journal of Sound and Vibration. 1999,223(5): 703-722.
[3] Zhou D. Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method[J].International Journal of Solids and Structures. 2001, 38(32-33): 5565-5580.
[4] Chakraverty S, Bhat R B, Stiharu I. Free Vibration of Annular Elliptic Plates Using Boundary Characteristic Orthogonal Polynomials as Shape Functions in the Rayleigh-Ritz Method[J]. Journal of Sound and Vibration. 2001, 241(3): 524-539.
[5] Iwata Y, Sato H, Komatsuzaki T. Analytical method for steady state vibration of system with localized non-linearities using convolution integral and Galerkin method[J]. Journal of Sound and Vibration. 2003,262(1): 11-23.
[6] Chen X L, Liu G R, Lim S P. An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape[J]. Composite Structures. 2003, 59(2): 279-289.
[7] Gristchak V Z, Ganilova O A. A hybrid WKB-Galerkin method applied to a piezoelectric sandwich plate vibration problem considering shear force effects[J].Journal of Sound and Vibration. 2008, 317(1-2): 366-377.
[8] Sheu H O, Chen L I. A Lumped Mass Model for Parametric Instability Analysis of Cantilever Shaft-Disk Systems[J]. Journal of Sound and Vibration. 2000, 234(2):331-348.
[9] Dwivedy S K, Kar R C. Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions[J].International Journal of Non-Linear Mechanics. 2001, 36(6): 927-945.
[10] Li Q S, Wu J R, Xu J. Longitudinal vibration of multi-step non-uniform structures with lumped masses and spring supports[J]. Applied Acoustics. 2002,63(3): 333-350.
[11] Jing J, Ye L, Qian J, et al. Seismic design and inelastic seismic response of lumped mass mdof dual structure[J]. 2002: 746739.
[12] Wu S R. Lumped mass matrix in explicit finite element method for transient dynamics of elasticity[J]. Computer Methods in Applied Mechanics and Engineering.2006,195(44-47): 5983-5994.
[13] Lee U. Vibration analysis of one-dimensional structures using the spectral transfer matrix method[J]. Engineering Structures. 2000,22(6): 681-690.
[14] Li Q S, Yang K, Zhang L, et al. Frequency domain analysis of fluid-structure interaction in liquid-filled pipe systems by transfer matrix method[J].International Journal of Mechanical Sciences.2002,44(10):2067-2087.
[15]Lee D H,Kwon Y P.Estimation of the absorption performance of multiple layer perforated panel systems by transfer matrix method[J].Journal of Sound and Vibration.2004,278(4-5):847-860.
[16]Liu H,Lee J J,Cai Z M.Analysis of nonlinear acoustoelastic effect of surface acoustic waves in laminated structures by transfer matrix method[J].Mechanics Research Communications.2004,31(6):667-675.
[17]Hsieh S C,Chen J H,Lee A C.A modified transfer matrix method for the coupling lateral and torsional vibrations of symmetric rotor-bearing systems[J].Journal of Sound and Vibration.2006,289(1-2):294-333.
[18]Hsieh S C,Chen J H,Lee A C.A modified transfer matrix method for the coupled lateral and torsional vibrations of asymmetric rotor-bearing systems[J].Journal of Sound and Vibration.2008,312(4-5):563-571.
[19]何斌,芮筱亭,陆毓琪.多体系统离散时间传递矩阵法与有限元法混合方法[J].南京理工大学学报(自然科学版).2006(04).
[20]芮筱亭,何斌,陆毓琪.刚柔多体系统动力学离散时间传递矩阵法[J].南京理工大学学报(自然科学版).2006(04).
[21]Hartmann F,Katz C.Structural Analysis with Finite Elements[M].Berlin Heidelberg:Springer,2007.
[22]Ohga M,Shigematsu T,Hara T.A Finite Element-Transfer Matrix Method For Dynamic Analysis Of Frame Structures[J].Journal of Sound and Vibration.1993,167(3):401-411.
[23]Yuhua C.Large deflection analysis of structures by an improved combined finite element-transfer matrix method[J].Computers & Structures.1995,55(1):167-171.
[24]Bhutani N,Loewy R G.Combined Finite Element-Transfer Matrix Method[J].Journal of Sound and Vibration.1999,226(5):1048-1052.
[25]Ohga M,Shigematsu T,Hara T.Structural analysis by a combined boundary element-transfer matrix method[J].Computers & Structures.1986,24(3):385-389.
[26]Ohga M,Shigematsu T.Bending analysis of plates with variable thickness by boundary element-transfer matrix method[J].Computers & Structures.1988,28(5):635-640.
[27]Ohga M,Shigematsu T.Analysis of continuous plates by a combined boundary element-transfer matrix method[J].Computers & Structures.1990,36(1):81-89.
[28]刘子建,徐丽茹.多刚体动力学的STEP描述及其映射研究[J].湖南大学学报(自然科学版).2004(05).
[29]车仁炜,陆念力.多刚体系统动力学建模的一种新方法[J].汽轮机技术.2003(06).
[30]谢先海,廖道训.基于多刚体离散元模型的柔顺机构动力分析新方法[J].机械工程学报.2003(05).
[31]任伟新,郑兆昌.平面刚架弹塑性大位移分析的多刚体离散元法[J].计算力学学报.1996(04).
[32]殷学纲杜思义.应用多刚体离散化方法对梁的动力屈曲和后屈曲分析[J].应用数学和力学.2005(09).
[33]Vampola T,Valasek M.Composite rigid body formalism for flexible multibody systems[J].Multibody System Dynamics.2007,18(3):413-433.
[34]Ardema M D.Analytical Dynamics:Theory and Applications[M].New York:Kluwer Academic / Plenum Publishers,2005.
[35]Dankowicz H J.Multibody Mechanics and Visualization[M].London:Springer-Verlag,2005.
[36]Wittbrodt E,Adamiec-w I,Wojciech S.Dynamics of Flexible Multibody Systems:Rigid Finite Element Method[M].Berlin:Springer-Verlag,2006.
[37]Amirouche F.Fundamentals of Multibody Dynamics:Theory and Applications[M].Boston:Birkhauser,2006.
[38]Onate E.Advances in Computational Multibody Systems[M].Dordrecht:Springer,2008.
[39]Wittenburg J.Dynamics of Multibody Systems[M].Berlin:Springer-Verlag,2008.
[40]Flores P,Ambr J,Claro P,et al.Kinematics and Dynamics of Multibody Systems with Imperfect Joints:Models and Case Studies[M].Berlin:Springer-Verlag,2008.
[41]Garc A O,Goicolea J M,Cuadrado J A.Multibody Dynamics:Computational Methods and Applications[M].Dordrecht:Springer,2008.
[42]刘延柱.多刚体系统动力学[M].北京:高等教育出版社,1989.
[43]陆佑方.柔性多体系统动力学[M].北京:高等教育出版社,1996.
[44]洪嘉振.计算多体系统动力学[M].北京:高等教育出版社,1999.
[45]张景绘.动力学系统建模[M].北京:国防工业出版社,2000.
