车辆与道路/桥梁耦合随机动力分析及优化
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摘要
随着国民经济的迅速发展,铁路和公路交通日渐繁忙；而行车速度不断提高,车辆负荷逐渐增大,使得交通车辆与支承(道路或桥梁)结构动力相互作用越来越受到重视。由于移动车辆对道路／桥梁结构的动力冲击作用使结构工作状态和使用寿命发生改变；而且运行车辆的平顺性和安全性又是评价结构设计参数合理与否的重要考虑因素。因此车辆-道路／桥梁相互作用系统的综合研究对于车、路和桥的设计和制造至关重要。由于路面的不平度,车辆与结构相互作用具有很强的随机性。然而传统随机振动分析方法的低效率限制了人们对该工具的应用。迄今为止,关于车辆与结构随机振动分析的研究成果还不多。本文在随机振动理论框架下,采用虚拟激励法,精细积分法等高效、精确的计算力学方法,研究车辆随机振动、车辆与道路／桥梁耦合随机振动,以及各种动力响应的统计特性。并且根据车辆与道路／桥梁相互作用的特点对上述方法进行扩展,提出了一系列快捷精确的车辆随机振动灵敏度分析方法,高效地针对车辆结构的随机振动特性进行优化设计,提高车辆平顺性、降低对结构物的不良影响。主要工作包括以下几方面。
1.车辆与道路结构垂向耦合随机振动分析
对于车辆-公路垂向耦合振动系统,通过建立随车辆同步移动的坐标系,推导出了适用于车辆与路面相互作用动力分析的二维移动单元形式。在移动坐标系下,路面模型单元被看作沿道路随车辆“流动”的概念单元,在这些单元上车辆是相对静止的,作用点的力和位移向量不用随着车辆位置的变化而更新。因此,运动微分方程的右端时间积分项消失,而行驶速度、地基参数等耦合因素对系统的影响被累加进振动方程的质量、阻尼、刚度矩阵中,使固定坐标系下的时变耦合振动问题转化为移动坐标系下的拟静力问题分析。该方法构造简单,将耦合非平稳随机振动问题方便地转化为拟静力问题进行分析,具有较高的精度和效率。
2.车辆平稳随机振动灵敏度分析及优化
基于传统随机振动分析方法的结构动力优化一直存在着分析过程复杂,计算量庞大,动力灵敏度分析难于实施等困难。本文将虚拟激励法在结构随机响应优化领域进行推广,针对车辆平顺性优化的灵敏度分析,提出了一种求解灵敏度信息的快速、精确方法。此方法在采用虚拟激励法对结构进行动力分析的基础上,根据响应信息对结构振动方程关于设计变量进行求导,可得到与原振动方程结构一致的灵敏度方程。通过对灵敏度方程激励项的虚拟模拟,将平稳随机荷载作用下具有阻尼系统的动力响应灵敏度计算问题转化为虚拟荷载作用下的动力响应问题进行求解,从而避免了求解特征向量的繁重计算量。同时该方法在一阶灵敏度分析的基础上可以方便快速地进行二阶灵敏度(Hessian矩阵)的分析。
3.基于模拟技术的车辆随机振动多目标优化
结构随机响应优化问题因不可避免地要对随机振动分析过程进行反复迭代而致计算量异常繁重,很难得到工程应用。尤其在多目标优化领域,迄今为止,目标函数的统一、有效的灵敏度分析还没有找到现实可行的高效方法,使得基于灵敏度的优化方法不易实现。本文基于模拟技术,寻求反映设计变量和响应之间关系的“替代函数”,将Kriging模型引入车辆随机振动领域,经过对样本的改造,在优化迭代过程中用替代函数代替目标函数进行优化,同时对替代函数进行必要的修正,以保证更好的精度。这样避免了过多的重分析过程,显著提高了计算效率。多目标函数通过中心法来处理,亦即对每一个目标函数自适应地引入一个上界,形成目标函数的水平截集,并重复地计算由原约束集和目标函数水平截集组成的交集的中心来达到求解多目标优化问题的目的。
4.车辆与道路／桥梁耦合随机振动分析及优化设计
对于车桥耦合时变系统,采用虚拟激励法将路面随机不平度转化为一系列简谐不平度的叠加,根据荷载形式使用相应的精细积分格式进行时域积分。这种虚拟激励-精细积分方法(PEM-PIM)较之传统的逐步积分方法解决了载荷“突变”和积分步过小的问题,极大地提高了耦合振动分析效率,使得耦合振动动力优化灵敏度分析的高效计算得以实现。本文基于这种方法,通过对耦合振动方程的一阶、二阶求导,得到一阶、二阶灵敏度方程的状态空间表达形式,将多点部分相干非平稳阻尼系统动力响应灵敏度分析问题转化为一系列虚拟荷载作用下的普通动力响应问题求解。应用本文方法可以高效地给出计算机意义下的敏度和Hessian矩阵精确解。
5.基于有限元方法的车辆-道路／桥梁耦合动力系统随机振动力学行为研究
该耦合系统随机振动力学行为的研究涉及随机振动分析、优化设计、疲劳寿命估计等多项力学难题,而且需要对大型有限元模型进行耦合随机振动分析,动辄成千上万的自由度,传统方法庞大的计算量成为这类问题的瓶颈。其随机分析若采用传统方法是不堪忍受的,甚至有些问题不能进行求解。为此,本文将虚拟激励法,耦合振动分析的PEM-PIM方法,高效的灵敏度分析方法等先进的计算手段相结合,并应用到实际车辆中。最终通过对客车车辆、车桥耦合系统等有限元模型的数值计算,研究了其随机疲劳寿命、冲击系数等力学行为,并验证了以上方法在工程应用中的高效性。
With the rapid development of national economy, railway and highway transportations are getting increasingly busy. Higher speeds and heavier loads of the vehicles have caused the dynamic interactions between vehicles and road/bridge structures received much attention. As the dynamic impacts applying on the supporting (road or bridge) structures by moving vehicles affect the working status and service lives of these structures significantly; and the running smoothness and safety of vehicles have become the main factors in evaluating the reasonability of structural design parameters, therefore a comprehensive research of the interactions between vehicles and road/bridges are of great importance for their design and construction. The vibrations of vehicles and road/bridge coupled systems induced by road irregularity are essentially random, but the research work associated with such random vibration has not been well developed because of the high complexity and cost of conventional methods for random vibration analysis. Up to date, not much research work on vehicle-road/bridge system random vibration can be found in the literature. In the present thesis, some advanced computational mechanics methodology, including the pseudo excitation method (PEM) for random vibration, the precise integration method (PIM) for time history integration, etc, are introduced into the present research on dynamic analyses and optimum of various coupled vehicle and supporting structure systems based on the theoretical framework of random vibration. Furthermore some innovative schemes based on the above methodologies have been developed, which can be summarized as follows:
1. Vertical random vibration analysis of vehicle-pavement coupled systems
For vertical random vibration analysis of vehicle-pavement (or road) coupled system, the two-dimensional moving element method (MEM) is derived by using a coordinate system which moves with the vehicle. The pavement elements are regarded as conceptual elements that'flow'with the moving vehicle along the pavement in this coordinate system, and vehicle is static. It is never necessary to cross from one element into another, which avoids the updating of force or displacement vectors due to change of the contact point with the elements. It can be found that the element stiffness and damping matrices thus easily obtained are simply a revision of the corresponding static element stiffness and damping matrices by superposing the terms with the velocity, foundation parameter and other coupled effects. So the non-stationary random vibration can be transformed conveniently into a stationary one, and it is accurate and efficient.
2. The sensitivity analysis and optimum for vehicle stationary random vibration The complicated analysis process and costly computation efforts are always the mainly difficulties for the random vibration optimum design based on conventional methods, which lead to the difficulty of the random vibration sensitivity analysis. In this thesis, an accurate and efficient sensitivity analysis formula for optimizing the ride comfort of vehicle suspension system is derived. Based on the dynamic responses analysis using PEM, the random equations of motion with the right-hand side random acceleration is replaced by a pseudo acceleration excitation, thus various first and second orders of sensitivity formulas are calculated conveniently by differentiating these equations. Using the method the random dynamic sensitivity analysis is transformed into a deterministic one, and the optimal solutions when vehicle ride comfort is the objective function are derived by means of these flexibilities. The optimization efficiency and the computational accuracy are numerically justified.
3. Multi-objective stochastic dynamic optimum design for vehicles based on simulation technology
It is particularly unacceptable for stochastic dynamic optimum of structures in practical engineering field, which requires usually many re-analyses and complicated analyses process. Especially to multi-objective optimum, the unified and efficient sensitivity analysis method applied to the objective functions has not been well developed. In this thesis, the Kriging model is extended to vehicle multi-objective optimum problems, a method of filled function is set up to build the approximate mapping relationship between the design variables and the responses, and the random responses analysis is performed using the filled function instead of the objective function, with necessary modification for the filled function in every step to keep the precision. The optimization efficiency is thus enhanced remarkably by avoiding too many re-analyses. The multi-objective function is processed by means of the method of centers, i.e. by self-adaptively introducing an upper bound on each objective function that forms the level sets of the objective functions, and repeatedly calculating the center of the intersection sets consisting of the original constraint sets and the level sets of the objective functions.
4. The random vibration analysis and optimum design for vehicle-bridge coupled random vibration
For dynamic analysis of vehicle-bridge coupled system, the PEM has been applied to transform the random surface roughness into the superposition of a series of deterministic pseudo-harmonic surface unevenness. The PIM has also been extended to simulate the continuous variation of the contact forces, both in their magnitudes and positions, within each time step. As a result, the solution of the uniformly modulated, multi-point, different-phase, non-stationary random vibration can be obtained efficiently by means of PEM-PIM. An innovative method (PEM-PIM Based Sensitivity) for first and second order sensitivity analyses of structural random responses is developed based on PEM-PIM. For the random equations of motion, by replacing the right-hand side random excitation by the pseudo-excitation, various first and second order sensitivity formulae can be derived conveniently and accurately.
5. FEM-based random vibration analysis and associated mechanical behaviors study of vehicle-road/bridge coupled systems
This subject is concerned with many problems, including random vibration analysis, stochastic dynamic optimum and fatigue life estimation, and so on. Analysis of such random vibration mechanical behaviors has long been regarded as very difficult, particularly if finite element models with many degrees of freedom are used. Optimum design is even more difficult although it is of great concern and significance. To overcome these difficulties, some advanced computational mechanics methodology, such as PEM for random vibration, PIM for the numerical integration in the time domain or space domain and some efficient sensitivity analysis methods are used in this paper to study the random vibration mechanical behaviors in the vehicle engineering field. Some useful results about structure random fatigue life, vehicle dynamic impact influence and structure random dynamic optimum are obtained, and the efficiency and computational accuracy of the proposed methods are justified.
