导引头伺服机构若干强度与动力学问题研究
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摘要
导引头系统具有实现对目标的捕获、跟踪、瞄准和稳定等功能,在精确制导武器中得到广泛应用。导引头伺服机构用于为光电探测器提供惯性稳定的物理平台,是导引头系统的核心部件之一,其结构性能的优劣直接影响着导引头系统的整体性能。随着超音速末制导导弹对飞行速度、制导精度等要求的提高,导引头伺服机构的工作环境越来越严酷,这就对伺服机构的强度设计和动力学特性设计提出了更新的要求。深入研究伺服机构,特别是轻量化高精度伺服机构的强度计算方法和动力学特性的影响机理显得十分迫切。正是在这种背景下,本文从结构强度和动力学特性两个方面展开研究工作,主要目的是研究复杂动力载荷下结构强度设计的一般准则和高效计算方法,以及研究结构参数对动力学特性的影响规律,以为新型导引头伺服机构的机械和控制的综合优化设计提供理论依据。
围绕导引头结构强度计算和动力学特性分析两个方面,论文所开展的具体研究内容为：
1.在结构强度计算方面,传统设计方法分析过程复杂、求解效率差、计算误差大。为了提高结构强度设计的性能,论文采用并行计算技术,研究了结构强度并行分析的计算方法、软件实现和具体应用问题。
首先基于有限元EBE(Element-By-Element)并行策略提出并实现了确定性载荷下结构响应分析的有限元N-EBE-PCG并行算法,同时结合虚拟激励法,进一步实现了随机载荷下结构响应分析的并行虚拟激励法PPEM(Parallel Pseudo Excitation Method)。结构响应并行算法的研究与实现,有利于提高复杂动力载荷下伺服机构的结构强度分析效率。
采用结构强度并行算法,在网络集群并行环境下,基于MPI(Message Passing Interface)消息传递编程模式自主开发了强度并行分析程序,然后利用参数化设计语言APDL(ANSYS Parameter Design Language)将自主并行分析程序无缝集成到有限元分析软件ANSYS中,从而实现了结构强度的并行计算。
详细分析了导引头伺服机构在服役期间所处的动力载荷环境,利用结构强度并行计算方法,分别分析了冲击、随机振动载荷作用下伺服机构内外框架的结构强度,以及结构设计参数对强度的灵敏度,为框架结构的轻量化设计提供了理论分析和计算依据。研究结果表明,文中实现的结构强度并行分析程序计算精度和效率较高,能够满足复杂工况环境下导引头结构强度计算与优化设计的需要。
2.在动力学特性分析方面,传统的伺服机构动力学研究主要采用理想模型,较少考虑设计公差、制造误差、摩擦磨损等随机因素对系统动力学特性的影响,难以准确描述实际的动力学特性。为此,论文建立了伺服机构的动力学模型,分析了随机因素的影响,并运用基于概率统计的分析方法进行了随机动力学仿真。
首先基于Hamilton力学原理建立了导引头伺服机构的动力学仿真模型,分析了摩擦非线性、框架间的非线性耦合以及能量耗散对动力学特性的影响。在该模型的基础上,结合相关试验结果,较全面地分析了伺服机构中存在的随机因素并且提出了相应的研究方法。
为了准确分析评价随机激励下伺服机构的随机响应特性,研究了拟Hamilton系统的随机平均法,实现了求解随机动力学FPK (Fokker-Planck-Kolmogorov)方程的点插值无网格法。综合运用随机平均法和无网格法,计算得到了随机激励下伺服机构的随机响应并且研究了结构参数对随机响应统计特征的影响,为评价机构的动力学特性提供了理论依据。
针对内部摩擦随机性的问题,基于滚动轴承的基本分析方法,研究了摩擦力矩的产生机理和计算方法。在伺服机构动力学模型的基础上,运用蒙特卡罗方法进行随机模拟试验,分析了结构参数的随机性对动力学特性的影响,为进一步研究伺服机构的动力行为演变规律打下了基础。
论文所研究的结构强度并行分析方法和非线性随机动力学仿真技术,为开展伺服机构的结构与控制的综合优化设计提供理论分析和计算依据。
Seeker system, which can possess some functions such as capture, tracking, aiming and stabilization, is applied to the precision guided weapon widely. As an important part of seeker system, seeker servo mechanism can provide inertia stabilized platform for photoelectric detector, and its structural performance has a direct effect on the performance of seeker system. With the improvement of the flight speed and guidance precision of the final guidance supersonic missile, operating condition in missile is worse and worse, and the newer demands is put forward for the strength design and the dynamics analysis of servo mechanism. So it is very urgent that the strength design methods and the influence mechanism of dynamics of the high precision lightweighting servo mechanism are researched in depth. Under this circumstance, this dissertation suggests two research aspects included strength and dynamics, namely study on the guide lines and the high performance calculation methods of strength design when complicated dynamic load and study on the influence of structural parameters on dynamics. These studies can provide the foundations for the optimum design of the structure and control of the new-style seeker servo mechanism.
The detailed contents and innovative work are organized as follows:
1. In the structural strength respect, the traditional design methods are complex and low performance. In order to improve the performance of the strength design, computing methods, software realization and technical application problems are researched with parallel computing.
Firstly, on the basis of finite element EBE parallel policy, finite element N-EBE-PCG parallel algorithm is presented and realized to calculate the structural response when deterministic load. Ulteriorly, combining N-EBE-PCG algorithm with pseudo excitation method, parallel pseudo excitation method is presented to calculate the structural response when stochastic load. The research and realization of the strength parallel algorithms is of advantage to improve the efficiency of the structural strength analysis when complicated dynamic load.
Under the cluster of workstation (COW) environment, the strength parallel algorithms are applied to develop the strength parallel computing home-code based on the parallel programming mode of Message Passing Interface (MPI). In order to make these parallel algorithms take the form of software, the strength parallel computing home-code is integrated into ANSYS software seamlessly with the use of ANSYS Parameter Design Language (APDL).
The dynamic environments which seeker servo mechanism suffers in its enlistment are analyzed systematically. And then, the strength parallel computing program is applied to calculate the mechanical strength of the inner and outer framework of a typical servo mechanism respectively under the shock and random vibration environments. Also, the strength sensitivity of structural design parameters is analyzed. It shows by simulation that the strength parallel computing program proposed has a high calculation precision and efficiency, and is applicable for the structural strength optimum design of the seeker servo mechanism under the complicated dynamic environments.
2. In the dynamics respect, the traditional research of servo dynamics uses the ideal model and seldom allows for the random factors such as design tolerance, mismatchining tolerance and wear. So it can not describe the actual dynamics correctly. Therefor, the dynamic models with random factors which can describe the influence mechanism of dynamics better are researched based on the stochastic analysis methods.
Firstly, the dynamic simulation model of the seeker servo mechanism is established based on the Hamilton mechanics principles and the influences of friction, nonlinear coupling and energy dissipation on the servo dynamic characteristics are analyzed. On the basis of the dynamic model, the random factors which affect the driving moment and inner friction of the servo mechanism are illuminated in full length according to the correlative experimental results, and the processing methods for these random factors are proposed.
In order to analyze and evaluate the random response characteristic of the servo mechanism affected by the random excitation, the stochastic averaging methods of quasi Hamiltonian systems are investigated, and the points interpolation meshless (PIM) methods are studied to solve the FPK (Fokker-Planck-Kolmogorov) equations of stochastic dynamics. Following that, the random response of the servo mechanism is solved by the stochastic averaging methods and the the PIM methods. And then, the influence of the structural parameters on the stochastic response characteristic is studied. This work can provide theory foundations for evulating the dynamics of the mechanism.
Aiming at the problem of the random friction, the mechanism and the calculation methods of the friction torque are studied systematically based on the basic theory of rolling bearing. Using these methods, the influence of the structural parameters on the dynamics is investigated in the Monte Carlo simulation test. This work makes preparations for the farther study on the evolvement rules of the servo dynamics.
In a word, the parallel analysis technique of structural strength and the simulation method of nonlinear stochastic dynamics which are studied in this dissertation can be applicable for the optimum design of the servo structure and control.