[46]覃正.多体系统动力学压缩建模[M].北京:科学出版社,2000.
[47]许本文,焦群英.机械振动与模态分析基础[M].北京:机械工业出版社,1998.
[48]傅志方,华宏星.模态分析理论与应用[M].上海:上海交通大学出版社,2000.
[49]Schiehlen W.Research trends in multibody system dynamics[J].Multibody System Dynamics.2007,18(1):3-13.
[50]Eberhard P,Schiehlen W.Computational Dynamics of Multibody Systems:History, Formalisms, and Applications[J]. Journal of Computational and Nonlinear Dynamics.2006,1:3-12.
[51] Schiehlen W. Computational dynamics: theory and applications of multibody systems[J]. European Journal of Mechanics A/Solids. 2006,25: 566-594.
[52] Schiehlen W, Guse N, Seifried R. Multibody dynamics in computational mechanics and engineering applications[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(41-43): 5509-5522.
[53] Schiehlen W. Multibody System dynamics: Roots and Perspectives[J]. Multibody System Dynamics. 1997,1: 149-188.
[54] Schiehlen W. Computational aspects in multibody system dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 1991,90(1-3): 569-582.
[55] Hemami H. Evolutionary trends in rigid body dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2003,192(5-6): 635-654.
[56] Dwivedy S K, Eberhard P. Dynamic analysis of flexible manipulators, a literature review[J]. Mechanism and Machine Theory. 2006,41(7): 749-777.
[57] Shimizu N, Imanishi E, Sugano N. Multibody dynamics research in Japan[J].Research Bulletin of Iwaki Meisei University. 2003(16): 7-16.
[58] Yoo W S, Kim S S, Park T W, et al. Multibody dynamics research in Korea[J].JSME Int Journal. Ser C. Mech Systems, Mach Elem Manuf. 2003,46(2): 449-458.
[59] Sun Y L. Multibody dynamics formulations based on variational principle[J].Journal of Shanghai University (English Edition). 2003,7(2): 131-137.
[60] Schiehlen W. Computational aspects in multibody system dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 1991,90(1-3): 569-582.
[61] Blajer W, Schiehlen W, Schirm W. Dynamic analysis of constrained multibody systems using inverse kinematics[J]. Mechanism and Machine Theory. 1993, 28(3):397-405.
[62] Dupuis C, Rousselet J. Application of the transfer matrix method to non-conservative systems involving fluid flow in curved pipes[J]. J Mass Spectrom.1985, 37(3): 415-429.
[63] Hu B, Eberhard P, Schiehlen W. Symbolical Impact Analysis for a Falling Conical Rod Against the Rigid Ground[J]. Eur J Clin Pharmacol. 2001,240(1): 41-57.
[64] R A, Schiehlen W. Simulation of modular dynamic systems[J]. Mathematics and Computers in Simulation. 1998,46(5-6): 535-542.
[65] Anh N D, Schiehlen W. A technique for obtaining approximate solutions in Gaussian equivalent linearization[J]. Computer Methods in Applied Mechanics and Engineering. 1999, 168(1-4): 113-119.
[66] Dignath F, Schiehlen W. Control of the vibrations of a tethered satellite system[J]. Journal of Applied Mathematics and Mechanics. 2000, 64(5): 715-722.
[67] Hu B, Eberhard P, Schiehlen W. Symbolical Impact Analysis for a Falling Conical Rod Against the Rigid Ground[J]. Journal of Sound and Vibration. 2001, 240(1):41-57.
[68] Schiehlen W. An energy analysis of the prescribed motion of an oscillator[J].Journal of Applied Mathematics and Mechanics. 2001,65(4): 671-679.
[69] Claus H, Schiehlen W. Symbolic-Numeric Analysis of Flexible Multibody Systems[J]. Mechanics Based Design of Structures and Machines. 2002, 30(1): 1-30.
[70] Schiehlen W, Hu B. Spectral simulation and shock absorber identification[J].International Journal of Non-Linear Mechanics. 2003,38(2): 161-171.
[71] Lakrad F, Schiehlen W. Effects of a low frequency parametric excitation[J]. Chaos,Solitons & Fractals. 2004,22(5): 1149-1164.
[72] Seifried R, Schiehlen W, Eberhard P. Numerical and experimental evaluation of the coefficient of restitution for repeated impacts[J]. International Journal of Impact Engineering. 2005, 32(1-4): 508-524.
[73] Yanzhu L. Screw-matrix method in dynamics of multibody systems[J]. Acta Mechanica Sinica. 1988,39(2): 132-135.
[74] Ding J Y, Pan Z K, Chen L Q. Second order adjoint sensitivity analysis of multibody systems described by differential-algebraic equations[J]. Anal Chem. 2007,18(4): 2453-2461.
[75] Schiehlen W, Seifried R, Eberhard P. Elastoplastic phenomena in multibody impact dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(50-51): 6874-6890.
[76] Schiehlen W, Guse N, Seifried R. Multibody dynamics in computational mechanics and engineering applications[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(41-43): 5509-5522.
[77] Ackermann M, Schiehlen W. Design of prosthetic devices by means of musculoskeletal models[J]. Journal of Biomechanics. 2006, 39(Supplement 1): 46-46.
[78] Gontier C, Li Y. Lagrangian formulation and linearization of multibody system equations[J]. Computers & Structures. 1995, 57(2): 317-331.
[79] Bayo E, Ledesma R. Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics[J]. Nonlinear Dynamics. 1996, 9(1):113-130.
[80] Forehand D I, Khanin R, Cartmell M P. A Lagrangian multibody code for deriving the symbolic state-space equations of motion for open-loop systems containing flexible beams[J]. Mathematics and Computers in Simulation. 2004, 67(1-2): 85-98.
[81] Kool P. An analytical expression for the generalized forces in multibody Lagrange equations[J].IEEE Transactions on Robotics.2004,20(2):340-343.
[82]Santini P,Gasbarri P.Dynamics of multibody systems in space environment;Lagrangian vs.Eulerian approach[J].Acta Astronautica.2004,54(1):1-24.
[83]Simeon B.On Lagrange multipliers in flexible multibody dynamics[J].Computer Methods in Applied Mechanics and Engineering.2006,195(50-51):6993-7005.
[84]Duindam V,Stramigioli S.Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints[C].2007.
[85]Zheng Z,Simeon B,Petzold L.A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems[J].Journal of Computational Physics.2008,227(10):5272-5285.
[86]孙京,邵成勋.用拉格朗日键图建立复杂航天器系统的动力学方程[J].哈尔滨工业大学学报.2000(02).
[87]Mcphee J J,Redmond S M.Modelling multibody systems with indirect coordinates[J].Computer Methods in Applied Mechanics and Engineering.2006,195(50-51):6942-6957.
[88]Huston R L,Yung S L,Chengqun L.Use of absolute coordinates in computational multibody dynamics[J].Computers & Structures.1994,52(1):17-25.