1.车辆与道路结构垂向耦合随机振动分析
对于车辆-公路垂向耦合振动系统,通过建立随车辆同步移动的坐标系,推导出了适用于车辆与路面相互作用动力分析的二维移动单元形式。在移动坐标系下,路面模型单元被看作沿道路随车辆“流动”的概念单元,在这些单元上车辆是相对静止的,作用点的力和位移向量不用随着车辆位置的变化而更新。因此,运动微分方程的右端时间积分项消失,而行驶速度、地基参数等耦合因素对系统的影响被累加进振动方程的质量、阻尼、刚度矩阵中,使固定坐标系下的时变耦合振动问题转化为移动坐标系下的拟静力问题分析。该方法构造简单,将耦合非平稳随机振动问题方便地转化为拟静力问题进行分析,具有较高的精度和效率。
2.车辆平稳随机振动灵敏度分析及优化
基于传统随机振动分析方法的结构动力优化一直存在着分析过程复杂,计算量庞大,动力灵敏度分析难于实施等困难。本文将虚拟激励法在结构随机响应优化领域进行推广,针对车辆平顺性优化的灵敏度分析,提出了一种求解灵敏度信息的快速、精确方法。此方法在采用虚拟激励法对结构进行动力分析的基础上,根据响应信息对结构振动方程关于设计变量进行求导,可得到与原振动方程结构一致的灵敏度方程。通过对灵敏度方程激励项的虚拟模拟,将平稳随机荷载作用下具有阻尼系统的动力响应灵敏度计算问题转化为虚拟荷载作用下的动力响应问题进行求解,从而避免了求解特征向量的繁重计算量。同时该方法在一阶灵敏度分析的基础上可以方便快速地进行二阶灵敏度(Hessian矩阵)的分析。
3.基于模拟技术的车辆随机振动多目标优化
结构随机响应优化问题因不可避免地要对随机振动分析过程进行反复迭代而致计算量异常繁重,很难得到工程应用。尤其在多目标优化领域,迄今为止,目标函数的统一、有效的灵敏度分析还没有找到现实可行的高效方法,使得基于灵敏度的优化方法不易实现。本文基于模拟技术,寻求反映设计变量和响应之间关系的“替代函数”,将Kriging模型引入车辆随机振动领域,经过对样本的改造,在优化迭代过程中用替代函数代替目标函数进行优化,同时对替代函数进行必要的修正,以保证更好的精度。这样避免了过多的重分析过程,显著提高了计算效率。多目标函数通过中心法来处理,亦即对每一个目标函数自适应地引入一个上界,形成目标函数的水平截集,并重复地计算由原约束集和目标函数水平截集组成的交集的中心来达到求解多目标优化问题的目的。
4.车辆与道路／桥梁耦合随机振动分析及优化设计
对于车桥耦合时变系统,采用虚拟激励法将路面随机不平度转化为一系列简谐不平度的叠加,根据荷载形式使用相应的精细积分格式进行时域积分。这种虚拟激励-精细积分方法(PEM-PIM)较之传统的逐步积分方法解决了载荷“突变”和积分步过小的问题,极大地提高了耦合振动分析效率,使得耦合振动动力优化灵敏度分析的高效计算得以实现。本文基于这种方法,通过对耦合振动方程的一阶、二阶求导,得到一阶、二阶灵敏度方程的状态空间表达形式,将多点部分相干非平稳阻尼系统动力响应灵敏度分析问题转化为一系列虚拟荷载作用下的普通动力响应问题求解。应用本文方法可以高效地给出计算机意义下的敏度和Hessian矩阵精确解。
5.基于有限元方法的车辆-道路／桥梁耦合动力系统随机振动力学行为研究
该耦合系统随机振动力学行为的研究涉及随机振动分析、优化设计、疲劳寿命估计等多项力学难题,而且需要对大型有限元模型进行耦合随机振动分析,动辄成千上万的自由度,传统方法庞大的计算量成为这类问题的瓶颈。其随机分析若采用传统方法是不堪忍受的,甚至有些问题不能进行求解。为此,本文将虚拟激励法,耦合振动分析的PEM-PIM方法,高效的灵敏度分析方法等先进的计算手段相结合,并应用到实际车辆中。最终通过对客车车辆、车桥耦合系统等有限元模型的数值计算,研究了其随机疲劳寿命、冲击系数等力学行为,并验证了以上方法在工程应用中的高效性。
With the rapid development of national economy, railway and highway transportations are getting increasingly busy. Higher speeds and heavier loads of the vehicles have caused the dynamic interactions between vehicles and road/bridge structures received much attention. As the dynamic impacts applying on the supporting (road or bridge) structures by moving vehicles affect the working status and service lives of these structures significantly; and the running smoothness and safety of vehicles have become the main factors in evaluating the reasonability of structural design parameters, therefore a comprehensive research of the interactions between vehicles and road/bridges are of great importance for their design and construction. The vibrations of vehicles and road/bridge coupled systems induced by road irregularity are essentially random, but the research work associated with such random vibration has not been well developed because of the high complexity and cost of conventional methods for random vibration analysis. Up to date, not much research work on vehicle-road/bridge system random vibration can be found in the literature. In the present thesis, some advanced computational mechanics methodology, including the pseudo excitation method (PEM) for random vibration, the precise integration method (PIM) for time history integration, etc, are introduced into the present research on dynamic analyses and optimum of various coupled vehicle and supporting structure systems based on the theoretical framework of random vibration. Furthermore some innovative schemes based on the above methodologies have been developed, which can be summarized as follows:
1. Vertical random vibration analysis of vehicle-pavement coupled systems
For vertical random vibration analysis of vehicle-pavement (or road) coupled system, the two-dimensional moving element method (MEM) is derived by using a coordinate system which moves with the vehicle. The pavement elements are regarded as conceptual elements that'flow'with the moving vehicle along the pavement in this coordinate system, and vehicle is static. It is never necessary to cross from one element into another, which avoids the updating of force or displacement vectors due to change of the contact point with the elements. It can be found that the element stiffness and damping matrices thus easily obtained are simply a revision of the corresponding static element stiffness and damping matrices by superposing the terms with the velocity, foundation parameter and other coupled effects. So the non-stationary random vibration can be transformed conveniently into a stationary one, and it is accurate and efficient.
2. The sensitivity analysis and optimum for vehicle stationary random vibration The complicated analysis process and costly computation efforts are always the mainly difficulties for the random vibration optimum design based on conventional methods, which lead to the difficulty of the random vibration sensitivity analysis. In this thesis, an accurate and efficient sensitivity analysis formula for optimizing the ride comfort of vehicle suspension system is derived. Based on the dynamic responses analysis using PEM, the random equations of motion with the right-hand side random acceleration is replaced by a pseudo acceleration excitation, thus various first and second orders of sensitivity formulas are calculated conveniently by differentiating these equations. Using the method the random dynamic sensitivity analysis is transformed into a deterministic one, and the optimal solutions when vehicle ride comfort is the objective function are derived by means of these flexibilities. The optimization efficiency and the computational accuracy are numerically justified.
3. Multi-objective stochastic dynamic optimum design for vehicles based on simulation technology
It is particularly unacceptable for stochastic dynamic optimum of structures in practical engineering field, which requires usually many re-analyses and complicated analyses process. Especially to multi-objective optimum, the unified and efficient sensitivity analysis method applied to the objective functions has not been well developed. In this thesis, the Kriging model is extended to vehicle multi-objective optimum problems, a method of filled function is set up to build the approximate mapping relationship between the design variables and the responses, and the random responses analysis is performed using the filled function instead of the objective function, with necessary modification for the filled function in every step to keep the precision. The optimization efficiency is thus enhanced remarkably by avoiding too many re-analyses. The multi-objective function is processed by means of the method of centers, i.e. by self-adaptively introducing an upper bound on each objective function that forms the level sets of the objective functions, and repeatedly calculating the center of the intersection sets consisting of the original constraint sets and the level sets of the objective functions.
4. The random vibration analysis and optimum design for vehicle-bridge coupled random vibration
For dynamic analysis of vehicle-bridge coupled system, the PEM has been applied to transform the random surface roughness into the superposition of a series of deterministic pseudo-harmonic surface unevenness. The PIM has also been extended to simulate the continuous variation of the contact forces, both in their magnitudes and positions, within each time step. As a result, the solution of the uniformly modulated, multi-point, different-phase, non-stationary random vibration can be obtained efficiently by means of PEM-PIM. An innovative method (PEM-PIM Based Sensitivity) for first and second order sensitivity analyses of structural random responses is developed based on PEM-PIM. For the random equations of motion, by replacing the right-hand side random excitation by the pseudo-excitation, various first and second order sensitivity formulae can be derived conveniently and accurately.
5. FEM-based random vibration analysis and associated mechanical behaviors study of vehicle-road/bridge coupled systems
This subject is concerned with many problems, including random vibration analysis, stochastic dynamic optimum and fatigue life estimation, and so on. Analysis of such random vibration mechanical behaviors has long been regarded as very difficult, particularly if finite element models with many degrees of freedom are used. Optimum design is even more difficult although it is of great concern and significance. To overcome these difficulties, some advanced computational mechanics methodology, such as PEM for random vibration, PIM for the numerical integration in the time domain or space domain and some efficient sensitivity analysis methods are used in this paper to study the random vibration mechanical behaviors in the vehicle engineering field. Some useful results about structure random fatigue life, vehicle dynamic impact influence and structure random dynamic optimum are obtained, and the efficiency and computational accuracy of the proposed methods are justified.
引文
[1]柳岩,管晓方,宋玉泉.中国轿车走向世界面临的关键问题.吉林大学学报(工学版),2009,39(1)：274-280
[2]余志生.汽车理论.北京：机械工业出版社,2009.
[3]中华人民共和国国家标准.工程结构可靠性设计统一标准(征求意见稿).北京,2006.
[4]Grandall S H. Random Vibration:The MIT Press,1958.
[5]李彤华,唐春海,于亚伦.爆破振动的频谱特征及其工程应用.工程爆破,2000,6(2)：1-5.
[6]张洪欣,林宁,林逸,傅炳锋.改善大客车行驶平顺性的研究.汽车工程,1987,2：52-61.
[7]沈林.基于小波方法的线性时变系统参数识别.(硕士学位论文),南京：南京航空航天大学,2006.
[8]王铁,张国忠,周淑文.路面不平度影响的的汽车驱动桥动载荷.东北大学学报(自然科学版),2003,24(1)：50-53.
[9]陶向华,黄晓明.人-车-路相互卓雍三质量车辆模型分析.交通运输工程学报,2004,4(3)：11-15.
[10]易当祥,吕国志,张驰.随机路面激励下车载无人机的载荷响应与仿真.飞机设计,2004(3)：21-24.
[11]邹晓华,张立军,郑春娇.车辆悬架系统振动仿真.辽宁工学院学报,2004,24(2)：37-40.
[12]王开云,蔡成标,徐志胜.基于频域方法的轨道随机振动特性及实验验证分析.机械工程学报,2005,41(11)：149-152.