围绕导引头结构强度计算和动力学特性分析两个方面,论文所开展的具体研究内容为：
1.在结构强度计算方面,传统设计方法分析过程复杂、求解效率差、计算误差大。为了提高结构强度设计的性能,论文采用并行计算技术,研究了结构强度并行分析的计算方法、软件实现和具体应用问题。
首先基于有限元EBE(Element-By-Element)并行策略提出并实现了确定性载荷下结构响应分析的有限元N-EBE-PCG并行算法,同时结合虚拟激励法,进一步实现了随机载荷下结构响应分析的并行虚拟激励法PPEM(Parallel Pseudo Excitation Method)。结构响应并行算法的研究与实现,有利于提高复杂动力载荷下伺服机构的结构强度分析效率。
采用结构强度并行算法,在网络集群并行环境下,基于MPI(Message Passing Interface)消息传递编程模式自主开发了强度并行分析程序,然后利用参数化设计语言APDL(ANSYS Parameter Design Language)将自主并行分析程序无缝集成到有限元分析软件ANSYS中,从而实现了结构强度的并行计算。
详细分析了导引头伺服机构在服役期间所处的动力载荷环境,利用结构强度并行计算方法,分别分析了冲击、随机振动载荷作用下伺服机构内外框架的结构强度,以及结构设计参数对强度的灵敏度,为框架结构的轻量化设计提供了理论分析和计算依据。研究结果表明,文中实现的结构强度并行分析程序计算精度和效率较高,能够满足复杂工况环境下导引头结构强度计算与优化设计的需要。
2.在动力学特性分析方面,传统的伺服机构动力学研究主要采用理想模型,较少考虑设计公差、制造误差、摩擦磨损等随机因素对系统动力学特性的影响,难以准确描述实际的动力学特性。为此,论文建立了伺服机构的动力学模型,分析了随机因素的影响,并运用基于概率统计的分析方法进行了随机动力学仿真。
首先基于Hamilton力学原理建立了导引头伺服机构的动力学仿真模型,分析了摩擦非线性、框架间的非线性耦合以及能量耗散对动力学特性的影响。在该模型的基础上,结合相关试验结果,较全面地分析了伺服机构中存在的随机因素并且提出了相应的研究方法。
为了准确分析评价随机激励下伺服机构的随机响应特性,研究了拟Hamilton系统的随机平均法,实现了求解随机动力学FPK (Fokker-Planck-Kolmogorov)方程的点插值无网格法。综合运用随机平均法和无网格法,计算得到了随机激励下伺服机构的随机响应并且研究了结构参数对随机响应统计特征的影响,为评价机构的动力学特性提供了理论依据。
针对内部摩擦随机性的问题,基于滚动轴承的基本分析方法,研究了摩擦力矩的产生机理和计算方法。在伺服机构动力学模型的基础上,运用蒙特卡罗方法进行随机模拟试验,分析了结构参数的随机性对动力学特性的影响,为进一步研究伺服机构的动力行为演变规律打下了基础。
论文所研究的结构强度并行分析方法和非线性随机动力学仿真技术,为开展伺服机构的结构与控制的综合优化设计提供理论分析和计算依据。
Seeker system, which can possess some functions such as capture, tracking, aiming and stabilization, is applied to the precision guided weapon widely. As an important part of seeker system, seeker servo mechanism can provide inertia stabilized platform for photoelectric detector, and its structural performance has a direct effect on the performance of seeker system. With the improvement of the flight speed and guidance precision of the final guidance supersonic missile, operating condition in missile is worse and worse, and the newer demands is put forward for the strength design and the dynamics analysis of servo mechanism. So it is very urgent that the strength design methods and the influence mechanism of dynamics of the high precision lightweighting servo mechanism are researched in depth. Under this circumstance, this dissertation suggests two research aspects included strength and dynamics, namely study on the guide lines and the high performance calculation methods of strength design when complicated dynamic load and study on the influence of structural parameters on dynamics. These studies can provide the foundations for the optimum design of the structure and control of the new-style seeker servo mechanism.
The detailed contents and innovative work are organized as follows:
1. In the structural strength respect, the traditional design methods are complex and low performance. In order to improve the performance of the strength design, computing methods, software realization and technical application problems are researched with parallel computing.
Firstly, on the basis of finite element EBE parallel policy, finite element N-EBE-PCG parallel algorithm is presented and realized to calculate the structural response when deterministic load. Ulteriorly, combining N-EBE-PCG algorithm with pseudo excitation method, parallel pseudo excitation method is presented to calculate the structural response when stochastic load. The research and realization of the strength parallel algorithms is of advantage to improve the efficiency of the structural strength analysis when complicated dynamic load.
Under the cluster of workstation (COW) environment, the strength parallel algorithms are applied to develop the strength parallel computing home-code based on the parallel programming mode of Message Passing Interface (MPI). In order to make these parallel algorithms take the form of software, the strength parallel computing home-code is integrated into ANSYS software seamlessly with the use of ANSYS Parameter Design Language (APDL).
The dynamic environments which seeker servo mechanism suffers in its enlistment are analyzed systematically. And then, the strength parallel computing program is applied to calculate the mechanical strength of the inner and outer framework of a typical servo mechanism respectively under the shock and random vibration environments. Also, the strength sensitivity of structural design parameters is analyzed. It shows by simulation that the strength parallel computing program proposed has a high calculation precision and efficiency, and is applicable for the structural strength optimum design of the seeker servo mechanism under the complicated dynamic environments.
2. In the dynamics respect, the traditional research of servo dynamics uses the ideal model and seldom allows for the random factors such as design tolerance, mismatchining tolerance and wear. So it can not describe the actual dynamics correctly. Therefor, the dynamic models with random factors which can describe the influence mechanism of dynamics better are researched based on the stochastic analysis methods.
Firstly, the dynamic simulation model of the seeker servo mechanism is established based on the Hamilton mechanics principles and the influences of friction, nonlinear coupling and energy dissipation on the servo dynamic characteristics are analyzed. On the basis of the dynamic model, the random factors which affect the driving moment and inner friction of the servo mechanism are illuminated in full length according to the correlative experimental results, and the processing methods for these random factors are proposed.
In order to analyze and evaluate the random response characteristic of the servo mechanism affected by the random excitation, the stochastic averaging methods of quasi Hamiltonian systems are investigated, and the points interpolation meshless (PIM) methods are studied to solve the FPK (Fokker-Planck-Kolmogorov) equations of stochastic dynamics. Following that, the random response of the servo mechanism is solved by the stochastic averaging methods and the the PIM methods. And then, the influence of the structural parameters on the stochastic response characteristic is studied. This work can provide theory foundations for evulating the dynamics of the mechanism.
Aiming at the problem of the random friction, the mechanism and the calculation methods of the friction torque are studied systematically based on the basic theory of rolling bearing. Using these methods, the influence of the structural parameters on the dynamics is investigated in the Monte Carlo simulation test. This work makes preparations for the farther study on the evolvement rules of the servo dynamics.
In a word, the parallel analysis technique of structural strength and the simulation method of nonlinear stochastic dynamics which are studied in this dissertation can be applicable for the optimum design of the servo structure and control.
引文
[1]Masten, Michael K., and Henry. R. Line of sight stabilization/tracking systems: an overview. Proceeding of the American Control Conference.1987:1477～1482
[2]郭富强,于波,王叔华.陀螺稳定装置与应用.西安：西北工业大学出版社,1995
[3]李保平.战术导弹导引头技术,弹箭与制导学报,2005,22(1)：1～5