[89]Mcphee J J.A unified graph--Theoretic approach to formulating multibody dynamics equations in absolute or joint coordinates[J].Journal of the Franklin Institute.1997,334(3):431-445.
[90]Gaikwad J L,Dasgupta B,Joshi U.Static equilibrium analysis of compliant mechanical systems using relative coordinates and loop closure equations[J].Mechanism and Machine Theory.2004,39(5):501-517.
[91]de Garc J,Unda J,Avello A.Natural coordinates for the computer analysis of multibody systems[J].Computer Methods in Applied Mechanics and Engineering.1986,56(3):309-327.
[92]Brauchli H,Weber R.Dynamical equations in natural coordinates[J].Computer Methods in Applied Mechanics and Engineering.1991,91(1-3):1403-1414.
[93]Mcphee J J.Automatic generation of motion equations for planar mechanical systems using the new set of "branch coordinates"[J].Mechanism and Machine Theory.1998,33(6):805-823.
[94]陈立群,刘延柱.任意圆轨道上磁性刚体航天器的混沌姿态运动及其控制[J].Drug Metab Dispos.2001,21(04):889-901.
[95]Wittenburg J.Dynamics of Multibody Systems[M].Berlin:Springer-Verlag,2008.
[96]Huston R L,Yung S L,Chengqun L.Use of absolute coordinates in computational multibody dynamics[J].Computers & Structures.1994,52(1):17-25.
[97]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. 2005(05).
[98]洪在地,陈力.漂浮基空间机器人双臂协调操作逆运动学的完全笛卡尔坐标方法[J].机械科学与技术.2003(06).
[99]张成新,余跃庆.基于绝对坐标的柔性机器人逆动力学建模和轨迹跟踪[J].机械科学与技术.2002(01).
[100]戈新生,张涌.完全笛卡尔坐标描述的机械系统动力学分析及软件研究[J].机械科学与技术.2000(01).
[101]戈新生,刘延柱.空间机械手逆问题的完全笛卡尔坐标方法[J].机械科学与技术.1998(03).
[102]戈新生,刘延柱.基于自然坐标的自由浮动空间机械臂动力学分析[J].力学与实践.2001(03).
[103]Lee S H,Park T W,Seo J H,et al.The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation[J].Multibody System Dynamics.
[104]Dmitrochenko O.Finite elements using absolute nodal coordinates for large-deformation flexible multibody dynamics[J].Journal of Computational and Applied Mathematics.2008,215(2):368-377.
[105]Gerstmayr J,Irsehik H.On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach[J].Journal of Sound and Vibration.2008,In Press,Corrected Proof.
[106]Bauehau O A.On the modeling of prismatic joints in flexible multi-body systems[J].Computer Methods in Applied Mechanics and Engineering.2000,181(1):38-42.
[107]罗跃纲,彭永恒,闻邦椿.工程结构损伤的集成神经网络识别研究[J].振动与冲击ZDCJ.2006(01):287.
[108]Ider S K,Amirouche F M.Numerical stability of the constraints near singular positions in the dynamics of multibody systems[J].Computers & Structures.1989,33(1):129-137.
[109]Robe T R,Kane T R.Dynamics of an elastic satellite—I[J].International Journal of Solids and Structures.1967,17(3):333-352.
[110]Jeng Y,Chien-chun C.Automatic generation and numerical integration of differential-algebraic equations of multibody dynamics[J].Computer Methods in Applied Mechanics and Engineering.1993,104(3):317-331.
[111]Fisette P,Vaneghem B.Numerical integration of multibody system dynamic equations using the coordinate partitioning method in an implicit Newmark scheme[J].Computer Methods in Applied Mechanics and Engineering.1996,135(1-2):85-105.
[112] Sudarsan R, Sathiya K S. Numerical approaches for solution of differential equations on manifolds[J]. Applied Mathematics and Computation. 1998, 92(2-3):153-193.
[113] Pogorelov D Y. On numerical methods of modeling large multibody systems[J].Mechanism and Machine Theory. 1999,34(5): 791-800.
[114] Levinson D A, Kane T R. A usable solution of the hanging cable problem[J]. Anal Bioanal Chem. 1993, 378(4): 821-844.
[115] Huston R L, Kamman J W. Testing the accuracy of numerical simulations of multibody systems[J]. Mechanics Research Communications. 2001,28(1): 1-6.
[116] Hamann P, Mehrmann V. Numerical solution of hybrid systems of differential-algebraic equations[J]. Computer Methods in Applied Mechanics and Engineering. 2008,197(6-8): 693-705.
[117] Br O, Golinval J C. On the numerical damping of time integrators for coupled mechatronic systems[J]. Computer Methods in Applied Mechanics and Engineering.2008, 197(6-8): 577-588.
[118] Ohga M, Shigematsu T. Bending analysis of plates with variable thickness by boundary element-transfer matrix method[J]. Chirality. 1988,14(5): 635-640.
[119] Tseng F C, Ma Z D, Hulbert G M. Efficient numerical solution of constrained multibody dynamics systems[J]. Computer Methods in Applied Mechanics and Engineering. 2003,192(3-4): 439-472.
[120] Lim J H, Yim H, Lim S H, et al. A study on numerical solution method for efficient dynamic analysis of constrained multibody systems[J]. Journal of Mechanical Science and Technology. 2008,22(4): 714-721.
[121] Hale A L, Meirovitch L. Derivation of the equations of motion for complex structures by symbolic manipulation[J]. Computers & Structures. 1978,9(6): 639-649.
[122] Lieh J, Haque I. Symbolic Closed-Form Modeling and Linearization of Multibody Systems Subject to Control[J]. Journal of Mechanical Design. 1991,113(2): 124-132.
[123] Ju M S, Hsu C J. Automatic modeling of mechatronic systems via symbolic approach[J]. Mechatronics. 1991,1(2): 157-174.
[124] Charbonneau G, Vinarnick S, N P, et al. Symbolic modelling of controlled mechanisms[J]. Computer Methods in Applied Mechanics and Engineering. 1992,98(1): 23-40.
[125] Cui K, Haque I, Thirumalai M. On configurations of symbolic equations of motion for rigid multibody systems[J]. Mechanism and Machine Theory. 1995, 30(8):1149-1170.
[126] Vibet C. Symbolic modeling of robot kinematics and dynamics[J]. Robotics and Autonomous Systems. 1995, 14(4): 301-314.
[127]Lynch A G,Vanderploeg M J.A Symbolic Formulation for Linearization of Multibody Equations of Motion[J].Journal of Mechanical Design.1995,117(3):441-445.
[128]Kwatny H G,Blankenship G L.Symbolic construction of models for multibody dynamics[J].IEEE Transactions on Robotics and Automation.1995,11(2):271-281.
[129]Villard D,Arnaldi B.Symbolic differentiation library for simulation of multibody rigid systems[J].Mathematics and Computers in Simulation.1996,42(4-6):659-673.
[130]倪纯双,洪嘉振,贺启庸.车辆系统动力学的符号化多体方法[J].中国铁道科学.1996(04).