[13]郭兴旺,邹家祥.对机械振动系统的六种动态响应分析方法评述.振动与冲击,1996,15(2)：43-46.
[14]张淼.结构动力响应分析的多重网格方法研究.吉林大学博士学位论文,2008.
[15]郑兆昌.机械振动.北京：机械工业出版社,1986.
[16]林家浩,张亚辉.随机振动的虚拟激励法[M].北京：科学出版社,2004.
[17]Lin J H, Zhang Y H. Seismic Random Vibration of Long-span Structures, In:Silva C W D, editor. Vibration and Shock Handbook. Boca Raton, Florida:CRC Press,2005.
[18]Lin J H, Zhao Y, Zhang Y H. Accurate and Highly Efficient Algorithms for Structural Stationary/non-stationary Random Responses. Computer Method in Applied Mechanics and Engineering.2001,191(1-2):103-111.
[19]Lin JH, Zhang YH, Li QS, Williams FW. Seismic Spatial Effects for Long-span Bridges,using the Pseudo Excitation Method. Engineering Structures 2004; 26(9):1207-1216.
[20]Lin JH, Lu X, Zhong WX. Dynamic Response of Jacket Platform to Random Waves. In:Schreffes, Zienkiewicz, editors. Computer Modeling in Ocean Engineering. New York:Taylor and Francis, Inc. 1988:539-545.
[21]Lin JH, Che WY, Yu YS. Structural Optimization on Geometrical Configuration and Element Sizing with Statical and Dynamical Constraints. Computers and Structures 1982; 15(5):507-515.
[22]钟万勰.结构动力方程的精细时程积分法.大连理工大学学报.1993,34(2)：131-136
[23]钟万勰.计算结构力学与最优控制.大连：大连理工大学出版社,1993.
[24]钟万勰.应用力学的辛数学方法.北京：高等教育出版社,2006.
[25]姚伟岸,钟万勰.辛弹性力学.北京：高等教育出版社,2001.
[26]钟万勰.卡尔曼-布西滤波的精细积分.大连理工大学学报,1999,39(2)：191-200.
[27]Huang D, Allen T T, Notz W I, et al. Sequential Kriging Optimization using Multiple_Fidelitv Evaluations. Struct. Multidisc. Optim.,2006,32(5):369-382.
[28]HASAN K, BABUR O, TUNCAY E. Effective Warpage Optimization of Thin Shell Plastic Parts using Response Surface Methodology and Genetic Algorithm.Int. Adv. Manuf. Technol.,2006, 27(5):468-472.
[29]DONALD R J, MATTHIAS S, WILLIAM J W. Efficient Global Optimization of Expensive Black-box Functions. Journal of Global optimization,1998,13:455-492.
[30]HAWE G I, SYKULSKI J K. A Hybrid One-then-two Stage Algorithm for Computationally Expensive Electromagnetic Design Optimization. Proceedings of the 9th Workshop on Optimization and Inverse Problems in Electromagnetics, Sorrento, Italy,2006, pp 191-192.
[31]Koh CG, Ong JSY, Chua DKH, Feng J. Moving Element Method for Train-track Dynamics.Int. J. Numer. Meth. Engrg.2003; 56(10):1549-1567
[32]公路桥梁抗震设计细则JTG/T B02-01-2008.北京：中华人民共和国交通运输部,2008.
[33]王连华,彭河星,金怡新,张辉.基于虚拟激励法的大跨度斜拉拱桥随机响应.公路工程,2008,33(2)：80-84.
[34]何晴光,杜永峰,程选生.基于虚拟激励法的消能减震结构随机响应分析.西北地震学报,2008,30(4)：366-368.
[35]孙建梅,叶继红,程文瀼.考虑空间相干的虚拟激励法在大跨度空间结构随机振动分析中的应用.铁道科学与工程学报,2009,4(5)：11-21.
[36]彭文海,谭平,候家健,周福霖.非对称双塔连体结构柔性连接体系参数研究.2009,29(1)：8-16.
[37]许林汕,赵林,葛耀军.超大型冷却塔随机风振响应分析.振动与冲击,2009,28(4)：180-193.
[38]李杰,秦玉英,赵旗,张伟.虚拟激励法在汽车振动分析中的应用.机械科学与技术,2009,28(3)：282-285.
[39]林家浩,张守云,吕峰,张亚辉.移动简谐荷载作用下桥梁响应的高效计算.计算力学学报,2006,23(4)：385-390.
[40]吕峰,林家浩,张亚辉.移动随机荷载作用下桥梁振动分析.振动与冲击,2008,27(12)：73-78.
[41]张志超,张亚辉,赵岩,林家浩.车桥系统非平稳随机振动的PEM-PIM算法.计算力学学报,2009,26(1)：26-32.
[42]吕彭民,和丽梅,尤晋闽.基于舒适性和轮胎动载的车辆悬架参数优化.中国公路学报,2007,20(1)：112-117.
[43]李士松,潘文军,杨旭.微型汽车五自由度模型动态仿真.计算机仿真,1998,15(1)：69-71.
[44]宋永刚.路面平整度均方差指标与行车舒适性的关系研究.路面机械与施工技术,2005,12：18-21.
[45]Gao W H. Dynamic Analysis of Coupled Road Vehicle and Long Span Cable-stayed Bridge System under Cross Winds. (A Thesis for the Degree of Doctor), HongKong:HongKong Polytechnic University,2003
[46]常志权,罗虹,褚志刚.谐波叠加路面输入模型的建立及数字模拟.重庆大学学报(自然科学版),2004,27(12)：5-8.
[47]Au F T K, Cheng Y S, Cheung Y K. Effects of Random Road Surface Roughness and Long-term Deflection of Pre-stressed Concrete Grider and Cable-stayed Bridges on Impact due to Moving Vehicle. Computes and Structures,2001,79:853-872.
[48]Schiehlen W, Hu B. Spectral Simulation and Shock Absorber Identification. International Journal of Non-Linear Mechanics,2003,38:161-171.
[49]孙建民.车辆主动悬架系统控制技术研究.(博士学位论文),哈尔滨：哈尔滨工程大学,2003.
[50]王其东.基于多体理论的汽车悬架系统分析、设计与控制研究.(博士学位论文),合肥：合肥工业大学,2002.
[51]张湘伟.一维路面模拟及其数值模拟方法.重庆大学学报,1998,11(1)：106-112.
[52]张亚欧,马吉盛,吴大林.基于Fourier逆变换法的路面不平度模拟.河北工业大学学报,2005,34(6)：66-69.
[53]张永林,李诗龙,杨建林.汽车道路随机不平顺的时序模型重构.武汉理工大学学报(交通科学与工程版),2005,29(6)：883-886.
[54]马训鸣,林晓焕.路面不平度的统计特性分析及建模研究.机床与液压,2004,7：99-100.
[55]侯占峰,鲁植雄.车轮随机动载性能的Simulink仿真分析.交通与计算机,2006,24(4)：92-94.
[56]Rick T. Ride Control-a Two-state Design for Heavy Vehicle Suspension. (A Thesis for the Degree of Doctor), Chicago:University of Illinois at Chicago,2001.
[57]吴业森,罗明廉.随机振动.北京：机械工业出版社,1989.
[58]林茂成,赵济海.GB 7031-1987车辆振动输入——路面平度表示方法.北京：中国标准出版社,1987.
[59]Youn I, Hac A. Semi-active Suspension with Adaptive Capability. Journal of Sound and Vibration, 1995,180(3):475-492.
[60]Thompson A G, Pearce CE M. Performance Index for a Preview Active Suspension Applied to a Quarter-car Model. Vehicle System Dynamics,2001,35(1):55-66.
[61]陶向华,黄晓明.人-车-路相互作用三质量车辆模型分析.交通运输工程学报,2004,4(3)：11-15.
[62]张洪信,尹玉川,牟红波.主动悬架改善重型车辆性能的方针研究.青岛大学学报,2003,18(2)：1-4.
[63]David J C. Fundamental Issues in Suspension Design for Heavy Road Vehicles. Vehicle System Dynamics,2001,35(4-5):319-360.
[64]牛军川,孙玲玲,张蔚波.随机路面激励输入下四自由度悬架的特性研究.中国公路学报,2003,16(4)：106-110.
[65]Abdelhady M B A. Aerodynamic Effects on Ride Comfort and Road Holding of Actively Suspended Vehicles. SEA Paper,2002-01-2205.
[66]沈铁军.时域内双轴载重汽车行驶平顺性建模仿真与实验研究.(硕士学位论文),长春：吉林大学,2006.
[67]倪晋尚,阮米庆.车辆的平顺性优化与仿真试验.现代机械,2006,2：8-10.
[68]Thompson A G, Davis B R. RMS Values for Force, Stoke and Tire Deflection in a Half-car Model with Preview Controlled Active Suspension. Vehicle System Dynamics,2003,39(3):245-253.
[69]Zhou H Y. Development and Control of an Automotive Smart Suspension System. (A Thesis for the Degree of Doctor), Toronto:University of Toronto,2002.
[70]Mohamed B, Marc J R. An Optimization Method Designed to Improve 3-D Vehicle Comfort and Road Holding Capability through the Use of Active and Semi-active Suspensions. Eur. J. Mech. A/Solids,2001,20:509-520.
[71]李强,周济.重型越野车的非平稳随机激励系统优化设计方法.机械强度,1998,20(1)45-52.
[72]冯锡曙,万叶青.车辆乘坐舒适性的评价指标及其发展.拖拉机,1990,8：13-16.
[73]马广发,赵六奇,卢士富.GB／T 4970-1996汽车平顺性随机输入行驶试验方法.北京：中国标准出版社,1996.
[74]韩万水,陈艾荣.侧风与桥梁振动对车辆行驶舒适性影响研究.土木工程学报,2008,41(4)：55-60.
[75]周华祥,曾霞文.车辆悬架系统的乘坐舒适性研究.湖南工业职业技术学院学报2006,6(2)：8-9.
[76]Fritz F.改善铁道车辆的舒适性.结构.设计,2003,4：8-15.
[77]胡振东,万华林.告诉车辆过桥时的舒适性分析.振动与冲击,2002,21(4)：102-105.
[78]赵又群,何小明,郭孔辉.汽车有路面激发的演变随机响应预测.机械工程学报,2004,40(1)：179-182.
[79]赵又群,郭孔辉,张桂玉.具有随机道路输入的驾驶员-汽车闭环系统的操纵安全性评价.中国机械工程,2000,11(4)：465-469.
[80]赵又群,张桂玉,郭孔辉.具有演变随机道路输入的驾驶员-汽车-道路闭环系统主动安全性的仿真评价.中国公路学报,1999,12(2)：105-109.
[81]陈刚.内腔声-结构耦合系统的数值模拟与优化设计.(博士学位论文),大连：大连理工大学,2008.
[82]曹群豪.军用客车车身骨架结构随机振动特性与疲劳强度分析.(硕士学位论文),上海：上海交通大学,2007.