[4]Wander K., and Korcher H. J. The pointing control system of SOFIA. SPIE, 2000,4014:360～369
[5]范大鹏. 《光电稳定伺服机构控制技术》专题文章导读,光学精密工程,2006,14(4)：673
[6]张智永.光电稳定伺服机构的关键测控问题研究：博士学位论文.长沙：国防科学技术大学,2006
[7]Ruffatto D., Brown D., and Pohle R. Stablizied high-accuracy optical tracking system(shots). SPIE,2001,4365:10～18
[8]范斌.机载光电探测系统稳定平台CAD技术研究及软件开发：硕士学位论文.北京：北京航空航天大学,2000
[9]李颖晖,郭阳宽,王勇等.伺服转台机械结构方案设计探讨.机械研究与应用,2005,18(6)：88～89
[10]柳朝军.捷联式三轴稳定跟踪台的建模及动态模糊神经网络控制研究：博士学位论文.北京：北京理工大学,2000
[11]邱吉宝,谭志勇,王建民.运载火箭结构动力学分析的一些新技术,第一部分：模态综合技术.导弹与航天运载技术,2001,(2)：29～34
[12]邱吉宝,谭志勇,王建民.运载火箭结构动力学分析的一些新技术,第二部分：运载火箭结构动力学分析.导弹与航天运载技术,2001,(4)：16～21
[13]Qiu J. B., and Wang J. M. Dynamic analysis of strap-on launch vehicle. In:Proc of Asian-Pacific Conference on Aerospace Technology and Science. Beijing International Academic Publishers. Hangzhou,1994-10-10-13,1994,387～391
[14]杨朋军,王卿,王佳民.惯性平台台体结构实验模态参数识别及灵敏度分析.中国惯性技术学报,2004,12(4)：7～11
[15]杨朋军,王卿,王佳民.惯性平台台体结构的实验模态分析.导航与控制,2004,3(2)：3-8
[16]王卿,王佳民,杨朋军.惯性平台框架类结构件的试验模态分析.宇航学报,2005,26(6)：753～757
[17]张小安,张艳.天线座结构的试验模态与理论模态的分析比较.电子机械工程,2005,21(1)：37～40
[18]王跃钢,彭云辉.过载—振动复合环境下液浮陀螺仪动力学分析.中国惯性技术学报,2003,11(6)：80～83
[19]杨朋军,靳长权,王佳民.基于UG/CAE环境下的惯性平台台体有限元分析.导航与控制,2003,2(4)：37～40
[20]聂旭涛,范大鹏.基于COSMOSWorks的三轴稳定平台框架的优化设计.机电工程技术,2005,(1)：74～76
[21]程畅,吕勇.MSC/PATRAN、 DYTRAN软件在机电产品结构件抗冲击强度仿真分析中的应用.机电元件,2002,22(3)：15～17
[22]Blakly K. MSC/NASTRAN dynamic analysis user's guide. Los Angeles:The MacNeal-Schwendler Corporation,1993
[23]Keith B. Doyle, Vincent J. Cerrati, and Steven E. Forman, etc. Optimal structural design of the Airborne Infrared imager. SPIE,1993,2542:11～22
[24]汪元贵,雷勇军.飞行过程中惯导系统的随机振动响应分析.湖南理工大学学报,2004,17(3)：39～41
[25]Lin J. H. A fast CQC algorithm of PSD matrices for random seismic responses. Computers and Structures,1992,44(3):683～687
[26]Einstein A. Investigation on the theory of Brownian movement. English Translations of Einstein Papers, Dover Publications,1956
[27]Rice S. O. Mathematical analysis of random noise. Bell Sys. Tech. J.,1944, 23::282～332
[28]Cooley J. W., and Tukey J. W. An algorithm for the machine calculation of complex Fourier series. Math. Comp.,1965,19:297～301
[29]梅玉林.结构随机振动响应分析理论与算法研究：硕士学位论文.大连：大连理工大学,2000
[30]Shaw D. E. Seismic structural response analysis for multiple support excitation. Proc.3rd Int. SMIRT Conf., London,1975
[31]Vashi K. M. Seismic spectral analysis structural systems subjected to nonuniform excitation at supports. Proc.2nd ASME Spec. Conf., New Orleans,1975
[32]Smeby W., and Kiureghian A. D. Modal combination rules for multi-component earthquake excitation. Earthquake Engineering and Structural Dynamics,1985, 13(1):1～12
[33]Menun C., and Kiureghian A. D. A replacement for the 30%,40% and SRSS rules for multicomponent seismic analysis. Earthquake Spectra,1998, 14(1):153～163
[34]Berrah M., and Kausel E. Response spectrum analysis of structures subjected to spatially varying motions. Earthquake Engineering and Structural Dynamics, 1992,21(1):461～470
[35]孙焕纯,章元崧,张晓志.在双向地震波同时作用下空间框架剪扭弹塑性地震波反应分析.大连工学院学报,1982,21(4)：215～220
[36]胡松,王肇民.洛阳电视塔的结构抗震分析.建筑结构,2000,30(1)：57～59
[37]刘季,王前信.多维与多支座地震输入及结构扭转反应.中国工程抗震研究四十年.北京：地震出版社,1989
[38]王光远.建筑结构的振动.北京：科学出版社,1978
[39]Krenk S., Madsen H. O., and Madsen P. H. Stationary and transient response envelopes. J. Engineering Mechanics, ASCE,1983,109:263～278
[40]Gasparini D. A. Response of MDOF systems to nonstationary random excitation. J. Engineering Mechanics, ASCE,1979,105(EM1):13～28
[41]Zerva A. Lifeline response to spatially variable ground motions. Earthquake Engineering and Structural Dynamics,1988,16(3):361～379
[42]Harichandran R. S., and Vanmarcke E. H. Stochastic variation of earthquake ground motion in space and time. J. Engineering Mechanics, ASCE,1986, 112(2):154～175
[43]Ernesto H. Z., and Vanmarcke E. H. Seismic random vibration analysis of multisupport structural systems. J. Engineering Mechanics, ASCE,1994, 120(5):1107～1128
[44]Masri S. F. Response of a multi-degree-of-freedom system to nonstationary random excitation. J. of Applied Mechanics, ASME,1978,45(3):649-656
[45]王敏,王小静.弹载天线随机振动的仿真分析.制导与引信,2007,28(2)：57-60
[46]于旭东,龙兴武,汤建勋.机抖激光陀螺动力学分析及优化设计.中国惯性技术学报,2007,15(2)：241～244
[47]Lin Y. K. Probability theory of structural dynamics. New York:McGraw-Hill, 1967
[48]Crandall S. H., and Mark W. D. Random vibration in mechanical system. New York:Academic Press,1963
[49]Newland D. E. An introduction to random vibration and spectral analysis. London:Longman,1975
[50]Nigam N. C. Introduction to random vibrations. Cambridge:The MIT Press,
1983
[51]李国豪.工程结构抗震动力学.上海：上海科学技术出版社,1980
[52]Lin J. H., Zhang W. S., and Li J. J. Structural responses to arbitrarily coherent stationary random excitations. Computers and Structures,1994,50:629～633
[53]Lin J. H., Zhang W. S., and Williams F. W. Pseudo-Excitation algorithm for non-stationary random seismic responses. Engineering Structures,1994, 16:270～276
[54]Lin J. H., Wang W. X., and Williams F. W. Asynchronous parallel computing of structural non-stationary random seismic responses. International Journal of Numerical Method in Engineering,1997,40:2133～2148
[55]Lin J. H., Zhong W. X., and Zhang W. S., etc. High efficiency computation of the variances of structural evolutionary random responses. Shock and Vibration,2000,7(4):209～216
[56]Lin J. H., Zhao Y., and Zhang Y. H. Accurate and Highly efficient algorithms for structural stationary/non-stationary random responses. Computer Method in Applied Mechanics and Engineering,2001,191:103～111
[57]Noor A., and Fulton R. E. Impact of the CDC-STAR-100 Computer on Finite Element Systems. Journal of the Structural Division, ASCE,1975,101:731～750
[58]Geist G. A., and Romine C. H. LU factorization on distributed-memory multiprocessors. Proceedings of the 3rd SIAM Conference on Parallel Processing for Scientific Computing, CA. USA,1987,15～18
[59]Jiangning Qin, and Nguyen D. T. A parallel-vector equation solver for distributed-memory computers. Computing Systems in Engineering,1994,5(1): 19～25
[60]Lin A., and Zhang H. A new parallel algorithm for linear triangular systems. Proceedings of the 3rd SIAM Conference on Parallel Processing for Scientific Computing, CA. USA,1987,36～39
[61]Farhat C., and Wilson E. A parallel active column equation solver. Computers and Structures,1988,28(2):289～304
[62]Goehlich D., Komzsik L., and Fulton R. E. Application of a parallel equation solver to static FEM problems. Computers and Structures,1989,31(2):121～129
[63]迟学斌.Transputer上 Cholesky分解的并行实现.计算数学,1993,(3)：289～294
[64]张健飞,姜弘道.对称正定矩阵的并行LDLT分解算法实现.计算机工程与设计,2003,24(10)：75～77
[65]孙家昶等.网络并行计算与分布式编程环境.北京：科学出版社,1997
[66]Mandel J. Balancing domain decomposition. Communications in Numerical Method in Engineering,1993,9:233～241
[67]Levit I. Element by element solvers of order N. Computers and Structures,1987, 27(1):357～360
[68]Pattrick M. P., Prat T. W. Communication oriented programming of parallel iterative solutions for sparse linear systems. Communications in Applied Numerical Method,1986,2:255～261
[69]Akiko H., Robert J., and Utku Senol. Variation in efficiency of parallel algorithm. Computers and Structures,1985,21(5):1025～1034