[131]Tummarakota S R,Lieh J U.Symbolic Finite Element Modeling of Structural Systems[J].Journal of Symbolic Computation.1996,22(1):105-119.
[132]Melzer F.Symbolic computations in flexible multibody systems[J].Nonlinear Dynamics.1996,9(1):147-163.
[133]Fisette P,Johnson D A,Samin J C.A fully symbolic generation of the equations of motion of multibody systems containing flexible beams[J].Computer Methods in Applied Mechanics and Engineering.1997,142(1-2):123-152.
[134]Carpanzano E,Maffezzoni C.Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems[J].Mathematics and Computers in Simulation.1998,48(2):133-150.
[135]Cui K,Haque I.Symbolic equations of motion for hybrid multibody systems using a matrix--vector formulation[J].Mechanism and Machine Theory.1997,32(6):743-763.
[136]Zhou W,Jeffrey D,Reid G.Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical Systems[J].Symbolic-Numeric Computation.2007,2007:335-347.
[137]Soh C W,Mahomed F M.Linearization criteria for a system of second-order ordinary differential equations[J].International Journal of Non-Linear Mechanics.2001,36(4):671-677.
[138]Ramon H,De B J.A modelling procedure for linearized motions of tree structured multibodies--1:Derivation of the equations of motion[J].Computers & Structures.1996,59(2):347-360.
[139]Ramon H,De B J.A modelling procedure for linearized motions of tree structured multibodies--2:Design of an active spray boom suspension on a spraying-machine[J].Computers & Structures.1996,59(2):361-375.
[140]Anthonis J,Hostens I,M M A,et al.A generalized modelling technique for linearized motions of mechanisms with flexible parts[J].Journal of Sound and Vibration.2003,266(3):553-572.
[141] Kang J S, Bae S, Lee J M, et al. Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics[J]. Journal of Mechanical Design. 2003,125: 143-149.
[142] Minaker B, Frise P. Linearizing the Equations of Motion for Multibody Systems Using an Orthogonal Complement Method[J]. Journal of Vibration and Control. 2005,11:51-66.
[143] Roy D, Kumar R. A multi-step transversal linearization (MTL) method in non-linear structural dynamics[J]. Journal of Sound and Vibration. 2005,287(1-2): 203-226.
[144] Ramos J I. Linearization techniques for singularly-perturbed initial-value problems of ordinary differential equations[J]. Applied Mathematics and Computation. 2005,163(3): 1143-1163.
[145] Ramos J I. Linearization techniques for singular initial-value problems of ordinary differential equations[J]. Applied Mathematics and Computation. 2005, 161(2):525-542.
[146] Negrut D, Ortiz J L. A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations[J]. Journal of Computational and Nonlinear Dynamics. 2006, 1(3): 230-239.
[147] Pott A, Kecskemethy A, Hiller M. A simplified force-based method for the linearization and sensitivity analysis of complex manipulation systems[J]. Mechanism and Machine Theory. 2007,42(11): 1445-1461.
[148] Lin T C, Yae K H. Recursive Linearization of Multibody Dynamics and Application to Control Design[J]. Journal of Mechanical Design. 1994, 116(2): 445-451.
[149] Stone T A, Santos J L, Haug E J. An interactive pre-processor for structural design sensitivity analysis and optimization[J]. Computers & Structures. 1990, 34(3):375-385.
[150] Zhang Y, Chen S, Liu Q. The sensitivity of multibody systems with respect to a design variable matrix[J]. Mechanics Research Communications. 1994, 21(3):223-230.
[151] Wasfy T M, Noor A K. Modeling and sensitivity analysis of multibody systems using new solid, shell and beam elements[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 138(1-4): 187-211.
[152] Liu X. Sensitivity analysis of constrained flexible multibody systems with stability considerations[J]. Mechanism and Machine Theory. 1996, 31(7): 859-863.
[153] Schulz M, Brauchli H. Two methods of sensitivity analysis for multibody systems with collisions[J]. Mechanism and Machine Theory. 2000,35(10): 1345-1365.
[154] Sohl G A, Bobrow J E. A Recursive Multibody Dynamics and Sensitivity Algorithm for Branched Kinematic Chains[J]. Journal of Dynamic Systems, Measurement, and Control. 2001,123(3): 391-399.
[155] Van K F, Haftka R T, Kim N H. Review of options for structural design sensitivity analysis. Part 1: Linear systems[J]. Computer Methods in Applied Mechanics and Engineering Structural and Design Optimization. 2005, 194(30-33): 3213-3243.
[156] Maly T, Petzold L R. Numerical methods and software for sensitivity analysis of differential-algebraic systems[J]. Applied Numerical Mathematics. 1996, 20(1-2):57-79.
[157] Li S, Petzold L. Software and algorithms for sensitivity analysis of large-scale differential algebraic systems[J]. Journal of Computational and Applied Mathematics.2000, 125(1-2): 131-146.
[158] Li S, Petzold L, Zhu W. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem[J]. Applied Numerical Mathematics.2000,32(2): 161-174.
[159] Cao Y, Li S, Petzold L. Adjoint sensitivity analysis for differential-algebraic equations: algorithms and software[J]. Journal of Computational and Applied Mathematics. 2002,149(1): 171-191.
[160] Li S, Petzold L. Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement[J]. Journal of Computational Physics. 2004,198(1): 310-325.
[161] Petzold L, Li S, Cao Y, et al. Sensitivity analysis of differential-algebraic equations and partial differential equations[J]. Computers & Chemical Engineering. 2006,30(10-12): 1553-1559.
[162] Anderson K S, Hsu Y. Analytical Fully-Recursive Sensitivity Analysis for Multibody Dynamic Chain Systems[J]. Multibody System Dynamics. 2002, 8: 1-27.
[163] Anderson K S, Hsu Y. Order-(n+m) direct differentiation determination of design sensitivity for constrained multibody dynamic systems[J]. Structural and Multidisciplinary Optimization. 2004,26: 171-182.
[164] Hsu Y, Anderson K S. Recursive sensitivity analysis for constrained multi-rigid-body dynamic systems design optimization[J]. Structural and Multidisciplinary Optimization. 2008,24: 312-324.
[165] Mukherjee R M, Bhalerao K D, Anderson K S. A divide-and-conquer direct differentiation approach for multibody system sensitivity analysis[J]. Structural and Multidisciplinary Optimization. 2008, 35: 413-429.
[166] Ding J Y, Pan Z K, Chen L Q. Second order adjoint sensitivity analysis of multibody systems described by differential-algebraic equations[J]. Multibody System Dynamics. 2007, 18(4): 599-617.
[167]潘振宽,赵维加.多体系统动力学设计灵敏度分析与动态优化设计方法[J].青岛大学学报(工程技术版).2002(04).
[168]余显忠.100nm步进扫描投影光刻机结构动力学建模研究[D].武汉:华中科技大学,2008.
[2] Cheung K Y, Zhou D. The Free Vibrations of Tapered Rectangular Plates Using a New Set of Beam Functions with the Rayleigh-Ritz Method[J]. Journal of Sound and Vibration. 1999,223(5): 703-722.