[83]龙梁,胡爱华,范子杰.基于有限元仿真的特种越野车结构疲劳寿命预测.计算机仿真,2006,23(12)：253-256.
[84]王国平.多体系统动力学数值解法.计算机仿真,2006,23(12)：86-89.
[85]李俊峰,张雄,任革学.理论力学,北京：清华大学施普林格出版社,2001.
[86]Kane T R, Ryan R R, et al. Dynamics of Cantilever Beam Attached to a Moving Base. Journal of Guidance, Control and Dynamics,1987,10(2):139-151.
[87]洪嘉振.计算多体系统动力学.北京：高等教育出版社,1999.
[88]郭二生.空气悬架大客车操纵稳定性和行驶平顺性仿真与试验研究.(硕士学位论文),长春：吉林大学.
[89]夏禾.车辆与结构动力相互作用.北京：科学出版社,2002.
[90]石洪峰.时域内平衡悬架牵引车行驶平顺性仿真及试验研究.(硕士学位论文).长春：吉林大学,2005.
[91]杨波.计及车架弹性的多轴重型越野车整车动态性能研究.(博士学位论文),武汉：华中科技大学,2004.
[92]秦玉英.车辆行驶平顺性建模与仿真的新方法研究及应用.(博士学位论文).长春：吉林大学.
[93]彭献,刘晓晖,文桂林.基于虚拟激励法的变速行驶车辆振动分析.湖南大学学报：自然科学版.2007,34(11)：37-41.
[94]李杰,秦玉英,赵旗,张伟.用于分析车辆随机振动的一种新方法.机械设计.2009,10(4)：14-17.
[95]周劲松,李大光,沈钢,张祥韦.磁浮车辆运行平稳性的虚拟激励分析方法.交通运输工程学报.2008,8(1)：5-9.
[96]Tung C C. Random Response of Highway Bridges to Vehicle Loads. J.Engrg.Mech.Proc. ASCE93. 1967,93(5):73-94.
[97]L.Fryba, Non-Stationary Vibrations of Bridges under Random Moving Load, in Eighth Congress of the International Association for Bridge and Strucutral Engineering.1968:NewYork.
[98]L.Fryba. Non-Stationary Response of a Beam to a Moving Random Force. Journal of Sound and Vibration.1976,46(3):323-338.
[99]Iwankiewicz R, Sniady P. Vibration of a Beam under a Random Stream of Moving Forces. Journal of Structure Mechanics.1984,12:13-26.
[100]Ricciardi G. Random Vibration of Beam under Moving Loads. Journal of Engineering Mechanics-ASCE 1994,120:2361-2380.
[101]Wang R T, Lin T Y. Random Vibration of Multi-Span Timoshenko Beam due to a Moving Load. Journal of Sound and Vibration.1998,213:127-138.
[102]Sniady P, Biernat S, Sieniawska R, et al. Vibrations of The Beam due to a Load Moving with Stochastic Velocity. Probabilistic Engineering Mechanics.2001,16(1):53-59.
[103]Zibdeh H S, Rackwitz R. Moving Loads on Beams with General Boundary Conditions. Journal of Sound and Vibration.1996,195(1):85-102.
[104]Zibdeh H S, Abu-Hilal M. Stochastic Vibration of Laminated Composite Coated Beam Traversed by a Random Moving Load. Engineering Structures.2003,25(3):397-404.
[105]Zibdeh H S, Juma H S. Dynamic Response of a Rotating Beam Subjected to a Random Moving Load. Journal of Sound and Vibration.1999,223(5):741-758.
[106]Abu Hilal M, Zibdeh H S. Vibration Analysis of Beams with General Boundary Conditions Traversed by a Moving Force. Journal of Sound and Vibration.2000,229(2):377-388.
[107]Willis R Appendix of the Report of Commissioners Appointed to Inquire Application of Iron to Rail way Structures. His Majesty's Stationary Office, London,1849.
[108]曾庆元,郭向荣.列车桥梁时变系统振动分析理论与应用.北京：中国铁道出版社,1999.
[109]杨永斌,姚达忠.高速铁路车桥互制理论.台北：图文技术服务有限公司,2000.
[110]Wu Y S. Dynamic Interactions of Train-Rail-Bridge System under Normal and Seismic Conditions: (Ph.d Thesis). National Taiwan University:Taipei,2000.
[111]Chu K H, Garg V K, Wiriyachai A. Dynamic Interaction of Railway Train and Bridge. Vehicle
System Dynamics.1980,9(4):207-236.
[112]Wiriyachai A, Chu K H, Gary V K. Impact Study by Various Bridge Models. Earthquake Engineering and Structural Dynamics.1982,10(1):31-45.
[113]Chu K H, Garg V K, Dhar C L. Railway-Bridge Impact:Simplified Train and Bridge Model. Journal of the Structural Division, ASCE.1979,105(9):1823-1844.
[114]Bhatti M H. Vertical and Lateral Dynamic Response of Railway Bridges due to Nonlinear Vehicle and Track Irregularities.(Ph.d Thesis). Chicago:Illinois Institute of Technology:,1982.
[115]Wang T L, Chu K H. Railway Bridge Vehicle Interaction Studies with New Vehicle Model. Journal of Structural Engineering.1991,117(7):2099-2116.
[116]Wang T L, Impact and Fatigue in Open Deck Steel Truss and Ballasted Prestressed Concrete Railway Bridges..(Ph.d Thesis) Chicago:Illinois Institute of Technology,1984.
[117]李小珍.高速铁路列车桥梁系统耦合振动理论及应用研究.(博士学位论文),成都：西南交通大学,2000.
[118]宁晓骏.高速铁路列车桥梁基础空间耦合振动研究.(博士学位论文).成都：西南交通大学,1998.
[119]沈锐利.高速铁路桥梁与车辆耦合振动研究.(博士学位论文).成都：西南交通大学,1998.
[120]何发礼.高速铁路中下跨度曲线桥梁车桥耦合振动研究.(博士学位论文).成都：西南交通大学,1999.
[121]单德山.高速铁路曲线桥梁车桥耦合振动分析及大跨度曲线桥梁设计研究.(博士学位论文).成都：西南交通大学,1999.
[122]夏禾,陈英俊.车—粱—墩体系动力相互作用分析.土木工程学报.1992,25(2)：3—12.
[123]张楠,夏禾.地震对多跨简支桥梁上列车运行安全的影响.世界地震工程.2001,17(4)：43-49.
[124]Xia H, Xu Y L, Chan T H T. Dynamic Interaction of Long Suspension Bridges with Running Trains. Journal of Sound and Vibration.2000,237(2):263-280.
[125]曾庆元.弹性系统动力学总势能不变值原理.华中理工大学学报.2000,28(1)：1—3.
[126]郭向荣,曾庆元.高速铁路结合粱桥与列车系统振动分析模型.华中理工大学学报.2000,28(3)：60-62.
[127]曾庆元.列车桥梁时变系统的横向振动分析.铁道学报.1991,13(2)：38-46.
[128]程庆国,许慰平.大跨度铁路斜拉桥列车走性行探讨,武汉：全国桥梁结构学术大会.1992.
[129]程庆国,潘家英.大跨度铁路斜拉桥竖向刚度分析,武汉：全国桥梁结构学术大会.1992.
[130]许慰平.大跨度铁路桥梁车桥空间耦合振动研究.(博士学位论文).北京：铁道科学研究院,1988.
[131]高芒芒.高速铁路列车—线路—桥梁耦合振动及列车走行性研究.北京：铁道科学研究院,2002.
[132]高岩,沈锐利,柯在田,张煅.提速对桥梁振动与车辆过桥走行性的影响以及对策.中国铁道科学.2000,21(2)：19-25.
[133]王刚,曹雪琴.高速铁路大跨度斜拉桥车桥动力分析.上海铁道大学学报.2000,21(8)：7—11.
[134]Au F T K, Cheng Y S, Cheung Y K. Effects of Random Road Surface Roughness and Long-Term Deflection of Prestressed Concrete Girder and Cable-Stayed Bridges on Impact due to Moving Vehicles. Computers & Structures.2001,79(8):853-872.
[135]Au F T K, Wang J J, Cheung Y K. Impact Study of Cable-Stayed Railway Bridge with Random Rail Irregularities. Engineering Structures.2002,24(5):529-541.
[136]王解军.运行列车作用下桥梁的动力反应.(博士学位论文),长沙：湖南大学：2000.
[137]晋智斌.车_线_桥耦合系统及车_桥随机振动.(博士学位论文),成都：西南交通大学,2007.
[138]王旺平,胡先龙.汽车悬架随机疲劳寿命计算模型.武汉工业学院学报,2007,26(2)：40-42.
[139]倪侃,张圣坤,钱仍影.结构构件疲劳损伤累积的可靠性分析.中国造船,1997,4：53-60.
[140]徐灏.疲劳强度.北京：高等教育出版社,1988.
[141]倪侃.结构疲劳可靠性二维概率Miner准则及其应用.(博士学位论文),北京：北京航空航天大学,1994.
[142]程育人,缪龙秀,侯炳麟.疲劳强度.北京：中国铁道出版社,1990.
[143]吕彭民.宽带随机载荷谱下结构疲劳寿命的计算.长安大学学报,2004,24(1)：76-78.
[144]吴利辉,陈昌明.基于随机振动方法的白车身疲劳寿命研究.北京汽车,2007,5：17-22.
[145]吴义生.随机载荷下的疲劳损伤计算公式.海洋工程,1994,21(1)：94-103.
[146]赵文礼,李忠学,赵邦华.客车随机响应计算与车轴疲劳寿命预测.1998,20(4)：120-125.
[147]周华飞,蒋建群,毛根海.路面不平度引起的车辆动荷载分析.中国市政工程,2002,3：10-13.
[148]鲍钟岳.公路桥涵设计通用规范及条文说明JTG D60-2004.北京：人民交通出版社,1987.
[149]吴启宏.动力系数的影响因素实验研究.中国公路学报,1991,4(2)：57-64.
[150]毛清华,项海帆.公路桥梁车辆振动的理论和实验研究.土木工程学报,1990,23(3)：61-68.
[151]陈彦江,刘保忠,傅金科.桥面平整度对桥梁振动影响的实验研究.东北三省公路学会年会,1993,120-125.
[152]Hutton S G, Cheung Y K. Dynamic Response of Single Span Highway Bridges. Earthquake Engineering and Structural Dynamic,1979,7:543-553.
[153]郭毅之,金先龙,丁俊宏,杨洪杰.不平整路面上的非平稳车流荷载研究及应用.岩土力学,2007,28(2)：395-398.
[154]王解军,张伟,吴卫祥.重型汽车荷载作用下简支桥梁的动力反映分析.中南公路工程,2005,30(2)：55-58.
[155]余卓平,黄锡朋,张洪欣.减轻重型汽车对道路的损伤—汽车悬架优化设计.1994,7(3)：83-87.