[70]胡宁,张汝清.一种迭代格式的有限元并行算法.应用数学和力学,1992,13(4)：287～295
[71]邓绍忠,周树荃.不规则结构分析有限元方程组的并行迭代算法及其实现.全国第三届并行算法学术会议文集.武汉：华中理工大学出版社,1992：116～120
[72]迟利华,刘杰,李晓梅.稀疏近似条件子及其并行计算.计算机学报,2000,23(3)：255～260
[73]Noor A., Kamel H., and Fulton R. E. Substructuring techniques-status and projections. Computers and Structures,1977,8:621～632
[74]Escaig Y., Touzot G., and Vayssad M. Parallelization of a multilevel domain decomposition method. Computing Systems in Engineering,1994,5(3):253～263
[75]Dracopoulos M. C., and Crisfield M. A. A partially sequential preconditional for a parallel and efficient finite element solution. Computing Systems in Engineering,1995,6(6):549～561
[76]Law K. H. A parallel finite element solution method. Computers and Structures, 1986,23(6):845～858
[77]王健一,张卫等.有限元问题的并行求解.哈尔滨工业大学学报,1994,26(2)：37～40
[78]李强,邹经湘.独立子结构并行计算方法.哈尔滨工业大学学报,1996,28(2)：144～148
[79]Hughes T. J. R., Levit I., and Winget J. Element by element implicit algorithm for heat conduction. Journal of Engineering Mechanics Division, ASCE,1983, 109:576～585
[80]Hughes T. J. R., Levit I., and Winget J. An element by element solution algorithm for problems of structural and solid mechanics. Computer Methods in Applied Mechanics and Engineering,1983,36:241～254
[81]Barragy E., and Carey G. F. A parallel element-by-element solution scheme. International Journal for Numerical Method in Engineering,1988, 26:2367～2382
[82]Khan A. I., and Topping B. H. V. Parallel finite element analysis using Jacobi-conditioned conjugate gradient algorithm. Advances in Engineering Software,1996,25:309～319
[83]Gullerud Arne S., and Dodds Jr Robert H. MPI-based implementation of a PCG solver using an EBE architecture and precondition for implicit,3-D finite element analysis. Computers and Structures,2001,79:553～575
[84]周树荃,梁维泰,邓绍忠.有限元结构分析并行计算.北京：科学出版社,1999
[85]刘耀儒,周维垣,杨强.有限元并行EBE方法及应用.岩石力学与工程学报,2005,24(17)：3023～3028
[86]厉天威,阮江军,张宇等.基于区域分解法的电磁场并行计算研究.高电压技术,2007,33(5)：58～61
[87]陈荣征,李代平,何驰等.并行PCG算法在电法勘探中的应用研究.微计算机信息,2007,23(3)：254～256
[88]亓文果,金先龙,张晓云等.汽车碰撞有限元仿真的并行计算及其性能研究.系统仿真学报,2004,16(11)：2428～2431
[89]谢晖,钟志华,李光耀等.板料冲压数值模拟的并行计算与应用.中国机械工程,2003,14(21)：1842～1844
[90]李丽君,金先龙.空间多点地震动模拟的并行计算方法及软件.系统仿真学报,2003,17(5)：1068～1071
[91]Bhaskar Dasgupta, Prasun Choudhury. A general strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators. Mechanism and Machine Theory,1999,34(6):801～824
[92]Bayo E., Dejalon J. G., and Serna M. A. A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems. Computer Methods in Applied Mechanics and Engineering,1988,71:183～195
[93]周瑞青,吕善伟,刘新华.捷联式天线稳定平台动力学建模与仿真分析.北京航空航天大学学报,2005,31(9)：953～957
[94]黄一,卢广山,陈宗基.三自由度机载光电跟瞄平台建模与校核.系统仿真学报,2004,16(9)：1948～1952
[95]刘延柱.多刚体系统动力学.北京：高等教育出版社,1986
[96]王济民.双轴陀螺稳定机构动力学建模与仿真.西北大学学报(自然科学版),2005,35(2)：167～169
[97]梅晓榕,陈明,张卯瑞.三轴仿真转台的建模与仿真.系统仿真学报,2001,13(3)：278～279
[98]Guo Kang Er. Multi-gaussian closure method for randomly excited non-linear systems. International Journal of Non-Linear Mechanics,1998,33(2):201～214
[99]Tomasiello S. An application of neural networks to a non-linear dynamics problem. Journal of Sound and Vibration,2004,272:461-467
[100]Lai Ah Wong, and Jay Chung Chen. Nonlinear and chaotic behavior of structural system investigated by wavelet transform techniques. International Journal of Non-Linear Mechanics,2001,36:221～235
[101]Sheng M. P. Statistical energy analysis for complicated coupled system and its application in engineering. Journal of Sound and Vibration,2004,274:877～891
[102]戎海武,王向东,孟光等.简谐与随机噪声联合激励下Van der Pol-Duffing系统的响应.振动工程学报,2003,16(4)：502～505
[103]Caughey T. K., and Dienes J. K. Analysis of a non-linear first-order system with a white noise input. Journal of Applied Physics,1961,23:2476～2479
[104]Kramer H. A. Brownian motion in a field of force and diffusion of chemical reactions. Physics,1940,7:284～304
[105]Caughey T. K., and Ma F. The exact steady-state solution of a class of nonlinear stochastic systems. International Journal of Non-Linear Mechanics,1983, 17:137-142
[106]Cai G. Q., and Lin Y. K. A new approximate solution technique for randomly excited non-linear oscillators. International Journal of Non-Linear Mechanics, 1988a,23(5/6):409～420
[107]Bhandari R. G., and Sherrer R. E. Random vibration in discrete non-linear dynamics systems. Journal of Mechanical Engineering Science,1968, 10:168～174
[108]Wen Y. K. Approximate method for non-linear random vibration. Proceedings of the ASCE Journal of the Engineering Mechanics Division,1975,101:389-401
[109]Langley R. S. A finite element method for the statistics of non-linear random vibration. Journal of Sound and Vibration,1985,101:41～54
[110]Roberts J. B. First-passage time for randomly excited non-linear oscillators. Journal of Sound and Vibration,1986,109:33～50
[111]Toland R. H., Yang C. Y., and Hsu C. K. C. Non-stationary random vibration of non-linear structures. International Journal of Non-Linear Mechanics,1972, 7:395～406
[112]Roberts J. B. Transient response of non-linear systems to random excitation. Journal of Sound and Vibration,1981,74:11～29
[113]Yu J. S., Cai G. Q., and Lin Y. K. A new path integration procedure based on Gauss-Legendre scheme. International Journal of Non-Linear Mechanics, 1997,32:759～768
[114]Naess A. N., and Johnsen J. M. Response statistics of nonlinear compliant structures by the path integration solution method. Probabilistic Engineering Mechanics,1997,12:257～260
[115]Booton R. C. The analysis of nonlinear control systems with random inputs. IRE Trans. Circuit Theory,1954,1:32～34
[116]Iwan W. D., and Yang I. Application of statistical linearization technique to nonlinear multi-degree-of-freedom systems. Journal of Applied Mechanics, 1972,39:545～550
[117]Lutes L. D. Approximate technique for treating random vibration of hysteretic systems. Journal of Acoust. Soc. Am.,1970,48:299～306
[118]Cai G. Q., Lin Y. K., and Elishakoff I. A new approximate solution technique for randomly excited non-linear oscillators 2. International Journal of Non-Linear Mechanics,1992,27(6):969～979
[119]Spanos P. D., and Donley M. G. Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization. International Journal of Non-Linear Mechanics,1992,27(5):735-748
[120]Stratonovitch R. L., Topics in the theory of random noise. Godon and Breach, 1963,1; 1967,2
[121]Khasminskii R. Z. A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probabilistic Application.,1966,11:390～405
[122]Roberts J. B. Stationary response of oscillators with non-linear damping to random excitation. Journal of Sound and Vibration,1977,50:145～156
[123]Spanos P. D. Stochastic analysis of oscillators with non-linear damping. International Journal of Non-Linear Mechanics,1978,13:249～259
[124]Roberts J. B. The energy envelope of a randomly excited nonlinear oscillator. Journal of Sound and Vibration,1978,60:177～185
[125]朱位秋.随机振动.北京：科学出版社,1998
[126]Zhu W. Q., Lin Y. K. Stochastic averaging of energy envelope. Journal of Engineering Mechanics, ASCE,1991,117(8):1890-1905
[127]Zhu W. Q. Stochastic averaging of Quasi-Hamiltonian systems. Science in China, Series A,1996,39(1):97～108