[3] Zhou D. Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method[J].International Journal of Solids and Structures. 2001, 38(32-33): 5565-5580.
[4] Chakraverty S, Bhat R B, Stiharu I. Free Vibration of Annular Elliptic Plates Using Boundary Characteristic Orthogonal Polynomials as Shape Functions in the Rayleigh-Ritz Method[J]. Journal of Sound and Vibration. 2001, 241(3): 524-539.
[5] Iwata Y, Sato H, Komatsuzaki T. Analytical method for steady state vibration of system with localized non-linearities using convolution integral and Galerkin method[J]. Journal of Sound and Vibration. 2003,262(1): 11-23.
[6] Chen X L, Liu G R, Lim S P. An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape[J]. Composite Structures. 2003, 59(2): 279-289.
[7] Gristchak V Z, Ganilova O A. A hybrid WKB-Galerkin method applied to a piezoelectric sandwich plate vibration problem considering shear force effects[J].Journal of Sound and Vibration. 2008, 317(1-2): 366-377.
[8] Sheu H O, Chen L I. A Lumped Mass Model for Parametric Instability Analysis of Cantilever Shaft-Disk Systems[J]. Journal of Sound and Vibration. 2000, 234(2):331-348.
[9] Dwivedy S K, Kar R C. Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions[J].International Journal of Non-Linear Mechanics. 2001, 36(6): 927-945.
[10] Li Q S, Wu J R, Xu J. Longitudinal vibration of multi-step non-uniform structures with lumped masses and spring supports[J]. Applied Acoustics. 2002,63(3): 333-350.
[11] Jing J, Ye L, Qian J, et al. Seismic design and inelastic seismic response of lumped mass mdof dual structure[J]. 2002: 746739.
[12] Wu S R. Lumped mass matrix in explicit finite element method for transient dynamics of elasticity[J]. Computer Methods in Applied Mechanics and Engineering.2006,195(44-47): 5983-5994.
[13] Lee U. Vibration analysis of one-dimensional structures using the spectral transfer matrix method[J]. Engineering Structures. 2000,22(6): 681-690.
[14] Li Q S, Yang K, Zhang L, et al. Frequency domain analysis of fluid-structure interaction in liquid-filled pipe systems by transfer matrix method[J].International Journal of Mechanical Sciences.2002,44(10):2067-2087.
[15]Lee D H,Kwon Y P.Estimation of the absorption performance of multiple layer perforated panel systems by transfer matrix method[J].Journal of Sound and Vibration.2004,278(4-5):847-860.
[16]Liu H,Lee J J,Cai Z M.Analysis of nonlinear acoustoelastic effect of surface acoustic waves in laminated structures by transfer matrix method[J].Mechanics Research Communications.2004,31(6):667-675.
[17]Hsieh S C,Chen J H,Lee A C.A modified transfer matrix method for the coupling lateral and torsional vibrations of symmetric rotor-bearing systems[J].Journal of Sound and Vibration.2006,289(1-2):294-333.
[18]Hsieh S C,Chen J H,Lee A C.A modified transfer matrix method for the coupled lateral and torsional vibrations of asymmetric rotor-bearing systems[J].Journal of Sound and Vibration.2008,312(4-5):563-571.
[19]何斌,芮筱亭,陆毓琪.多体系统离散时间传递矩阵法与有限元法混合方法[J].南京理工大学学报(自然科学版).2006(04).
[20]芮筱亭,何斌,陆毓琪.刚柔多体系统动力学离散时间传递矩阵法[J].南京理工大学学报(自然科学版).2006(04).
[21]Hartmann F,Katz C.Structural Analysis with Finite Elements[M].Berlin Heidelberg:Springer,2007.
[22]Ohga M,Shigematsu T,Hara T.A Finite Element-Transfer Matrix Method For Dynamic Analysis Of Frame Structures[J].Journal of Sound and Vibration.1993,167(3):401-411.
[23]Yuhua C.Large deflection analysis of structures by an improved combined finite element-transfer matrix method[J].Computers & Structures.1995,55(1):167-171.
[24]Bhutani N,Loewy R G.Combined Finite Element-Transfer Matrix Method[J].Journal of Sound and Vibration.1999,226(5):1048-1052.
[25]Ohga M,Shigematsu T,Hara T.Structural analysis by a combined boundary element-transfer matrix method[J].Computers & Structures.1986,24(3):385-389.
[26]Ohga M,Shigematsu T.Bending analysis of plates with variable thickness by boundary element-transfer matrix method[J].Computers & Structures.1988,28(5):635-640.
[27]Ohga M,Shigematsu T.Analysis of continuous plates by a combined boundary element-transfer matrix method[J].Computers & Structures.1990,36(1):81-89.
[28]刘子建,徐丽茹.多刚体动力学的STEP描述及其映射研究[J].湖南大学学报(自然科学版).2004(05).
[29]车仁炜,陆念力.多刚体系统动力学建模的一种新方法[J].汽轮机技术.2003(06).
[30]谢先海,廖道训.基于多刚体离散元模型的柔顺机构动力分析新方法[J].机械工程学报.2003(05).
[31]任伟新,郑兆昌.平面刚架弹塑性大位移分析的多刚体离散元法[J].计算力学学报.1996(04).
[32]殷学纲杜思义.应用多刚体离散化方法对梁的动力屈曲和后屈曲分析[J].应用数学和力学.2005(09).
[33]Vampola T,Valasek M.Composite rigid body formalism for flexible multibody systems[J].Multibody System Dynamics.2007,18(3):413-433.
[34]Ardema M D.Analytical Dynamics:Theory and Applications[M].New York:Kluwer Academic / Plenum Publishers,2005.
[35]Dankowicz H J.Multibody Mechanics and Visualization[M].London:Springer-Verlag,2005.
[36]Wittbrodt E,Adamiec-w I,Wojciech S.Dynamics of Flexible Multibody Systems:Rigid Finite Element Method[M].Berlin:Springer-Verlag,2006.
[37]Amirouche F.Fundamentals of Multibody Dynamics:Theory and Applications[M].Boston:Birkhauser,2006.
[38]Onate E.Advances in Computational Multibody Systems[M].Dordrecht:Springer,2008.
[39]Wittenburg J.Dynamics of Multibody Systems[M].Berlin:Springer-Verlag,2008.
[40]Flores P,Ambr J,Claro P,et al.Kinematics and Dynamics of Multibody Systems with Imperfect Joints:Models and Case Studies[M].Berlin:Springer-Verlag,2008.
[41]Garc A O,Goicolea J M,Cuadrado J A.Multibody Dynamics:Computational Methods and Applications[M].Dordrecht:Springer,2008.
[42]刘延柱.多刚体系统动力学[M].北京:高等教育出版社,1989.
[43]陆佑方.柔性多体系统动力学[M].北京:高等教育出版社,1996.
[44]洪嘉振.计算多体系统动力学[M].北京:高等教育出版社,1999.
[45]张景绘.动力学系统建模[M].北京:国防工业出版社,2000.