[156]王钧利,马春燕.公路桥梁受车辆动力作用的疲劳可靠性分析.重庆交通学院学报,1998,17(3)：31-37.
[157]Michael J M, Mahoney J P. Measurements on Dynamic Effects of Dual and Wide base Single Tyres. Technicla Research Centre of Finland,1992.
[158]Cassis J H, Schmit L A. Optimal Structural Designs with Dynamic Constrains. ASCE J Struct Div, 1976,102:2053-2071.
[159]Li G, Liu X, Liu Y, Yue Q J. Optimum Design of Ice-Resistant Offshore Jacket Platforms in the Bohai Gulf in Consideration of Fatigue Life of Tubular Joints. Ocean Engineering.2008,35(5-6): 484-493.
[160]Li G, Liu X, Yue Q J. An Efficient Reliability Evaluation Approach of Human Exposure to Ice-Induced Vibration of Offshore Platforms. In:Proc. Of International Conference on Enhancement and Promotion of Computational Method in Engineering Science and Mechanics (CMECM 2006),2006.
[161]Li G, Liu X, Cheng G D. Acceleration-Based Optimum Design of Offshore Platforms Subjected to Ice Load. IN:Proc. of 9th International Conference on Computational Structures Technology (CST 2008), Athens Greece.2008.
[162]Li G, Liu X, Liu Y. Optimum Design of Ice-Resistant Offshore Jacket Platforms in Consideration of Fatigue Life. In:Proc. of 7th World Congress on Computational Mechanics, Los Angeles, California, USA.2006.
[163]Li G, Lu H Y, Liu X. A Hybrid Simulated Annealing and Optimality Criteria Method for Optimum Design of RC Buildings. Structural Engineering and Mechanics an International Journal.2008 (under review).
[164]国巍,李宏男.随机输入下附属结构的位置优化.振动与冲击,2008,27(4)：23-26.
[165]张延年,李宏男.双向耦合地震作用下滑移隔震结构振动控制及其优化研究.地震工程与工程振动.2007,27(1)：141-146.
[166]柳国环,李宏男.高压输电塔-线体系风致动力响应分析与优化控制.中国电机工程学报.2008,28(19)：131-137.
[167]段红杰,陶浩.汽车双层隔振系统的随机振动隔离及参数优化.机械设计与制造.2007,13(3)：79-82.
[168]王春林,吕志涛.核筒悬挂结构随机动力响应的参数优化设计.工业建筑.2007,37(10)：28-32.
[169]田四朋,唐国金,雷勇军.非平稳随机激励下基于动力可靠性的结构优化设计.振动与冲击.2004,23(3)：42-49.
[170]田四朋,任钧国,张书俊.稳态随机过程激励下基于首次超越破坏的结构优化设计.国防科技大学学报.2002,5(1)：171-181.
[171]Rao S S. Oprimization of Airplane Wing Structures under Gust Loads. Computers and Structures, 1985,21(3):741-749.
[172]Rao S S. Oprimization of Airplane Wing Structures under Taxiing Loads. Computers and Structures, 1985,26(3):467-479.
[173]童卫华,姜节胜,顾松年.一种以均方响应作为约束的动力学设计方法.应用力学学报,1996,13(3)：94-98.
[174]童卫华,姜节胜.结构在随机激励下的一种动力学设计方法.机械强度.1996,18(2)：6-10.
[175]陈建军,车建文,崔明涛,戴君,马洪波.结构动力优化设计述评与展望.力学进展,2001,31(2)：181-192.
[176]Fox R L, Kapoor M P. Rates of Change of Eigenvalue and Eigenvectors. Journal AIAA,1968,6(12): 2426-2429.
[177]Rogers L C. Derivatives of Eigenvalues and Eigenvectors. Journal AIAA,1970,8(5):943-944.
[178]Neslon R B. Simplified Calculation of Eigenvector Derivatives. Journal AIAA,1976,14(9): 1201-1205.
[179]林家浩.结构动力优化中的灵敏度分析.震动与冲击,1985,4(1)：1-6.
[180]林树枝,程耿东.动力响应灵敏度分析的振型空间法.地震工程与振动工程,1990,10(3)：
57-64.
[181]林树枝,程耿东.结构动力问题的灵敏度分析及动力优化设计和CAD.(博士学位论文),大连：大连理工大学,1988.
[182]林树枝,程耿东.求谐振动力响应及其灵敏度分析的直接迭代法.计算结构力学及其应用,1990,7(2)：85-91.
[183]葛健全,唐乾刚.减振支架结构动力响应的灵敏度分析.(硕士学位论文),长沙：国防科学技术大学,2004.
[184]葛健全,唐乾刚,雷勇军.减振支架结构随机响应的灵敏度分析.北京：首届全国航空航天领域中的力学问题学术讨论会论文集.2003.
[185]Beliveau J G, Cogan S, Lallement G, Ayer F. Iterative Least-Squares Calculation for Modal Eigenvector Sensitivity. AIAA Journal,1996,34(2):385-391.
[186]Dutla A, Ranakrishnan C V. Accurate Computation of Design Sensitivities for Structures under Transient Dynamic Loads with Constraints on Stresses. Computers and Structures,1998,66(4): 463-472.
[187]姚昌仁,麻永平.结构随机激励的响应灵敏度分析.力学学报.1990,22(1)：438-444.
[186]乔红威,吕振宙.随机激励下随机结构动力可靠性灵敏度分析.振动工程学报.2008,21(4)：404-408.
[189]Durbin F. Numerical Inversion of Laplace Transforms:an Efficient Improvement to Dubner and Abate's method. Computer Journal,1974,17(4):371-376.
[190]Zimoch Z. Sensitivity Analysis of Vibrating Systems. Journal of Sound and Vibration,1987,115(3): 447-458.
[191]Lou P, Zeng Q Y. Formulation of Equations of Motion of Finite Element Form for Vehicle-track-bridge Interaction System with Two Type of Vehicle Model. International Journal for Numerical Methods in Engineering,2005,62:435-474.
[192]Xia H. Dynamic Interactions of Long Suspension Bridges with Running Trains. Journal of Sound and Vibration,2002,237(2):263-80.
[193]Xiao YL, Noda NA. Analyses of Dynamic Response of Vehicle and Track Coupling System with Random Irregularity of Track Vertical Profile. Journal of Sound and Vibration,2002,258(1): 147-165.
[194]翟婉明.车辆-轨道耦合动力学[M].北京：中国铁道出版社,2002.
[195]赵济海.路面平度谱分析应用研究报告.长春汽车研究所整车研究室,1985.
[196]吕峰.车辆与结构相互作用随机动力分析.(博士学术论文),大连：大连理工大学,2008.
[197]Kim S M, Roesset JM. Moving Loads on a Pate on Elastic Foundation. Journal of Engineering Mechanics,1998,124(9):1010-1017.
[198]Fryba L. Vibration of Solid and Structures Under Moving Loads. London:Thomas Telford,1999.
[199]Huang X M, Deng X J. The Mechanical Analysis of Plate on Visco-elastic Winkler Foundation Under Moving load. Journal of Chongqing Jiaotong University,1990,2:45-51.
[200]Sun L, Deng X J. Steady Response of Infinite Plate on Visco-elastic Kelvin Foundation to Moving load. Chinese Journal of Geotechnical Engineering,1997,2:14-22.
[201]Lou P, Zeng Q Y. Finite Element Analysis of Slab Track Subjected to Moving load. Journal of Traffic and Transportation Engineering,2004,4 (1):29-33.
[202]Jiang J Q, Zhou H F. Steady State Response of Infinite Plate on Visco-elastic Foundation Subjected to Moving Load. China Journal of Highway and Transport,2006,19(1):6-11.
[203]Koh C G, Ong J S Y, Chua D K H, Feng J. Moving Element Method for Train-track Dynamic. International Journal for Numerical Methods in Engineering,2003,56(10):1549-1567.
[204]Chen Y H, Huang Y H. Dynamic Stiffness of Infinite Timoshenko Beam on Viscoelastic Foundation in Moving Co-ordinate. International Journal for Numerical Methods in Engineering,2000,48:1-18.
[205]Beliveau J G, Cogan S, Lallement G, Ayer F. Iterative Least-squares Calculation for Modal Eigenvector Sensitivity. American Institute of Aeronautics and Astronautics Journal,1996,34(2): 385-391.
[206]Dutla A, Ranakrishnan C V. Accurate Computation of Design Sensitivities for Structures under Transient Dynamic Loads with Constraints on Stresses. Computers and Structures,1998,66(4): 463-472.
[207]Hrovat D. Optimal active suspensions for 3D vehicle models. Proceedings of American Control Conference,1991,2:1534-1541.
[208]Chen S H, Pan H H. Design Sensitivity Analysis of Vibration Modes by Finite Element Perturbation. In:Proceedings of 4th MAC,1986.
[209]He Y P, Mcphee J. Multidisciplinary Design Optimization of Mechatronic Vehicles with Active Suspensions. Journal of Sound and Vibration,2005,28(3):217-241.
[210]Naude A F, Snyman J A. Optimization of Road Vehicle Passive Suspension systems. Part 2. Qualification and case study. Applied Mathematical Modeling,2003,27(4):263-274.
[211]王洪礼,葛根,许佳.汽车半主动悬架随机振动稳定性与可靠性分析.机械强度,2009,31(3)：170-173.
[212]李兴斯,张崎,谭涛.多目标结构优化设计的中心法.力学学报,2005,37(5)：606-610.
[213]Kim C W, Kawatani W, Kwon Y R. Impact Coefficient of Reinforced Concrete Slab on a Steel Girder Bridge. Engineering Structures,2007,29(4):576-590.
[214]龚志浩.十五期间大中型客车需求预测.客车技术与研究,2001,23(5)：1-2.
[215]Der Kiureghian A, Neuenhofer A. Response Spectrum Method for Multi-Support Seismic Excitations. Earthquake Eng. and Struct. Dyn.,1992,21:713～740
[216]Ernesto H Z, Vanmarcke E H. Seismic Random Vibration Analysis of Multi-Support Structural Systems. ASCE, Journal of Engineering Mechanics,1994,120:1107～1128
[217]姚卫星.结构疲劳寿命分析.北京：国防工业出版社,2003.
[218]张志超,赵岩,林家浩.车桥耦合系统非平稳随机振动分析.振动工程学报.2007,20(5)：439-446.
[219]张志超,张亚辉,林家浩.车桥耦合系统非平稳随机振动分析的虚拟激励-精细积分法.工程力学.2008.25(11)：197-204.
[220]蔡坤.基于骨重建理论的连续体结构拓扑优化方法.(博士学术论文),大连：大连理工大学,2008
[2]余志生.汽车理论.北京：机械工业出版社,2009.
[3]中华人民共和国国家标准.工程结构可靠性设计统一标准(征求意见稿).北京,2006.
[4]Grandall S H. Random Vibration:The MIT Press,1958.