[128]Zhu W. Q. Recent developments and applications of stochastic averaging method in random vibration. Applied Mechanics Reviews, ASME,1996, Part 2,49(10): S72-S80
[129]Zhu W. Q., and Yang Y. Q. Stochastic averaging of Quasi-Nonintegrable-Hamiltonian systems.Journal of Applied Mechanics,ASME,1997, 39(1):157～164
[130]Zhu W. Q., Huang Z. L., and Yang Y. Q. Stochastic averaging of Quasi-Integrable-Hamiltonian systems. Journal of Applied Mechanics, ASME,1997, 64(4):975-984
[131]朱位秋,黄志龙,应祖光.非线性随机动力学与控制的哈密顿理论框架.力学与实践,2002,24(3)：1-9
[132]王勖成,邵敏.有限单元法基本原理和数值方法.北京：清华大学出版社,1997
[133]钟志荣.EBE-CG并行算法研究：硕士学位论文.广东：广东工业大学,2004
[134]张少波,胡明宝,张鹏.预处理共轭梯度法在VVP三维风场反演中的应用.气象科学,2004,24(3)：303～308
[135]周硕,郭丽杰,吴柏生.Jacobi迭代预处理中的条件数与迭代次数的关系.东北电力学院学报,2003,23(6)：57～60
[136]Khan A. I., Topping B. H. Parallel finite element analysis using Jacobi conditioned conjugate gradient algorithm. Adv. Engrg. Soft,1996,25:309～319
[137]David Kincaid, Ward Cheney.数值分析(原书第3版).北京：机械工业出版社,2005
[138]Hughes T. J. R., and Ferencz R. M. Large-scale vectorized implicit calculation in solid mechanics on a CRAY X-MP/48 utilizing EBE-PCG. Computer Methods in Applied Mechanics and Engineering,1987,61:215～248
[139]杨忠超.基于EBE策略的列车三维紊态外流场有限元法并行计算研究：博士学位论文.成都：西南交通大学,2002
[140]宫玉才,周洪伟,陈璞等.快速子空间迭代法、迭代Ritz向量法与迭代Lanczos法的比较,振动工程学报,2005,18(2)：227～232
[141]Subbaraj K., and Dokainish M. A. A survey of direct time integration methods in computational structural dynamics, Ⅰ Explicit methods, Ⅱ Implicit methods. Computers and Structures,1989,32(6):1371～1386,1387～1401
[142]Flynn, Michael J. Very high-speed computing systems. Proceedings of the IEEE,1966,54(12):1901～1909
[143]Flynn, Michael J., and Kevin W. Rudd. Parallel architectures. ACM Computing Surveys,1996,28(1):60～70
[144]王启平,王璐,伍毅等.结构高性能计算中的并行有限元方法.安徽工业大学学报,2005,22(2)：135～138
[145]Hipper G., and Tavangarian D. Advance workstation cluster architectures for parallel computing. Journal of Systems Architecture,1988,44:207～226
[146]张友良.岩土大规模高性能并行有限元系统研究：博士学位论文.北京：中国科学院研究生院,2003
[147]李海江.基于MPI的并行有限元计算集群的构建,数值计算与计算机应用,2004,(3)：198～209
[148]Ivan Lirkov. MPI solver for 3D elasticity problems. Mathematics and Computers in Simulation,2003,61:509～516
[149]Eppstein M. J., Dougherty D. E. A comparative study of PVM workstation cluster implementations of a two-phase subsurface flow model. International Journal of Rock Mechanics and Mining Sciences and Geomechanics,1995,32 A: 208-209
[150]任波.基于集群的接触／碰撞有限元法并行策略：博士学位论文.武汉：华中科技大学,2003
[151]Gropp, Lusk, and Skjellum. Using MPI:portable parallel programming with the Message-Passing-Interface, MIT. Press,1999
[152]龚曙光,谢桂兰.ANSYS操作命令与参数化编程.北京：机械工业出版社,2004
[153]向宇,黄玉盈,曾革委.精细时程积分法的误差分析与精度设计,计算力学学报,2002,19(3)：276～280
[154]张森文,曹开彬,陈奎孚.精细积分时域平均法和随机扩阶系统法,力学学报,2000,32(2)：191～197
[155]钟万勰.结构动力方程的精细时程积分法,大连理工学报,1994,34(2)：131～136
[156]Michael J. Quinn. MPI与OpenMP并行程序设计.北京：清华大学出版社,2004
[157]李丽君,金先龙,李渊印等.一种新型并行化有限元结构模态分析集成系统,计算力学学报.2004,21(5)：546～550
[158]朱美娴.防空导弹武器系统可靠性工程设计.北京：宇航出版社,1994
[159]张艳敏.复杂结构的冲击动力学分析与仿真：硕士学位论文.西安：西北工业大学,2005
[160]郭强岭,李立名.空空导弹挂飞振动试验条件探讨,航空兵器.2003,(6)：21～23
[161]Rajakumar C., and Rogers C. R., The Lanczos algorithm applied to unsymmetric generalized eigenvalue problems. International Journal for Numercial Method in Engineering.1991,32:1009～1026
[162]Wilson E. L., and Itoh Tetsuji. An eigensolution strategy for large systems. Computers and Structures.1983,16(1-4):259～265
[163]刘士华,赵德胜,谭天水等.ANSYS在钢架结构随机振动分析中的应用,机械,2004,31(4)：54～55
[164]Cooper C.J., and Hamilton. Sensor line-of-sight stabilization. SPIE,1991, 1498:34～46
[165]张爱梅.目标跟踪瞄准系统的虚拟现实研究：硕士学位论文.西安：西安电子科技大学,2004
[166]曾鸣,王忠山,王学智.基于非线性摩擦模型参数观测器的自适应摩擦补偿方法的研究,航空精密制造技术,2005,41(3)：17～22
[167]Dowson D. History of Tribology, London:Longman Ltd,1996
[168]付士慧,王琪,王士敏.带干摩擦的非光滑动力系统Lyapunov指数的数值计算,动力学与控制学报,2006,4(3)：210～216
[169]Stefanski A. Estimation of the largest Lyapunov exponent in systems with impacts. Chaos, Solitons & Fractals.2000,11:2443～2451
[170]Lamarque C. H., and Bastien J. Numerical study of a forced pendulum with friction. Nonlinear Dynamics,2000,23:335～352
[171]Andrzej S., and Tomasz K. Using chaos synchronization to estimate the largest Lyapunov exponent of nonsmooth systems. Discrete Dynamics in Nature and Society,2000,4:207～215
[172]Shin K., and Hammond J. K. The instantaneous Lyapunov exponent and its application to chaotic systems. Journal of Sound and Vibration,1998,218(3): 389-403
[173]Banbrook M., Ushaw G., and McLaughlin S. How to extract Lyapunov exponents from short and noisy time series. Signal Processing, IEEE Tranctions on Published,1997,45(5):1378～1382
[174]胡茑庆.转子碰摩非线性行为与故障辨识的研究：博士学位论文.长沙：国防 科学技术大学,2001
[175]陈娟,张淑梅,黄艳秋等.电机波动力矩的重复学习控制补偿,光学精密工程,2003,11(4)：390～393
[176]Hara S., Omata T., and Nakano M. Synthesis of repetitive control systems and its application. Proc 24th Conf Decision Contr,1985,1384～1392
[177]汪久根,鄢建辉,朱聘和等.球轴承的摩擦系数分析.机床与液压,2003,(4)：40～41
[178]Harris T. Ball motion in thrust-loaded, angular-contact bearings with Coulomb friction. Journal of Lubrication Technology, ASME,1971,93,32～38
[179]马小梅,邓四二,梁波等.航天轴承摩擦力矩的试验分析,轴承,2005,(10)：22～24
[180]胡浩军.运动平台捕获、跟踪与瞄准系统视轴稳定技术研究：博士学位论文.长沙：国防科学技术大学,2005
[181]Huang Z. L., Zhu W. Q., and Suzuki Y. Stochastic averaging of strongly non-linear oscillators under combined harmonic and white noise excitations. Journal of Sound Vibration,2000,238:233～256
[182]张雄,刘岩.无网格法.北京：清华大学出版社,2004
[183]王卫东,赵国群,栾贻国.无网格方法中本质边界条件的处理,力学季刊,2002,23(4)：521～527
[184]张延军,张晓炜.无网格迦辽金法应用的参数选择及内部边界处理,工程地质学报,2001,9(3)：321～325
[185]聂旭涛,范大鹏,陈峰军.无网格法在几何非线性力学中的应用,机械强度,2007,29(3)：437～441
[186]Liu G. R., and Gu Y. T. A point interpolation method for two-dimensional solids. International Journal for Numercial Method in Engineering,2001, 50:937～951
[187]Liu G. R. Mesh free methods, Boca Raton, Florida:CRC Press,2003
[188]Liu X., Liu G. R., and Tai K., etc. Radial point interpolation collocation method (RPICM) for patial differential equations. Int. J. Computers and Mathematics with Applications,2005,50:1425～1442
[189]宋康祖.紧支函数无网格方法研究：博士学位论文.北京：清华大学,2000
[190]Belytschko T., Lu Y. Y., and Gu L. Element free Galerkin methods. International Journal for Numercial Method in Engineering,1994,37:229～256
[191]Caughey T. K. Nonlinear theory of random vibrations. Advances in Applied Mechanics,1971,11:209～253
[192]Huang Z. L., and Zhu W. Q. Exact stationary solutions of average equations of stochastically and harmonically excited MDOF quasi-linear systems with internal and/or external resonances. Journal of Sound Vibration,1997,204:249～258
[193]朱位秋.非线性随机动力学与控制.北京：科学出版社,2003
[194]Hertz H. Uber die Beruhrung fester elastischer Korper. Journal fur die reine und angewandle Mathematik,1881,92:156～171
[195]冈本纯三.球轴承的设计计算.北京：机械工业出版社,2003
[196]Stribeck R. Kugellager fur beliebige Belastungen. VDI Z,1901,45:73～79, 118～125
[197]万长森.滚动轴承的分析方法.北京：机械工业出版社,1987
[198]Jones A. B. Ball motion and sliding friction in ball bearings. Journal of Basic Engineering, ASME,1959,81:1～12
[199]Harris T. A. Rolling element bearing dynamics. Wear,1973,23:311～337
[2]郭富强,于波,王叔华.陀螺稳定装置与应用.西安：西北工业大学出版社,1995
[3]李保平.战术导弹导引头技术,弹箭与制导学报,2005,22(1)：1～5