[46]覃正.多体系统动力学压缩建模[M].北京:科学出版社,2000.
[47]许本文,焦群英.机械振动与模态分析基础[M].北京:机械工业出版社,1998.
[48]傅志方,华宏星.模态分析理论与应用[M].上海:上海交通大学出版社,2000.
[49]Schiehlen W.Research trends in multibody system dynamics[J].Multibody System Dynamics.2007,18(1):3-13.
[50]Eberhard P,Schiehlen W.Computational Dynamics of Multibody Systems:History, Formalisms, and Applications[J]. Journal of Computational and Nonlinear Dynamics.2006,1:3-12.
[51] Schiehlen W. Computational dynamics: theory and applications of multibody systems[J]. European Journal of Mechanics A/Solids. 2006,25: 566-594.
[52] Schiehlen W, Guse N, Seifried R. Multibody dynamics in computational mechanics and engineering applications[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(41-43): 5509-5522.
[53] Schiehlen W. Multibody System dynamics: Roots and Perspectives[J]. Multibody System Dynamics. 1997,1: 149-188.
[54] Schiehlen W. Computational aspects in multibody system dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 1991,90(1-3): 569-582.
[55] Hemami H. Evolutionary trends in rigid body dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2003,192(5-6): 635-654.
[56] Dwivedy S K, Eberhard P. Dynamic analysis of flexible manipulators, a literature review[J]. Mechanism and Machine Theory. 2006,41(7): 749-777.
[57] Shimizu N, Imanishi E, Sugano N. Multibody dynamics research in Japan[J].Research Bulletin of Iwaki Meisei University. 2003(16): 7-16.
[58] Yoo W S, Kim S S, Park T W, et al. Multibody dynamics research in Korea[J].JSME Int Journal. Ser C. Mech Systems, Mach Elem Manuf. 2003,46(2): 449-458.
[59] Sun Y L. Multibody dynamics formulations based on variational principle[J].Journal of Shanghai University (English Edition). 2003,7(2): 131-137.
[60] Schiehlen W. Computational aspects in multibody system dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 1991,90(1-3): 569-582.
[61] Blajer W, Schiehlen W, Schirm W. Dynamic analysis of constrained multibody systems using inverse kinematics[J]. Mechanism and Machine Theory. 1993, 28(3):397-405.
[62] Dupuis C, Rousselet J. Application of the transfer matrix method to non-conservative systems involving fluid flow in curved pipes[J]. J Mass Spectrom.1985, 37(3): 415-429.
[63] Hu B, Eberhard P, Schiehlen W. Symbolical Impact Analysis for a Falling Conical Rod Against the Rigid Ground[J]. Eur J Clin Pharmacol. 2001,240(1): 41-57.
[64] R A, Schiehlen W. Simulation of modular dynamic systems[J]. Mathematics and Computers in Simulation. 1998,46(5-6): 535-542.
[65] Anh N D, Schiehlen W. A technique for obtaining approximate solutions in Gaussian equivalent linearization[J]. Computer Methods in Applied Mechanics and Engineering. 1999, 168(1-4): 113-119.
[66] Dignath F, Schiehlen W. Control of the vibrations of a tethered satellite system[J]. Journal of Applied Mathematics and Mechanics. 2000, 64(5): 715-722.
[67] Hu B, Eberhard P, Schiehlen W. Symbolical Impact Analysis for a Falling Conical Rod Against the Rigid Ground[J]. Journal of Sound and Vibration. 2001, 240(1):41-57.
[68] Schiehlen W. An energy analysis of the prescribed motion of an oscillator[J].Journal of Applied Mathematics and Mechanics. 2001,65(4): 671-679.
[69] Claus H, Schiehlen W. Symbolic-Numeric Analysis of Flexible Multibody Systems[J]. Mechanics Based Design of Structures and Machines. 2002, 30(1): 1-30.
[70] Schiehlen W, Hu B. Spectral simulation and shock absorber identification[J].International Journal of Non-Linear Mechanics. 2003,38(2): 161-171.
[71] Lakrad F, Schiehlen W. Effects of a low frequency parametric excitation[J]. Chaos,Solitons & Fractals. 2004,22(5): 1149-1164.
[72] Seifried R, Schiehlen W, Eberhard P. Numerical and experimental evaluation of the coefficient of restitution for repeated impacts[J]. International Journal of Impact Engineering. 2005, 32(1-4): 508-524.
[73] Yanzhu L. Screw-matrix method in dynamics of multibody systems[J]. Acta Mechanica Sinica. 1988,39(2): 132-135.
[74] Ding J Y, Pan Z K, Chen L Q. Second order adjoint sensitivity analysis of multibody systems described by differential-algebraic equations[J]. Anal Chem. 2007,18(4): 2453-2461.
[75] Schiehlen W, Seifried R, Eberhard P. Elastoplastic phenomena in multibody impact dynamics[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(50-51): 6874-6890.
[76] Schiehlen W, Guse N, Seifried R. Multibody dynamics in computational mechanics and engineering applications[J]. Computer Methods in Applied Mechanics and Engineering. 2006,195(41-43): 5509-5522.
[77] Ackermann M, Schiehlen W. Design of prosthetic devices by means of musculoskeletal models[J]. Journal of Biomechanics. 2006, 39(Supplement 1): 46-46.
[78] Gontier C, Li Y. Lagrangian formulation and linearization of multibody system equations[J]. Computers & Structures. 1995, 57(2): 317-331.
[79] Bayo E, Ledesma R. Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics[J]. Nonlinear Dynamics. 1996, 9(1):113-130.
[80] Forehand D I, Khanin R, Cartmell M P. A Lagrangian multibody code for deriving the symbolic state-space equations of motion for open-loop systems containing flexible beams[J]. Mathematics and Computers in Simulation. 2004, 67(1-2): 85-98.
[81] Kool P. An analytical expression for the generalized forces in multibody Lagrange equations[J].IEEE Transactions on Robotics.2004,20(2):340-343.
[82]Santini P,Gasbarri P.Dynamics of multibody systems in space environment;Lagrangian vs.Eulerian approach[J].Acta Astronautica.2004,54(1):1-24.
[83]Simeon B.On Lagrange multipliers in flexible multibody dynamics[J].Computer Methods in Applied Mechanics and Engineering.2006,195(50-51):6993-7005.
[84]Duindam V,Stramigioli S.Lagrangian dynamics of open multibody systems with generalized holonomic and nonholonomic joints[C].2007.
[85]Zheng Z,Simeon B,Petzold L.A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems[J].Journal of Computational Physics.2008,227(10):5272-5285.
[86]孙京,邵成勋.用拉格朗日键图建立复杂航天器系统的动力学方程[J].哈尔滨工业大学学报.2000(02).
[87]Mcphee J J,Redmond S M.Modelling multibody systems with indirect coordinates[J].Computer Methods in Applied Mechanics and Engineering.2006,195(50-51):6942-6957.
[88]Huston R L,Yung S L,Chengqun L.Use of absolute coordinates in computational multibody dynamics[J].Computers & Structures.1994,52(1):17-25.