[5]李彤华,唐春海,于亚伦.爆破振动的频谱特征及其工程应用.工程爆破,2000,6(2)：1-5.
[6]张洪欣,林宁,林逸,傅炳锋.改善大客车行驶平顺性的研究.汽车工程,1987,2：52-61.
[7]沈林.基于小波方法的线性时变系统参数识别.(硕士学位论文),南京：南京航空航天大学,2006.
[8]王铁,张国忠,周淑文.路面不平度影响的的汽车驱动桥动载荷.东北大学学报(自然科学版),2003,24(1)：50-53.
[9]陶向华,黄晓明.人-车-路相互卓雍三质量车辆模型分析.交通运输工程学报,2004,4(3)：11-15.
[10]易当祥,吕国志,张驰.随机路面激励下车载无人机的载荷响应与仿真.飞机设计,2004(3)：21-24.
[11]邹晓华,张立军,郑春娇.车辆悬架系统振动仿真.辽宁工学院学报,2004,24(2)：37-40.
[12]王开云,蔡成标,徐志胜.基于频域方法的轨道随机振动特性及实验验证分析.机械工程学报,2005,41(11)：149-152.
[13]郭兴旺,邹家祥.对机械振动系统的六种动态响应分析方法评述.振动与冲击,1996,15(2)：43-46.
[14]张淼.结构动力响应分析的多重网格方法研究.吉林大学博士学位论文,2008.
[15]郑兆昌.机械振动.北京：机械工业出版社,1986.
[16]林家浩,张亚辉.随机振动的虚拟激励法[M].北京：科学出版社,2004.
[17]Lin J H, Zhang Y H. Seismic Random Vibration of Long-span Structures, In:Silva C W D, editor. Vibration and Shock Handbook. Boca Raton, Florida:CRC Press,2005.
[18]Lin J H, Zhao Y, Zhang Y H. Accurate and Highly Efficient Algorithms for Structural Stationary/non-stationary Random Responses. Computer Method in Applied Mechanics and Engineering.2001,191(1-2):103-111.
[19]Lin JH, Zhang YH, Li QS, Williams FW. Seismic Spatial Effects for Long-span Bridges,using the Pseudo Excitation Method. Engineering Structures 2004; 26(9):1207-1216.
[20]Lin JH, Lu X, Zhong WX. Dynamic Response of Jacket Platform to Random Waves. In:Schreffes, Zienkiewicz, editors. Computer Modeling in Ocean Engineering. New York:Taylor and Francis, Inc. 1988:539-545.
[21]Lin JH, Che WY, Yu YS. Structural Optimization on Geometrical Configuration and Element Sizing with Statical and Dynamical Constraints. Computers and Structures 1982; 15(5):507-515.
[22]钟万勰.结构动力方程的精细时程积分法.大连理工大学学报.1993,34(2)：131-136
[23]钟万勰.计算结构力学与最优控制.大连：大连理工大学出版社,1993.
[24]钟万勰.应用力学的辛数学方法.北京：高等教育出版社,2006.
[25]姚伟岸,钟万勰.辛弹性力学.北京：高等教育出版社,2001.
[26]钟万勰.卡尔曼-布西滤波的精细积分.大连理工大学学报,1999,39(2)：191-200.
[27]Huang D, Allen T T, Notz W I, et al. Sequential Kriging Optimization using Multiple_Fidelitv Evaluations. Struct. Multidisc. Optim.,2006,32(5):369-382.
[28]HASAN K, BABUR O, TUNCAY E. Effective Warpage Optimization of Thin Shell Plastic Parts using Response Surface Methodology and Genetic Algorithm.Int. Adv. Manuf. Technol.,2006, 27(5):468-472.
[29]DONALD R J, MATTHIAS S, WILLIAM J W. Efficient Global Optimization of Expensive Black-box Functions. Journal of Global optimization,1998,13:455-492.
[30]HAWE G I, SYKULSKI J K. A Hybrid One-then-two Stage Algorithm for Computationally Expensive Electromagnetic Design Optimization. Proceedings of the 9th Workshop on Optimization and Inverse Problems in Electromagnetics, Sorrento, Italy,2006, pp 191-192.
[31]Koh CG, Ong JSY, Chua DKH, Feng J. Moving Element Method for Train-track Dynamics.Int. J. Numer. Meth. Engrg.2003; 56(10):1549-1567
[32]公路桥梁抗震设计细则JTG/T B02-01-2008.北京：中华人民共和国交通运输部,2008.
[33]王连华,彭河星,金怡新,张辉.基于虚拟激励法的大跨度斜拉拱桥随机响应.公路工程,2008,33(2)：80-84.
[34]何晴光,杜永峰,程选生.基于虚拟激励法的消能减震结构随机响应分析.西北地震学报,2008,30(4)：366-368.
[35]孙建梅,叶继红,程文瀼.考虑空间相干的虚拟激励法在大跨度空间结构随机振动分析中的应用.铁道科学与工程学报,2009,4(5)：11-21.
[36]彭文海,谭平,候家健,周福霖.非对称双塔连体结构柔性连接体系参数研究.2009,29(1)：8-16.
[37]许林汕,赵林,葛耀军.超大型冷却塔随机风振响应分析.振动与冲击,2009,28(4)：180-193.
[38]李杰,秦玉英,赵旗,张伟.虚拟激励法在汽车振动分析中的应用.机械科学与技术,2009,28(3)：282-285.
[39]林家浩,张守云,吕峰,张亚辉.移动简谐荷载作用下桥梁响应的高效计算.计算力学学报,2006,23(4)：385-390.
[40]吕峰,林家浩,张亚辉.移动随机荷载作用下桥梁振动分析.振动与冲击,2008,27(12)：73-78.
[41]张志超,张亚辉,赵岩,林家浩.车桥系统非平稳随机振动的PEM-PIM算法.计算力学学报,2009,26(1)：26-32.
[42]吕彭民,和丽梅,尤晋闽.基于舒适性和轮胎动载的车辆悬架参数优化.中国公路学报,2007,20(1)：112-117.
[43]李士松,潘文军,杨旭.微型汽车五自由度模型动态仿真.计算机仿真,1998,15(1)：69-71.
[44]宋永刚.路面平整度均方差指标与行车舒适性的关系研究.路面机械与施工技术,2005,12：18-21.
[45]Gao W H. Dynamic Analysis of Coupled Road Vehicle and Long Span Cable-stayed Bridge System under Cross Winds. (A Thesis for the Degree of Doctor), HongKong:HongKong Polytechnic University,2003
[46]常志权,罗虹,褚志刚.谐波叠加路面输入模型的建立及数字模拟.重庆大学学报(自然科学版),2004,27(12)：5-8.
[47]Au F T K, Cheng Y S, Cheung Y K. Effects of Random Road Surface Roughness and Long-term Deflection of Pre-stressed Concrete Grider and Cable-stayed Bridges on Impact due to Moving Vehicle. Computes and Structures,2001,79:853-872.
[48]Schiehlen W, Hu B. Spectral Simulation and Shock Absorber Identification. International Journal of Non-Linear Mechanics,2003,38:161-171.
[49]孙建民.车辆主动悬架系统控制技术研究.(博士学位论文),哈尔滨：哈尔滨工程大学,2003.
[50]王其东.基于多体理论的汽车悬架系统分析、设计与控制研究.(博士学位论文),合肥：合肥工业大学,2002.
[51]张湘伟.一维路面模拟及其数值模拟方法.重庆大学学报,1998,11(1)：106-112.
[52]张亚欧,马吉盛,吴大林.基于Fourier逆变换法的路面不平度模拟.河北工业大学学报,2005,34(6)：66-69.
[53]张永林,李诗龙,杨建林.汽车道路随机不平顺的时序模型重构.武汉理工大学学报(交通科学与工程版),2005,29(6)：883-886.
[54]马训鸣,林晓焕.路面不平度的统计特性分析及建模研究.机床与液压,2004,7：99-100.
[55]侯占峰,鲁植雄.车轮随机动载性能的Simulink仿真分析.交通与计算机,2006,24(4)：92-94.
[56]Rick T. Ride Control-a Two-state Design for Heavy Vehicle Suspension. (A Thesis for the Degree of Doctor), Chicago:University of Illinois at Chicago,2001.
[57]吴业森,罗明廉.随机振动.北京：机械工业出版社,1989.
[58]林茂成,赵济海.GB 7031-1987车辆振动输入——路面平度表示方法.北京：中国标准出版社,1987.
[59]Youn I, Hac A. Semi-active Suspension with Adaptive Capability. Journal of Sound and Vibration, 1995,180(3):475-492.
[60]Thompson A G, Pearce CE M. Performance Index for a Preview Active Suspension Applied to a Quarter-car Model. Vehicle System Dynamics,2001,35(1):55-66.
[61]陶向华,黄晓明.人-车-路相互作用三质量车辆模型分析.交通运输工程学报,2004,4(3)：11-15.
[62]张洪信,尹玉川,牟红波.主动悬架改善重型车辆性能的方针研究.青岛大学学报,2003,18(2)：1-4.
[63]David J C. Fundamental Issues in Suspension Design for Heavy Road Vehicles. Vehicle System Dynamics,2001,35(4-5):319-360.
[64]牛军川,孙玲玲,张蔚波.随机路面激励输入下四自由度悬架的特性研究.中国公路学报,2003,16(4)：106-110.
[65]Abdelhady M B A. Aerodynamic Effects on Ride Comfort and Road Holding of Actively Suspended Vehicles. SEA Paper,2002-01-2205.
[66]沈铁军.时域内双轴载重汽车行驶平顺性建模仿真与实验研究.(硕士学位论文),长春：吉林大学,2006.
[67]倪晋尚,阮米庆.车辆的平顺性优化与仿真试验.现代机械,2006,2：8-10.
[68]Thompson A G, Davis B R. RMS Values for Force, Stoke and Tire Deflection in a Half-car Model with Preview Controlled Active Suspension. Vehicle System Dynamics,2003,39(3):245-253.
[69]Zhou H Y. Development and Control of an Automotive Smart Suspension System. (A Thesis for the Degree of Doctor), Toronto:University of Toronto,2002.
[70]Mohamed B, Marc J R. An Optimization Method Designed to Improve 3-D Vehicle Comfort and Road Holding Capability through the Use of Active and Semi-active Suspensions. Eur. J. Mech. A/Solids,2001,20:509-520.
[71]李强,周济.重型越野车的非平稳随机激励系统优化设计方法.机械强度,1998,20(1)45-52.
[72]冯锡曙,万叶青.车辆乘坐舒适性的评价指标及其发展.拖拉机,1990,8：13-16.
[73]马广发,赵六奇,卢士富.GB／T 4970-1996汽车平顺性随机输入行驶试验方法.北京：中国标准出版社,1996.
[74]韩万水,陈艾荣.侧风与桥梁振动对车辆行驶舒适性影响研究.土木工程学报,2008,41(4)：55-60.