[4]Wander K., and Korcher H. J. The pointing control system of SOFIA. SPIE, 2000,4014:360～369
[5]范大鹏. 《光电稳定伺服机构控制技术》专题文章导读,光学精密工程,2006,14(4)：673
[6]张智永.光电稳定伺服机构的关键测控问题研究：博士学位论文.长沙：国防科学技术大学,2006
[7]Ruffatto D., Brown D., and Pohle R. Stablizied high-accuracy optical tracking system(shots). SPIE,2001,4365:10～18
[8]范斌.机载光电探测系统稳定平台CAD技术研究及软件开发：硕士学位论文.北京：北京航空航天大学,2000
[9]李颖晖,郭阳宽,王勇等.伺服转台机械结构方案设计探讨.机械研究与应用,2005,18(6)：88～89
[10]柳朝军.捷联式三轴稳定跟踪台的建模及动态模糊神经网络控制研究：博士学位论文.北京：北京理工大学,2000
[11]邱吉宝,谭志勇,王建民.运载火箭结构动力学分析的一些新技术,第一部分：模态综合技术.导弹与航天运载技术,2001,(2)：29～34
[12]邱吉宝,谭志勇,王建民.运载火箭结构动力学分析的一些新技术,第二部分：运载火箭结构动力学分析.导弹与航天运载技术,2001,(4)：16～21
[13]Qiu J. B., and Wang J. M. Dynamic analysis of strap-on launch vehicle. In:Proc of Asian-Pacific Conference on Aerospace Technology and Science. Beijing International Academic Publishers. Hangzhou,1994-10-10-13,1994,387～391
[14]杨朋军,王卿,王佳民.惯性平台台体结构实验模态参数识别及灵敏度分析.中国惯性技术学报,2004,12(4)：7～11
[15]杨朋军,王卿,王佳民.惯性平台台体结构的实验模态分析.导航与控制,2004,3(2)：3-8
[16]王卿,王佳民,杨朋军.惯性平台框架类结构件的试验模态分析.宇航学报,2005,26(6)：753～757
[17]张小安,张艳.天线座结构的试验模态与理论模态的分析比较.电子机械工程,2005,21(1)：37～40
[18]王跃钢,彭云辉.过载—振动复合环境下液浮陀螺仪动力学分析.中国惯性技术学报,2003,11(6)：80～83
[19]杨朋军,靳长权,王佳民.基于UG/CAE环境下的惯性平台台体有限元分析.导航与控制,2003,2(4)：37～40
[20]聂旭涛,范大鹏.基于COSMOSWorks的三轴稳定平台框架的优化设计.机电工程技术,2005,(1)：74～76
[21]程畅,吕勇.MSC/PATRAN、 DYTRAN软件在机电产品结构件抗冲击强度仿真分析中的应用.机电元件,2002,22(3)：15～17
[22]Blakly K. MSC/NASTRAN dynamic analysis user's guide. Los Angeles:The MacNeal-Schwendler Corporation,1993
[23]Keith B. Doyle, Vincent J. Cerrati, and Steven E. Forman, etc. Optimal structural design of the Airborne Infrared imager. SPIE,1993,2542:11～22
[24]汪元贵,雷勇军.飞行过程中惯导系统的随机振动响应分析.湖南理工大学学报,2004,17(3)：39～41
[25]Lin J. H. A fast CQC algorithm of PSD matrices for random seismic responses. Computers and Structures,1992,44(3):683～687
[26]Einstein A. Investigation on the theory of Brownian movement. English Translations of Einstein Papers, Dover Publications,1956
[27]Rice S. O. Mathematical analysis of random noise. Bell Sys. Tech. J.,1944, 23::282～332
[28]Cooley J. W., and Tukey J. W. An algorithm for the machine calculation of complex Fourier series. Math. Comp.,1965,19:297～301
[29]梅玉林.结构随机振动响应分析理论与算法研究：硕士学位论文.大连：大连理工大学,2000
[30]Shaw D. E. Seismic structural response analysis for multiple support excitation. Proc.3rd Int. SMIRT Conf., London,1975
[31]Vashi K. M. Seismic spectral analysis structural systems subjected to nonuniform excitation at supports. Proc.2nd ASME Spec. Conf., New Orleans,1975
[32]Smeby W., and Kiureghian A. D. Modal combination rules for multi-component earthquake excitation. Earthquake Engineering and Structural Dynamics,1985, 13(1):1～12
[33]Menun C., and Kiureghian A. D. A replacement for the 30%,40% and SRSS rules for multicomponent seismic analysis. Earthquake Spectra,1998, 14(1):153～163
[34]Berrah M., and Kausel E. Response spectrum analysis of structures subjected to spatially varying motions. Earthquake Engineering and Structural Dynamics, 1992,21(1):461～470
[35]孙焕纯,章元崧,张晓志.在双向地震波同时作用下空间框架剪扭弹塑性地震波反应分析.大连工学院学报,1982,21(4)：215～220
[36]胡松,王肇民.洛阳电视塔的结构抗震分析.建筑结构,2000,30(1)：57～59
[37]刘季,王前信.多维与多支座地震输入及结构扭转反应.中国工程抗震研究四十年.北京：地震出版社,1989
[38]王光远.建筑结构的振动.北京：科学出版社,1978
[39]Krenk S., Madsen H. O., and Madsen P. H. Stationary and transient response envelopes. J. Engineering Mechanics, ASCE,1983,109:263～278
[40]Gasparini D. A. Response of MDOF systems to nonstationary random excitation. J. Engineering Mechanics, ASCE,1979,105(EM1):13～28
[41]Zerva A. Lifeline response to spatially variable ground motions. Earthquake Engineering and Structural Dynamics,1988,16(3):361～379
[42]Harichandran R. S., and Vanmarcke E. H. Stochastic variation of earthquake ground motion in space and time. J. Engineering Mechanics, ASCE,1986, 112(2):154～175
[43]Ernesto H. Z., and Vanmarcke E. H. Seismic random vibration analysis of multisupport structural systems. J. Engineering Mechanics, ASCE,1994, 120(5):1107～1128
[44]Masri S. F. Response of a multi-degree-of-freedom system to nonstationary random excitation. J. of Applied Mechanics, ASME,1978,45(3):649-656
[45]王敏,王小静.弹载天线随机振动的仿真分析.制导与引信,2007,28(2)：57-60
[46]于旭东,龙兴武,汤建勋.机抖激光陀螺动力学分析及优化设计.中国惯性技术学报,2007,15(2)：241～244
[47]Lin Y. K. Probability theory of structural dynamics. New York:McGraw-Hill, 1967
[48]Crandall S. H., and Mark W. D. Random vibration in mechanical system. New York:Academic Press,1963
[49]Newland D. E. An introduction to random vibration and spectral analysis. London:Longman,1975
[50]Nigam N. C. Introduction to random vibrations. Cambridge:The MIT Press,
1983
[51]李国豪.工程结构抗震动力学.上海：上海科学技术出版社,1980
[52]Lin J. H., Zhang W. S., and Li J. J. Structural responses to arbitrarily coherent stationary random excitations. Computers and Structures,1994,50:629～633
[53]Lin J. H., Zhang W. S., and Williams F. W. Pseudo-Excitation algorithm for non-stationary random seismic responses. Engineering Structures,1994, 16:270～276
[54]Lin J. H., Wang W. X., and Williams F. W. Asynchronous parallel computing of structural non-stationary random seismic responses. International Journal of Numerical Method in Engineering,1997,40:2133～2148
[55]Lin J. H., Zhong W. X., and Zhang W. S., etc. High efficiency computation of the variances of structural evolutionary random responses. Shock and Vibration,2000,7(4):209～216
[56]Lin J. H., Zhao Y., and Zhang Y. H. Accurate and Highly efficient algorithms for structural stationary/non-stationary random responses. Computer Method in Applied Mechanics and Engineering,2001,191:103～111
[57]Noor A., and Fulton R. E. Impact of the CDC-STAR-100 Computer on Finite Element Systems. Journal of the Structural Division, ASCE,1975,101:731～750
[58]Geist G. A., and Romine C. H. LU factorization on distributed-memory multiprocessors. Proceedings of the 3rd SIAM Conference on Parallel Processing for Scientific Computing, CA. USA,1987,15～18
[59]Jiangning Qin, and Nguyen D. T. A parallel-vector equation solver for distributed-memory computers. Computing Systems in Engineering,1994,5(1): 19～25
[60]Lin A., and Zhang H. A new parallel algorithm for linear triangular systems. Proceedings of the 3rd SIAM Conference on Parallel Processing for Scientific Computing, CA. USA,1987,36～39
[61]Farhat C., and Wilson E. A parallel active column equation solver. Computers and Structures,1988,28(2):289～304
[62]Goehlich D., Komzsik L., and Fulton R. E. Application of a parallel equation solver to static FEM problems. Computers and Structures,1989,31(2):121～129
[63]迟学斌.Transputer上 Cholesky分解的并行实现.计算数学,1993,(3)：289～294
[64]张健飞,姜弘道.对称正定矩阵的并行LDLT分解算法实现.计算机工程与设计,2003,24(10)：75～77
[65]孙家昶等.网络并行计算与分布式编程环境.北京：科学出版社,1997
[66]Mandel J. Balancing domain decomposition. Communications in Numerical Method in Engineering,1993,9:233～241
[67]Levit I. Element by element solvers of order N. Computers and Structures,1987, 27(1):357～360
[68]Pattrick M. P., Prat T. W. Communication oriented programming of parallel iterative solutions for sparse linear systems. Communications in Applied Numerical Method,1986,2:255～261
[69]Akiko H., Robert J., and Utku Senol. Variation in efficiency of parallel algorithm. Computers and Structures,1985,21(5):1025～1034