[89]Mcphee J J.A unified graph--Theoretic approach to formulating multibody dynamics equations in absolute or joint coordinates[J].Journal of the Franklin Institute.1997,334(3):431-445.
[90]Gaikwad J L,Dasgupta B,Joshi U.Static equilibrium analysis of compliant mechanical systems using relative coordinates and loop closure equations[J].Mechanism and Machine Theory.2004,39(5):501-517.
[91]de Garc J,Unda J,Avello A.Natural coordinates for the computer analysis of multibody systems[J].Computer Methods in Applied Mechanics and Engineering.1986,56(3):309-327.
[92]Brauchli H,Weber R.Dynamical equations in natural coordinates[J].Computer Methods in Applied Mechanics and Engineering.1991,91(1-3):1403-1414.
[93]Mcphee J J.Automatic generation of motion equations for planar mechanical systems using the new set of "branch coordinates"[J].Mechanism and Machine Theory.1998,33(6):805-823.
[94]陈立群,刘延柱.任意圆轨道上磁性刚体航天器的混沌姿态运动及其控制[J].Drug Metab Dispos.2001,21(04):889-901.
[95]Wittenburg J.Dynamics of Multibody Systems[M].Berlin:Springer-Verlag,2008.
[96]Huston R L,Yung S L,Chengqun L.Use of absolute coordinates in computational multibody dynamics[J].Computers & Structures.1994,52(1):17-25.
[97]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. 2005(05).
[98]洪在地,陈力.漂浮基空间机器人双臂协调操作逆运动学的完全笛卡尔坐标方法[J].机械科学与技术.2003(06).
[99]张成新,余跃庆.基于绝对坐标的柔性机器人逆动力学建模和轨迹跟踪[J].机械科学与技术.2002(01).
[100]戈新生,张涌.完全笛卡尔坐标描述的机械系统动力学分析及软件研究[J].机械科学与技术.2000(01).
[101]戈新生,刘延柱.空间机械手逆问题的完全笛卡尔坐标方法[J].机械科学与技术.1998(03).
[102]戈新生,刘延柱.基于自然坐标的自由浮动空间机械臂动力学分析[J].力学与实践.2001(03).
[103]Lee S H,Park T W,Seo J H,et al.The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation[J].Multibody System Dynamics.
[104]Dmitrochenko O.Finite elements using absolute nodal coordinates for large-deformation flexible multibody dynamics[J].Journal of Computational and Applied Mathematics.2008,215(2):368-377.
[105]Gerstmayr J,Irsehik H.On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach[J].Journal of Sound and Vibration.2008,In Press,Corrected Proof.
[106]Bauehau O A.On the modeling of prismatic joints in flexible multi-body systems[J].Computer Methods in Applied Mechanics and Engineering.2000,181(1):38-42.
[107]罗跃纲,彭永恒,闻邦椿.工程结构损伤的集成神经网络识别研究[J].振动与冲击ZDCJ.2006(01):287.
[108]Ider S K,Amirouche F M.Numerical stability of the constraints near singular positions in the dynamics of multibody systems[J].Computers & Structures.1989,33(1):129-137.
[109]Robe T R,Kane T R.Dynamics of an elastic satellite—I[J].International Journal of Solids and Structures.1967,17(3):333-352.
[110]Jeng Y,Chien-chun C.Automatic generation and numerical integration of differential-algebraic equations of multibody dynamics[J].Computer Methods in Applied Mechanics and Engineering.1993,104(3):317-331.
[111]Fisette P,Vaneghem B.Numerical integration of multibody system dynamic equations using the coordinate partitioning method in an implicit Newmark scheme[J].Computer Methods in Applied Mechanics and Engineering.1996,135(1-2):85-105.
[112] Sudarsan R, Sathiya K S. Numerical approaches for solution of differential equations on manifolds[J]. Applied Mathematics and Computation. 1998, 92(2-3):153-193.
[113] Pogorelov D Y. On numerical methods of modeling large multibody systems[J].Mechanism and Machine Theory. 1999,34(5): 791-800.
[114] Levinson D A, Kane T R. A usable solution of the hanging cable problem[J]. Anal Bioanal Chem. 1993, 378(4): 821-844.
[115] Huston R L, Kamman J W. Testing the accuracy of numerical simulations of multibody systems[J]. Mechanics Research Communications. 2001,28(1): 1-6.
[116] Hamann P, Mehrmann V. Numerical solution of hybrid systems of differential-algebraic equations[J]. Computer Methods in Applied Mechanics and Engineering. 2008,197(6-8): 693-705.
[117] Br O, Golinval J C. On the numerical damping of time integrators for coupled mechatronic systems[J]. Computer Methods in Applied Mechanics and Engineering.2008, 197(6-8): 577-588.
[118] Ohga M, Shigematsu T. Bending analysis of plates with variable thickness by boundary element-transfer matrix method[J]. Chirality. 1988,14(5): 635-640.
[119] Tseng F C, Ma Z D, Hulbert G M. Efficient numerical solution of constrained multibody dynamics systems[J]. Computer Methods in Applied Mechanics and Engineering. 2003,192(3-4): 439-472.
[120] Lim J H, Yim H, Lim S H, et al. A study on numerical solution method for efficient dynamic analysis of constrained multibody systems[J]. Journal of Mechanical Science and Technology. 2008,22(4): 714-721.
[121] Hale A L, Meirovitch L. Derivation of the equations of motion for complex structures by symbolic manipulation[J]. Computers & Structures. 1978,9(6): 639-649.
[122] Lieh J, Haque I. Symbolic Closed-Form Modeling and Linearization of Multibody Systems Subject to Control[J]. Journal of Mechanical Design. 1991,113(2): 124-132.
[123] Ju M S, Hsu C J. Automatic modeling of mechatronic systems via symbolic approach[J]. Mechatronics. 1991,1(2): 157-174.
[124] Charbonneau G, Vinarnick S, N P, et al. Symbolic modelling of controlled mechanisms[J]. Computer Methods in Applied Mechanics and Engineering. 1992,98(1): 23-40.
[125] Cui K, Haque I, Thirumalai M. On configurations of symbolic equations of motion for rigid multibody systems[J]. Mechanism and Machine Theory. 1995, 30(8):1149-1170.
[126] Vibet C. Symbolic modeling of robot kinematics and dynamics[J]. Robotics and Autonomous Systems. 1995, 14(4): 301-314.
[127]Lynch A G,Vanderploeg M J.A Symbolic Formulation for Linearization of Multibody Equations of Motion[J].Journal of Mechanical Design.1995,117(3):441-445.
[128]Kwatny H G,Blankenship G L.Symbolic construction of models for multibody dynamics[J].IEEE Transactions on Robotics and Automation.1995,11(2):271-281.
[129]Villard D,Arnaldi B.Symbolic differentiation library for simulation of multibody rigid systems[J].Mathematics and Computers in Simulation.1996,42(4-6):659-673.