[75]周华祥,曾霞文.车辆悬架系统的乘坐舒适性研究.湖南工业职业技术学院学报2006,6(2)：8-9.
[76]Fritz F.改善铁道车辆的舒适性.结构.设计,2003,4：8-15.
[77]胡振东,万华林.告诉车辆过桥时的舒适性分析.振动与冲击,2002,21(4)：102-105.
[78]赵又群,何小明,郭孔辉.汽车有路面激发的演变随机响应预测.机械工程学报,2004,40(1)：179-182.
[79]赵又群,郭孔辉,张桂玉.具有随机道路输入的驾驶员-汽车闭环系统的操纵安全性评价.中国机械工程,2000,11(4)：465-469.
[80]赵又群,张桂玉,郭孔辉.具有演变随机道路输入的驾驶员-汽车-道路闭环系统主动安全性的仿真评价.中国公路学报,1999,12(2)：105-109.
[81]陈刚.内腔声-结构耦合系统的数值模拟与优化设计.(博士学位论文),大连：大连理工大学,2008.
[82]曹群豪.军用客车车身骨架结构随机振动特性与疲劳强度分析.(硕士学位论文),上海：上海交通大学,2007.
[83]龙梁,胡爱华,范子杰.基于有限元仿真的特种越野车结构疲劳寿命预测.计算机仿真,2006,23(12)：253-256.
[84]王国平.多体系统动力学数值解法.计算机仿真,2006,23(12)：86-89.
[85]李俊峰,张雄,任革学.理论力学,北京：清华大学施普林格出版社,2001.
[86]Kane T R, Ryan R R, et al. Dynamics of Cantilever Beam Attached to a Moving Base. Journal of Guidance, Control and Dynamics,1987,10(2):139-151.
[87]洪嘉振.计算多体系统动力学.北京：高等教育出版社,1999.
[88]郭二生.空气悬架大客车操纵稳定性和行驶平顺性仿真与试验研究.(硕士学位论文),长春：吉林大学.
[89]夏禾.车辆与结构动力相互作用.北京：科学出版社,2002.
[90]石洪峰.时域内平衡悬架牵引车行驶平顺性仿真及试验研究.(硕士学位论文).长春：吉林大学,2005.
[91]杨波.计及车架弹性的多轴重型越野车整车动态性能研究.(博士学位论文),武汉：华中科技大学,2004.
[92]秦玉英.车辆行驶平顺性建模与仿真的新方法研究及应用.(博士学位论文).长春：吉林大学.
[93]彭献,刘晓晖,文桂林.基于虚拟激励法的变速行驶车辆振动分析.湖南大学学报：自然科学版.2007,34(11)：37-41.
[94]李杰,秦玉英,赵旗,张伟.用于分析车辆随机振动的一种新方法.机械设计.2009,10(4)：14-17.
[95]周劲松,李大光,沈钢,张祥韦.磁浮车辆运行平稳性的虚拟激励分析方法.交通运输工程学报.2008,8(1)：5-9.
[96]Tung C C. Random Response of Highway Bridges to Vehicle Loads. J.Engrg.Mech.Proc. ASCE93. 1967,93(5):73-94.
[97]L.Fryba, Non-Stationary Vibrations of Bridges under Random Moving Load, in Eighth Congress of the International Association for Bridge and Strucutral Engineering.1968:NewYork.
[98]L.Fryba. Non-Stationary Response of a Beam to a Moving Random Force. Journal of Sound and Vibration.1976,46(3):323-338.
[99]Iwankiewicz R, Sniady P. Vibration of a Beam under a Random Stream of Moving Forces. Journal of Structure Mechanics.1984,12:13-26.
[100]Ricciardi G. Random Vibration of Beam under Moving Loads. Journal of Engineering Mechanics-ASCE 1994,120:2361-2380.
[101]Wang R T, Lin T Y. Random Vibration of Multi-Span Timoshenko Beam due to a Moving Load. Journal of Sound and Vibration.1998,213:127-138.
[102]Sniady P, Biernat S, Sieniawska R, et al. Vibrations of The Beam due to a Load Moving with Stochastic Velocity. Probabilistic Engineering Mechanics.2001,16(1):53-59.
[103]Zibdeh H S, Rackwitz R. Moving Loads on Beams with General Boundary Conditions. Journal of Sound and Vibration.1996,195(1):85-102.
[104]Zibdeh H S, Abu-Hilal M. Stochastic Vibration of Laminated Composite Coated Beam Traversed by a Random Moving Load. Engineering Structures.2003,25(3):397-404.
[105]Zibdeh H S, Juma H S. Dynamic Response of a Rotating Beam Subjected to a Random Moving Load. Journal of Sound and Vibration.1999,223(5):741-758.
[106]Abu Hilal M, Zibdeh H S. Vibration Analysis of Beams with General Boundary Conditions Traversed by a Moving Force. Journal of Sound and Vibration.2000,229(2):377-388.
[107]Willis R Appendix of the Report of Commissioners Appointed to Inquire Application of Iron to Rail way Structures. His Majesty's Stationary Office, London,1849.
[108]曾庆元,郭向荣.列车桥梁时变系统振动分析理论与应用.北京：中国铁道出版社,1999.
[109]杨永斌,姚达忠.高速铁路车桥互制理论.台北：图文技术服务有限公司,2000.
[110]Wu Y S. Dynamic Interactions of Train-Rail-Bridge System under Normal and Seismic Conditions: (Ph.d Thesis). National Taiwan University:Taipei,2000.
[111]Chu K H, Garg V K, Wiriyachai A. Dynamic Interaction of Railway Train and Bridge. Vehicle
System Dynamics.1980,9(4):207-236.
[112]Wiriyachai A, Chu K H, Gary V K. Impact Study by Various Bridge Models. Earthquake Engineering and Structural Dynamics.1982,10(1):31-45.
[113]Chu K H, Garg V K, Dhar C L. Railway-Bridge Impact:Simplified Train and Bridge Model. Journal of the Structural Division, ASCE.1979,105(9):1823-1844.
[114]Bhatti M H. Vertical and Lateral Dynamic Response of Railway Bridges due to Nonlinear Vehicle and Track Irregularities.(Ph.d Thesis). Chicago:Illinois Institute of Technology:,1982.
[115]Wang T L, Chu K H. Railway Bridge Vehicle Interaction Studies with New Vehicle Model. Journal of Structural Engineering.1991,117(7):2099-2116.
[116]Wang T L, Impact and Fatigue in Open Deck Steel Truss and Ballasted Prestressed Concrete Railway Bridges..(Ph.d Thesis) Chicago:Illinois Institute of Technology,1984.
[117]李小珍.高速铁路列车桥梁系统耦合振动理论及应用研究.(博士学位论文),成都：西南交通大学,2000.
[118]宁晓骏.高速铁路列车桥梁基础空间耦合振动研究.(博士学位论文).成都：西南交通大学,1998.
[119]沈锐利.高速铁路桥梁与车辆耦合振动研究.(博士学位论文).成都：西南交通大学,1998.
[120]何发礼.高速铁路中下跨度曲线桥梁车桥耦合振动研究.(博士学位论文).成都：西南交通大学,1999.
[121]单德山.高速铁路曲线桥梁车桥耦合振动分析及大跨度曲线桥梁设计研究.(博士学位论文).成都：西南交通大学,1999.
[122]夏禾,陈英俊.车—粱—墩体系动力相互作用分析.土木工程学报.1992,25(2)：3—12.
[123]张楠,夏禾.地震对多跨简支桥梁上列车运行安全的影响.世界地震工程.2001,17(4)：43-49.
[124]Xia H, Xu Y L, Chan T H T. Dynamic Interaction of Long Suspension Bridges with Running Trains. Journal of Sound and Vibration.2000,237(2):263-280.
[125]曾庆元.弹性系统动力学总势能不变值原理.华中理工大学学报.2000,28(1)：1—3.
[126]郭向荣,曾庆元.高速铁路结合粱桥与列车系统振动分析模型.华中理工大学学报.2000,28(3)：60-62.
[127]曾庆元.列车桥梁时变系统的横向振动分析.铁道学报.1991,13(2)：38-46.
[128]程庆国,许慰平.大跨度铁路斜拉桥列车走性行探讨,武汉：全国桥梁结构学术大会.1992.
[129]程庆国,潘家英.大跨度铁路斜拉桥竖向刚度分析,武汉：全国桥梁结构学术大会.1992.
[130]许慰平.大跨度铁路桥梁车桥空间耦合振动研究.(博士学位论文).北京：铁道科学研究院,1988.
[131]高芒芒.高速铁路列车—线路—桥梁耦合振动及列车走行性研究.北京：铁道科学研究院,2002.
[132]高岩,沈锐利,柯在田,张煅.提速对桥梁振动与车辆过桥走行性的影响以及对策.中国铁道科学.2000,21(2)：19-25.
[133]王刚,曹雪琴.高速铁路大跨度斜拉桥车桥动力分析.上海铁道大学学报.2000,21(8)：7—11.
[134]Au F T K, Cheng Y S, Cheung Y K. Effects of Random Road Surface Roughness and Long-Term Deflection of Prestressed Concrete Girder and Cable-Stayed Bridges on Impact due to Moving Vehicles. Computers & Structures.2001,79(8):853-872.
[135]Au F T K, Wang J J, Cheung Y K. Impact Study of Cable-Stayed Railway Bridge with Random Rail Irregularities. Engineering Structures.2002,24(5):529-541.
[136]王解军.运行列车作用下桥梁的动力反应.(博士学位论文),长沙：湖南大学：2000.
[137]晋智斌.车_线_桥耦合系统及车_桥随机振动.(博士学位论文),成都：西南交通大学,2007.
[138]王旺平,胡先龙.汽车悬架随机疲劳寿命计算模型.武汉工业学院学报,2007,26(2)：40-42.
[139]倪侃,张圣坤,钱仍影.结构构件疲劳损伤累积的可靠性分析.中国造船,1997,4：53-60.
[140]徐灏.疲劳强度.北京：高等教育出版社,1988.
[141]倪侃.结构疲劳可靠性二维概率Miner准则及其应用.(博士学位论文),北京：北京航空航天大学,1994.
[142]程育人,缪龙秀,侯炳麟.疲劳强度.北京：中国铁道出版社,1990.
[143]吕彭民.宽带随机载荷谱下结构疲劳寿命的计算.长安大学学报,2004,24(1)：76-78.
[144]吴利辉,陈昌明.基于随机振动方法的白车身疲劳寿命研究.北京汽车,2007,5：17-22.
[145]吴义生.随机载荷下的疲劳损伤计算公式.海洋工程,1994,21(1)：94-103.
[146]赵文礼,李忠学,赵邦华.客车随机响应计算与车轴疲劳寿命预测.1998,20(4)：120-125.
[147]周华飞,蒋建群,毛根海.路面不平度引起的车辆动荷载分析.中国市政工程,2002,3：10-13.