[70]胡宁,张汝清.一种迭代格式的有限元并行算法.应用数学和力学,1992,13(4)：287～295
[71]邓绍忠,周树荃.不规则结构分析有限元方程组的并行迭代算法及其实现.全国第三届并行算法学术会议文集.武汉：华中理工大学出版社,1992：116～120
[72]迟利华,刘杰,李晓梅.稀疏近似条件子及其并行计算.计算机学报,2000,23(3)：255～260
[73]Noor A., Kamel H., and Fulton R. E. Substructuring techniques-status and projections. Computers and Structures,1977,8:621～632
[74]Escaig Y., Touzot G., and Vayssad M. Parallelization of a multilevel domain decomposition method. Computing Systems in Engineering,1994,5(3):253～263
[75]Dracopoulos M. C., and Crisfield M. A. A partially sequential preconditional for a parallel and efficient finite element solution. Computing Systems in Engineering,1995,6(6):549～561
[76]Law K. H. A parallel finite element solution method. Computers and Structures, 1986,23(6):845～858
[77]王健一,张卫等.有限元问题的并行求解.哈尔滨工业大学学报,1994,26(2)：37～40
[78]李强,邹经湘.独立子结构并行计算方法.哈尔滨工业大学学报,1996,28(2)：144～148
[79]Hughes T. J. R., Levit I., and Winget J. Element by element implicit algorithm for heat conduction. Journal of Engineering Mechanics Division, ASCE,1983, 109:576～585
[80]Hughes T. J. R., Levit I., and Winget J. An element by element solution algorithm for problems of structural and solid mechanics. Computer Methods in Applied Mechanics and Engineering,1983,36:241～254
[81]Barragy E., and Carey G. F. A parallel element-by-element solution scheme. International Journal for Numerical Method in Engineering,1988, 26:2367～2382
[82]Khan A. I., and Topping B. H. V. Parallel finite element analysis using Jacobi-conditioned conjugate gradient algorithm. Advances in Engineering Software,1996,25:309～319
[83]Gullerud Arne S., and Dodds Jr Robert H. MPI-based implementation of a PCG solver using an EBE architecture and precondition for implicit,3-D finite element analysis. Computers and Structures,2001,79:553～575
[84]周树荃,梁维泰,邓绍忠.有限元结构分析并行计算.北京：科学出版社,1999
[85]刘耀儒,周维垣,杨强.有限元并行EBE方法及应用.岩石力学与工程学报,2005,24(17)：3023～3028
[86]厉天威,阮江军,张宇等.基于区域分解法的电磁场并行计算研究.高电压技术,2007,33(5)：58～61
[87]陈荣征,李代平,何驰等.并行PCG算法在电法勘探中的应用研究.微计算机信息,2007,23(3)：254～256
[88]亓文果,金先龙,张晓云等.汽车碰撞有限元仿真的并行计算及其性能研究.系统仿真学报,2004,16(11)：2428～2431
[89]谢晖,钟志华,李光耀等.板料冲压数值模拟的并行计算与应用.中国机械工程,2003,14(21)：1842～1844
[90]李丽君,金先龙.空间多点地震动模拟的并行计算方法及软件.系统仿真学报,2003,17(5)：1068～1071
[91]Bhaskar Dasgupta, Prasun Choudhury. A general strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators. Mechanism and Machine Theory,1999,34(6):801～824
[92]Bayo E., Dejalon J. G., and Serna M. A. A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems. Computer Methods in Applied Mechanics and Engineering,1988,71:183～195
[93]周瑞青,吕善伟,刘新华.捷联式天线稳定平台动力学建模与仿真分析.北京航空航天大学学报,2005,31(9)：953～957
[94]黄一,卢广山,陈宗基.三自由度机载光电跟瞄平台建模与校核.系统仿真学报,2004,16(9)：1948～1952
[95]刘延柱.多刚体系统动力学.北京：高等教育出版社,1986
[96]王济民.双轴陀螺稳定机构动力学建模与仿真.西北大学学报(自然科学版),2005,35(2)：167～169
[97]梅晓榕,陈明,张卯瑞.三轴仿真转台的建模与仿真.系统仿真学报,2001,13(3)：278～279
[98]Guo Kang Er. Multi-gaussian closure method for randomly excited non-linear systems. International Journal of Non-Linear Mechanics,1998,33(2):201～214
[99]Tomasiello S. An application of neural networks to a non-linear dynamics problem. Journal of Sound and Vibration,2004,272:461-467
[100]Lai Ah Wong, and Jay Chung Chen. Nonlinear and chaotic behavior of structural system investigated by wavelet transform techniques. International Journal of Non-Linear Mechanics,2001,36:221～235
[101]Sheng M. P. Statistical energy analysis for complicated coupled system and its application in engineering. Journal of Sound and Vibration,2004,274:877～891
[102]戎海武,王向东,孟光等.简谐与随机噪声联合激励下Van der Pol-Duffing系统的响应.振动工程学报,2003,16(4)：502～505
[103]Caughey T. K., and Dienes J. K. Analysis of a non-linear first-order system with a white noise input. Journal of Applied Physics,1961,23:2476～2479
[104]Kramer H. A. Brownian motion in a field of force and diffusion of chemical reactions. Physics,1940,7:284～304
[105]Caughey T. K., and Ma F. The exact steady-state solution of a class of nonlinear stochastic systems. International Journal of Non-Linear Mechanics,1983, 17:137-142
[106]Cai G. Q., and Lin Y. K. A new approximate solution technique for randomly excited non-linear oscillators. International Journal of Non-Linear Mechanics, 1988a,23(5/6):409～420
[107]Bhandari R. G., and Sherrer R. E. Random vibration in discrete non-linear dynamics systems. Journal of Mechanical Engineering Science,1968, 10:168～174
[108]Wen Y. K. Approximate method for non-linear random vibration. Proceedings of the ASCE Journal of the Engineering Mechanics Division,1975,101:389-401
[109]Langley R. S. A finite element method for the statistics of non-linear random vibration. Journal of Sound and Vibration,1985,101:41～54
[110]Roberts J. B. First-passage time for randomly excited non-linear oscillators. Journal of Sound and Vibration,1986,109:33～50
[111]Toland R. H., Yang C. Y., and Hsu C. K. C. Non-stationary random vibration of non-linear structures. International Journal of Non-Linear Mechanics,1972, 7:395～406
[112]Roberts J. B. Transient response of non-linear systems to random excitation. Journal of Sound and Vibration,1981,74:11～29
[113]Yu J. S., Cai G. Q., and Lin Y. K. A new path integration procedure based on Gauss-Legendre scheme. International Journal of Non-Linear Mechanics, 1997,32:759～768
[114]Naess A. N., and Johnsen J. M. Response statistics of nonlinear compliant structures by the path integration solution method. Probabilistic Engineering Mechanics,1997,12:257～260
[115]Booton R. C. The analysis of nonlinear control systems with random inputs. IRE Trans. Circuit Theory,1954,1:32～34
[116]Iwan W. D., and Yang I. Application of statistical linearization technique to nonlinear multi-degree-of-freedom systems. Journal of Applied Mechanics, 1972,39:545～550
[117]Lutes L. D. Approximate technique for treating random vibration of hysteretic systems. Journal of Acoust. Soc. Am.,1970,48:299～306
[118]Cai G. Q., Lin Y. K., and Elishakoff I. A new approximate solution technique for randomly excited non-linear oscillators 2. International Journal of Non-Linear Mechanics,1992,27(6):969～979
[119]Spanos P. D., and Donley M. G. Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization. International Journal of Non-Linear Mechanics,1992,27(5):735-748
[120]Stratonovitch R. L., Topics in the theory of random noise. Godon and Breach, 1963,1; 1967,2
[121]Khasminskii R. Z. A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probabilistic Application.,1966,11:390～405
[122]Roberts J. B. Stationary response of oscillators with non-linear damping to random excitation. Journal of Sound and Vibration,1977,50:145～156
[123]Spanos P. D. Stochastic analysis of oscillators with non-linear damping. International Journal of Non-Linear Mechanics,1978,13:249～259
[124]Roberts J. B. The energy envelope of a randomly excited nonlinear oscillator. Journal of Sound and Vibration,1978,60:177～185
[125]朱位秋.随机振动.北京：科学出版社,1998
[126]Zhu W. Q., Lin Y. K. Stochastic averaging of energy envelope. Journal of Engineering Mechanics, ASCE,1991,117(8):1890-1905
[127]Zhu W. Q. Stochastic averaging of Quasi-Hamiltonian systems. Science in China, Series A,1996,39(1):97～108