[130]倪纯双,洪嘉振,贺启庸.车辆系统动力学的符号化多体方法[J].中国铁道科学.1996(04).
[131]Tummarakota S R,Lieh J U.Symbolic Finite Element Modeling of Structural Systems[J].Journal of Symbolic Computation.1996,22(1):105-119.
[132]Melzer F.Symbolic computations in flexible multibody systems[J].Nonlinear Dynamics.1996,9(1):147-163.
[133]Fisette P,Johnson D A,Samin J C.A fully symbolic generation of the equations of motion of multibody systems containing flexible beams[J].Computer Methods in Applied Mechanics and Engineering.1997,142(1-2):123-152.
[134]Carpanzano E,Maffezzoni C.Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems[J].Mathematics and Computers in Simulation.1998,48(2):133-150.
[135]Cui K,Haque I.Symbolic equations of motion for hybrid multibody systems using a matrix--vector formulation[J].Mechanism and Machine Theory.1997,32(6):743-763.
[136]Zhou W,Jeffrey D,Reid G.Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical Systems[J].Symbolic-Numeric Computation.2007,2007:335-347.
[137]Soh C W,Mahomed F M.Linearization criteria for a system of second-order ordinary differential equations[J].International Journal of Non-Linear Mechanics.2001,36(4):671-677.
[138]Ramon H,De B J.A modelling procedure for linearized motions of tree structured multibodies--1:Derivation of the equations of motion[J].Computers & Structures.1996,59(2):347-360.
[139]Ramon H,De B J.A modelling procedure for linearized motions of tree structured multibodies--2:Design of an active spray boom suspension on a spraying-machine[J].Computers & Structures.1996,59(2):361-375.
[140]Anthonis J,Hostens I,M M A,et al.A generalized modelling technique for linearized motions of mechanisms with flexible parts[J].Journal of Sound and Vibration.2003,266(3):553-572.
[141] Kang J S, Bae S, Lee J M, et al. Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics[J]. Journal of Mechanical Design. 2003,125: 143-149.
[142] Minaker B, Frise P. Linearizing the Equations of Motion for Multibody Systems Using an Orthogonal Complement Method[J]. Journal of Vibration and Control. 2005,11:51-66.
[143] Roy D, Kumar R. A multi-step transversal linearization (MTL) method in non-linear structural dynamics[J]. Journal of Sound and Vibration. 2005,287(1-2): 203-226.
[144] Ramos J I. Linearization techniques for singularly-perturbed initial-value problems of ordinary differential equations[J]. Applied Mathematics and Computation. 2005,163(3): 1143-1163.
[145] Ramos J I. Linearization techniques for singular initial-value problems of ordinary differential equations[J]. Applied Mathematics and Computation. 2005, 161(2):525-542.
[146] Negrut D, Ortiz J L. A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations[J]. Journal of Computational and Nonlinear Dynamics. 2006, 1(3): 230-239.
[147] Pott A, Kecskemethy A, Hiller M. A simplified force-based method for the linearization and sensitivity analysis of complex manipulation systems[J]. Mechanism and Machine Theory. 2007,42(11): 1445-1461.
[148] Lin T C, Yae K H. Recursive Linearization of Multibody Dynamics and Application to Control Design[J]. Journal of Mechanical Design. 1994, 116(2): 445-451.
[149] Stone T A, Santos J L, Haug E J. An interactive pre-processor for structural design sensitivity analysis and optimization[J]. Computers & Structures. 1990, 34(3):375-385.
[150] Zhang Y, Chen S, Liu Q. The sensitivity of multibody systems with respect to a design variable matrix[J]. Mechanics Research Communications. 1994, 21(3):223-230.
[151] Wasfy T M, Noor A K. Modeling and sensitivity analysis of multibody systems using new solid, shell and beam elements[J]. Computer Methods in Applied Mechanics and Engineering. 1996, 138(1-4): 187-211.
[152] Liu X. Sensitivity analysis of constrained flexible multibody systems with stability considerations[J]. Mechanism and Machine Theory. 1996, 31(7): 859-863.
[153] Schulz M, Brauchli H. Two methods of sensitivity analysis for multibody systems with collisions[J]. Mechanism and Machine Theory. 2000,35(10): 1345-1365.
[154] Sohl G A, Bobrow J E. A Recursive Multibody Dynamics and Sensitivity Algorithm for Branched Kinematic Chains[J]. Journal of Dynamic Systems, Measurement, and Control. 2001,123(3): 391-399.
[155] Van K F, Haftka R T, Kim N H. Review of options for structural design sensitivity analysis. Part 1: Linear systems[J]. Computer Methods in Applied Mechanics and Engineering Structural and Design Optimization. 2005, 194(30-33): 3213-3243.
[156] Maly T, Petzold L R. Numerical methods and software for sensitivity analysis of differential-algebraic systems[J]. Applied Numerical Mathematics. 1996, 20(1-2):57-79.
[157] Li S, Petzold L. Software and algorithms for sensitivity analysis of large-scale differential algebraic systems[J]. Journal of Computational and Applied Mathematics.2000, 125(1-2): 131-146.
[158] Li S, Petzold L, Zhu W. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem[J]. Applied Numerical Mathematics.2000,32(2): 161-174.
[159] Cao Y, Li S, Petzold L. Adjoint sensitivity analysis for differential-algebraic equations: algorithms and software[J]. Journal of Computational and Applied Mathematics. 2002,149(1): 171-191.
[160] Li S, Petzold L. Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement[J]. Journal of Computational Physics. 2004,198(1): 310-325.
[161] Petzold L, Li S, Cao Y, et al. Sensitivity analysis of differential-algebraic equations and partial differential equations[J]. Computers & Chemical Engineering. 2006,30(10-12): 1553-1559.
[162] Anderson K S, Hsu Y. Analytical Fully-Recursive Sensitivity Analysis for Multibody Dynamic Chain Systems[J]. Multibody System Dynamics. 2002, 8: 1-27.
[163] Anderson K S, Hsu Y. Order-(n+m) direct differentiation determination of design sensitivity for constrained multibody dynamic systems[J]. Structural and Multidisciplinary Optimization. 2004,26: 171-182.
[164] Hsu Y, Anderson K S. Recursive sensitivity analysis for constrained multi-rigid-body dynamic systems design optimization[J]. Structural and Multidisciplinary Optimization. 2008,24: 312-324.
[165] Mukherjee R M, Bhalerao K D, Anderson K S. A divide-and-conquer direct differentiation approach for multibody system sensitivity analysis[J]. Structural and Multidisciplinary Optimization. 2008, 35: 413-429.
[166] Ding J Y, Pan Z K, Chen L Q. Second order adjoint sensitivity analysis of multibody systems described by differential-algebraic equations[J]. Multibody System Dynamics. 2007, 18(4): 599-617.
[167]潘振宽,赵维加.多体系统动力学设计灵敏度分析与动态优化设计方法[J].青岛大学学报(工程技术版).2002(04).
[168]余显忠.100nm步进扫描投影光刻机结构动力学建模研究[D].武汉:华中科技大学,2008.
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