[128]Zhu W. Q. Recent developments and applications of stochastic averaging method in random vibration. Applied Mechanics Reviews, ASME,1996, Part 2,49(10): S72-S80
[129]Zhu W. Q., and Yang Y. Q. Stochastic averaging of Quasi-Nonintegrable-Hamiltonian systems.Journal of Applied Mechanics,ASME,1997, 39(1):157～164
[130]Zhu W. Q., Huang Z. L., and Yang Y. Q. Stochastic averaging of Quasi-Integrable-Hamiltonian systems. Journal of Applied Mechanics, ASME,1997, 64(4):975-984
[131]朱位秋,黄志龙,应祖光.非线性随机动力学与控制的哈密顿理论框架.力学与实践,2002,24(3)：1-9
[132]王勖成,邵敏.有限单元法基本原理和数值方法.北京：清华大学出版社,1997
[133]钟志荣.EBE-CG并行算法研究：硕士学位论文.广东：广东工业大学,2004
[134]张少波,胡明宝,张鹏.预处理共轭梯度法在VVP三维风场反演中的应用.气象科学,2004,24(3)：303～308
[135]周硕,郭丽杰,吴柏生.Jacobi迭代预处理中的条件数与迭代次数的关系.东北电力学院学报,2003,23(6)：57～60
[136]Khan A. I., Topping B. H. Parallel finite element analysis using Jacobi conditioned conjugate gradient algorithm. Adv. Engrg. Soft,1996,25:309～319
[137]David Kincaid, Ward Cheney.数值分析(原书第3版).北京：机械工业出版社,2005
[138]Hughes T. J. R., and Ferencz R. M. Large-scale vectorized implicit calculation in solid mechanics on a CRAY X-MP/48 utilizing EBE-PCG. Computer Methods in Applied Mechanics and Engineering,1987,61:215～248
[139]杨忠超.基于EBE策略的列车三维紊态外流场有限元法并行计算研究：博士学位论文.成都：西南交通大学,2002
[140]宫玉才,周洪伟,陈璞等.快速子空间迭代法、迭代Ritz向量法与迭代Lanczos法的比较,振动工程学报,2005,18(2)：227～232
[141]Subbaraj K., and Dokainish M. A. A survey of direct time integration methods in computational structural dynamics, Ⅰ Explicit methods, Ⅱ Implicit methods. Computers and Structures,1989,32(6):1371～1386,1387～1401
[142]Flynn, Michael J. Very high-speed computing systems. Proceedings of the IEEE,1966,54(12):1901～1909
[143]Flynn, Michael J., and Kevin W. Rudd. Parallel architectures. ACM Computing Surveys,1996,28(1):60～70
[144]王启平,王璐,伍毅等.结构高性能计算中的并行有限元方法.安徽工业大学学报,2005,22(2)：135～138
[145]Hipper G., and Tavangarian D. Advance workstation cluster architectures for parallel computing. Journal of Systems Architecture,1988,44:207～226
[146]张友良.岩土大规模高性能并行有限元系统研究：博士学位论文.北京：中国科学院研究生院,2003
[147]李海江.基于MPI的并行有限元计算集群的构建,数值计算与计算机应用,2004,(3)：198～209
[148]Ivan Lirkov. MPI solver for 3D elasticity problems. Mathematics and Computers in Simulation,2003,61:509～516
[149]Eppstein M. J., Dougherty D. E. A comparative study of PVM workstation cluster implementations of a two-phase subsurface flow model. International Journal of Rock Mechanics and Mining Sciences and Geomechanics,1995,32 A: 208-209
[150]任波.基于集群的接触／碰撞有限元法并行策略：博士学位论文.武汉：华中科技大学,2003
[151]Gropp, Lusk, and Skjellum. Using MPI:portable parallel programming with the Message-Passing-Interface, MIT. Press,1999
[152]龚曙光,谢桂兰.ANSYS操作命令与参数化编程.北京：机械工业出版社,2004
[153]向宇,黄玉盈,曾革委.精细时程积分法的误差分析与精度设计,计算力学学报,2002,19(3)：276～280
[154]张森文,曹开彬,陈奎孚.精细积分时域平均法和随机扩阶系统法,力学学报,2000,32(2)：191～197
[155]钟万勰.结构动力方程的精细时程积分法,大连理工学报,1994,34(2)：131～136
[156]Michael J. Quinn. MPI与OpenMP并行程序设计.北京：清华大学出版社,2004
[157]李丽君,金先龙,李渊印等.一种新型并行化有限元结构模态分析集成系统,计算力学学报.2004,21(5)：546～550
[158]朱美娴.防空导弹武器系统可靠性工程设计.北京：宇航出版社,1994
[159]张艳敏.复杂结构的冲击动力学分析与仿真：硕士学位论文.西安：西北工业大学,2005
[160]郭强岭,李立名.空空导弹挂飞振动试验条件探讨,航空兵器.2003,(6)：21～23
[161]Rajakumar C., and Rogers C. R., The Lanczos algorithm applied to unsymmetric generalized eigenvalue problems. International Journal for Numercial Method in Engineering.1991,32:1009～1026
[162]Wilson E. L., and Itoh Tetsuji. An eigensolution strategy for large systems. Computers and Structures.1983,16(1-4):259～265
[163]刘士华,赵德胜,谭天水等.ANSYS在钢架结构随机振动分析中的应用,机械,2004,31(4)：54～55
[164]Cooper C.J., and Hamilton. Sensor line-of-sight stabilization. SPIE,1991, 1498:34～46
[165]张爱梅.目标跟踪瞄准系统的虚拟现实研究：硕士学位论文.西安：西安电子科技大学,2004
[166]曾鸣,王忠山,王学智.基于非线性摩擦模型参数观测器的自适应摩擦补偿方法的研究,航空精密制造技术,2005,41(3)：17～22
[167]Dowson D. History of Tribology, London:Longman Ltd,1996
[168]付士慧,王琪,王士敏.带干摩擦的非光滑动力系统Lyapunov指数的数值计算,动力学与控制学报,2006,4(3)：210～216
[169]Stefanski A. Estimation of the largest Lyapunov exponent in systems with impacts. Chaos, Solitons & Fractals.2000,11:2443～2451
[170]Lamarque C. H., and Bastien J. Numerical study of a forced pendulum with friction. Nonlinear Dynamics,2000,23:335～352
[171]Andrzej S., and Tomasz K. Using chaos synchronization to estimate the largest Lyapunov exponent of nonsmooth systems. Discrete Dynamics in Nature and Society,2000,4:207～215
[172]Shin K., and Hammond J. K. The instantaneous Lyapunov exponent and its application to chaotic systems. Journal of Sound and Vibration,1998,218(3): 389-403
[173]Banbrook M., Ushaw G., and McLaughlin S. How to extract Lyapunov exponents from short and noisy time series. Signal Processing, IEEE Tranctions on Published,1997,45(5):1378～1382
[174]胡茑庆.转子碰摩非线性行为与故障辨识的研究：博士学位论文.长沙：国防 科学技术大学,2001
[175]陈娟,张淑梅,黄艳秋等.电机波动力矩的重复学习控制补偿,光学精密工程,2003,11(4)：390～393
[176]Hara S., Omata T., and Nakano M. Synthesis of repetitive control systems and its application. Proc 24th Conf Decision Contr,1985,1384～1392
[177]汪久根,鄢建辉,朱聘和等.球轴承的摩擦系数分析.机床与液压,2003,(4)：40～41
[178]Harris T. Ball motion in thrust-loaded, angular-contact bearings with Coulomb friction. Journal of Lubrication Technology, ASME,1971,93,32～38
[179]马小梅,邓四二,梁波等.航天轴承摩擦力矩的试验分析,轴承,2005,(10)：22～24
[180]胡浩军.运动平台捕获、跟踪与瞄准系统视轴稳定技术研究：博士学位论文.长沙：国防科学技术大学,2005
[181]Huang Z. L., Zhu W. Q., and Suzuki Y. Stochastic averaging of strongly non-linear oscillators under combined harmonic and white noise excitations. Journal of Sound Vibration,2000,238:233～256
[182]张雄,刘岩.无网格法.北京：清华大学出版社,2004
[183]王卫东,赵国群,栾贻国.无网格方法中本质边界条件的处理,力学季刊,2002,23(4)：521～527
[184]张延军,张晓炜.无网格迦辽金法应用的参数选择及内部边界处理,工程地质学报,2001,9(3)：321～325
[185]聂旭涛,范大鹏,陈峰军.无网格法在几何非线性力学中的应用,机械强度,2007,29(3)：437～441
[186]Liu G. R., and Gu Y. T. A point interpolation method for two-dimensional solids. International Journal for Numercial Method in Engineering,2001, 50:937～951
[187]Liu G. R. Mesh free methods, Boca Raton, Florida:CRC Press,2003
[188]Liu X., Liu G. R., and Tai K., etc. Radial point interpolation collocation method (RPICM) for patial differential equations. Int. J. Computers and Mathematics with Applications,2005,50:1425～1442
[189]宋康祖.紧支函数无网格方法研究：博士学位论文.北京：清华大学,2000
[190]Belytschko T., Lu Y. Y., and Gu L. Element free Galerkin methods. International Journal for Numercial Method in Engineering,1994,37:229～256
[191]Caughey T. K. Nonlinear theory of random vibrations. Advances in Applied Mechanics,1971,11:209～253
[192]Huang Z. L., and Zhu W. Q. Exact stationary solutions of average equations of stochastically and harmonically excited MDOF quasi-linear systems with internal and/or external resonances. Journal of Sound Vibration,1997,204:249～258
[193]朱位秋.非线性随机动力学与控制.北京：科学出版社,2003
[194]Hertz H. Uber die Beruhrung fester elastischer Korper. Journal fur die reine und angewandle Mathematik,1881,92:156～171
[195]冈本纯三.球轴承的设计计算.北京：机械工业出版社,2003
[196]Stribeck R. Kugellager fur beliebige Belastungen. VDI Z,1901,45:73～79, 118～125
[197]万长森.滚动轴承的分析方法.北京：机械工业出版社,1987
[198]Jones A. B. Ball motion and sliding friction in ball bearings. Journal of Basic Engineering, ASME,1959,81:1～12
[199]Harris T. A. Rolling element bearing dynamics. Wear,1973,23:311～337
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