[148]鲍钟岳.公路桥涵设计通用规范及条文说明JTG D60-2004.北京：人民交通出版社,1987.
[149]吴启宏.动力系数的影响因素实验研究.中国公路学报,1991,4(2)：57-64.
[150]毛清华,项海帆.公路桥梁车辆振动的理论和实验研究.土木工程学报,1990,23(3)：61-68.
[151]陈彦江,刘保忠,傅金科.桥面平整度对桥梁振动影响的实验研究.东北三省公路学会年会,1993,120-125.
[152]Hutton S G, Cheung Y K. Dynamic Response of Single Span Highway Bridges. Earthquake Engineering and Structural Dynamic,1979,7:543-553.
[153]郭毅之,金先龙,丁俊宏,杨洪杰.不平整路面上的非平稳车流荷载研究及应用.岩土力学,2007,28(2)：395-398.
[154]王解军,张伟,吴卫祥.重型汽车荷载作用下简支桥梁的动力反映分析.中南公路工程,2005,30(2)：55-58.
[155]余卓平,黄锡朋,张洪欣.减轻重型汽车对道路的损伤—汽车悬架优化设计.1994,7(3)：83-87.
[156]王钧利,马春燕.公路桥梁受车辆动力作用的疲劳可靠性分析.重庆交通学院学报,1998,17(3)：31-37.
[157]Michael J M, Mahoney J P. Measurements on Dynamic Effects of Dual and Wide base Single Tyres. Technicla Research Centre of Finland,1992.
[158]Cassis J H, Schmit L A. Optimal Structural Designs with Dynamic Constrains. ASCE J Struct Div, 1976,102:2053-2071.
[159]Li G, Liu X, Liu Y, Yue Q J. Optimum Design of Ice-Resistant Offshore Jacket Platforms in the Bohai Gulf in Consideration of Fatigue Life of Tubular Joints. Ocean Engineering.2008,35(5-6): 484-493.
[160]Li G, Liu X, Yue Q J. An Efficient Reliability Evaluation Approach of Human Exposure to Ice-Induced Vibration of Offshore Platforms. In:Proc. Of International Conference on Enhancement and Promotion of Computational Method in Engineering Science and Mechanics (CMECM 2006),2006.
[161]Li G, Liu X, Cheng G D. Acceleration-Based Optimum Design of Offshore Platforms Subjected to Ice Load. IN:Proc. of 9th International Conference on Computational Structures Technology (CST 2008), Athens Greece.2008.
[162]Li G, Liu X, Liu Y. Optimum Design of Ice-Resistant Offshore Jacket Platforms in Consideration of Fatigue Life. In:Proc. of 7th World Congress on Computational Mechanics, Los Angeles, California, USA.2006.
[163]Li G, Lu H Y, Liu X. A Hybrid Simulated Annealing and Optimality Criteria Method for Optimum Design of RC Buildings. Structural Engineering and Mechanics an International Journal.2008 (under review).
[164]国巍,李宏男.随机输入下附属结构的位置优化.振动与冲击,2008,27(4)：23-26.
[165]张延年,李宏男.双向耦合地震作用下滑移隔震结构振动控制及其优化研究.地震工程与工程振动.2007,27(1)：141-146.
[166]柳国环,李宏男.高压输电塔-线体系风致动力响应分析与优化控制.中国电机工程学报.2008,28(19)：131-137.
[167]段红杰,陶浩.汽车双层隔振系统的随机振动隔离及参数优化.机械设计与制造.2007,13(3)：79-82.
[168]王春林,吕志涛.核筒悬挂结构随机动力响应的参数优化设计.工业建筑.2007,37(10)：28-32.
[169]田四朋,唐国金,雷勇军.非平稳随机激励下基于动力可靠性的结构优化设计.振动与冲击.2004,23(3)：42-49.
[170]田四朋,任钧国,张书俊.稳态随机过程激励下基于首次超越破坏的结构优化设计.国防科技大学学报.2002,5(1)：171-181.
[171]Rao S S. Oprimization of Airplane Wing Structures under Gust Loads. Computers and Structures, 1985,21(3):741-749.
[172]Rao S S. Oprimization of Airplane Wing Structures under Taxiing Loads. Computers and Structures, 1985,26(3):467-479.
[173]童卫华,姜节胜,顾松年.一种以均方响应作为约束的动力学设计方法.应用力学学报,1996,13(3)：94-98.
[174]童卫华,姜节胜.结构在随机激励下的一种动力学设计方法.机械强度.1996,18(2)：6-10.
[175]陈建军,车建文,崔明涛,戴君,马洪波.结构动力优化设计述评与展望.力学进展,2001,31(2)：181-192.
[176]Fox R L, Kapoor M P. Rates of Change of Eigenvalue and Eigenvectors. Journal AIAA,1968,6(12): 2426-2429.
[177]Rogers L C. Derivatives of Eigenvalues and Eigenvectors. Journal AIAA,1970,8(5):943-944.
[178]Neslon R B. Simplified Calculation of Eigenvector Derivatives. Journal AIAA,1976,14(9): 1201-1205.
[179]林家浩.结构动力优化中的灵敏度分析.震动与冲击,1985,4(1)：1-6.
[180]林树枝,程耿东.动力响应灵敏度分析的振型空间法.地震工程与振动工程,1990,10(3)：
57-64.
[181]林树枝,程耿东.结构动力问题的灵敏度分析及动力优化设计和CAD.(博士学位论文),大连：大连理工大学,1988.
[182]林树枝,程耿东.求谐振动力响应及其灵敏度分析的直接迭代法.计算结构力学及其应用,1990,7(2)：85-91.
[183]葛健全,唐乾刚.减振支架结构动力响应的灵敏度分析.(硕士学位论文),长沙：国防科学技术大学,2004.
[184]葛健全,唐乾刚,雷勇军.减振支架结构随机响应的灵敏度分析.北京：首届全国航空航天领域中的力学问题学术讨论会论文集.2003.
[185]Beliveau J G, Cogan S, Lallement G, Ayer F. Iterative Least-Squares Calculation for Modal Eigenvector Sensitivity. AIAA Journal,1996,34(2):385-391.
[186]Dutla A, Ranakrishnan C V. Accurate Computation of Design Sensitivities for Structures under Transient Dynamic Loads with Constraints on Stresses. Computers and Structures,1998,66(4): 463-472.
[187]姚昌仁,麻永平.结构随机激励的响应灵敏度分析.力学学报.1990,22(1)：438-444.
[186]乔红威,吕振宙.随机激励下随机结构动力可靠性灵敏度分析.振动工程学报.2008,21(4)：404-408.
[189]Durbin F. Numerical Inversion of Laplace Transforms:an Efficient Improvement to Dubner and Abate's method. Computer Journal,1974,17(4):371-376.
[190]Zimoch Z. Sensitivity Analysis of Vibrating Systems. Journal of Sound and Vibration,1987,115(3): 447-458.
[191]Lou P, Zeng Q Y. Formulation of Equations of Motion of Finite Element Form for Vehicle-track-bridge Interaction System with Two Type of Vehicle Model. International Journal for Numerical Methods in Engineering,2005,62:435-474.
[192]Xia H. Dynamic Interactions of Long Suspension Bridges with Running Trains. Journal of Sound and Vibration,2002,237(2):263-80.
[193]Xiao YL, Noda NA. Analyses of Dynamic Response of Vehicle and Track Coupling System with Random Irregularity of Track Vertical Profile. Journal of Sound and Vibration,2002,258(1): 147-165.
[194]翟婉明.车辆-轨道耦合动力学[M].北京：中国铁道出版社,2002.
[195]赵济海.路面平度谱分析应用研究报告.长春汽车研究所整车研究室,1985.
[196]吕峰.车辆与结构相互作用随机动力分析.(博士学术论文),大连：大连理工大学,2008.
[197]Kim S M, Roesset JM. Moving Loads on a Pate on Elastic Foundation. Journal of Engineering Mechanics,1998,124(9):1010-1017.
[198]Fryba L. Vibration of Solid and Structures Under Moving Loads. London:Thomas Telford,1999.
[199]Huang X M, Deng X J. The Mechanical Analysis of Plate on Visco-elastic Winkler Foundation Under Moving load. Journal of Chongqing Jiaotong University,1990,2:45-51.
[200]Sun L, Deng X J. Steady Response of Infinite Plate on Visco-elastic Kelvin Foundation to Moving load. Chinese Journal of Geotechnical Engineering,1997,2:14-22.
[201]Lou P, Zeng Q Y. Finite Element Analysis of Slab Track Subjected to Moving load. Journal of Traffic and Transportation Engineering,2004,4 (1):29-33.
[202]Jiang J Q, Zhou H F. Steady State Response of Infinite Plate on Visco-elastic Foundation Subjected to Moving Load. China Journal of Highway and Transport,2006,19(1):6-11.
[203]Koh C G, Ong J S Y, Chua D K H, Feng J. Moving Element Method for Train-track Dynamic. International Journal for Numerical Methods in Engineering,2003,56(10):1549-1567.
[204]Chen Y H, Huang Y H. Dynamic Stiffness of Infinite Timoshenko Beam on Viscoelastic Foundation in Moving Co-ordinate. International Journal for Numerical Methods in Engineering,2000,48:1-18.
[205]Beliveau J G, Cogan S, Lallement G, Ayer F. Iterative Least-squares Calculation for Modal Eigenvector Sensitivity. American Institute of Aeronautics and Astronautics Journal,1996,34(2): 385-391.
[206]Dutla A, Ranakrishnan C V. Accurate Computation of Design Sensitivities for Structures under Transient Dynamic Loads with Constraints on Stresses. Computers and Structures,1998,66(4): 463-472.
[207]Hrovat D. Optimal active suspensions for 3D vehicle models. Proceedings of American Control Conference,1991,2:1534-1541.
[208]Chen S H, Pan H H. Design Sensitivity Analysis of Vibration Modes by Finite Element Perturbation. In:Proceedings of 4th MAC,1986.
[209]He Y P, Mcphee J. Multidisciplinary Design Optimization of Mechatronic Vehicles with Active Suspensions. Journal of Sound and Vibration,2005,28(3):217-241.
[210]Naude A F, Snyman J A. Optimization of Road Vehicle Passive Suspension systems. Part 2. Qualification and case study. Applied Mathematical Modeling,2003,27(4):263-274.
[211]王洪礼,葛根,许佳.汽车半主动悬架随机振动稳定性与可靠性分析.机械强度,2009,31(3)：170-173.
[212]李兴斯,张崎,谭涛.多目标结构优化设计的中心法.力学学报,2005,37(5)：606-610.
[213]Kim C W, Kawatani W, Kwon Y R. Impact Coefficient of Reinforced Concrete Slab on a Steel Girder Bridge. Engineering Structures,2007,29(4):576-590.
[214]龚志浩.十五期间大中型客车需求预测.客车技术与研究,2001,23(5)：1-2.
[215]Der Kiureghian A, Neuenhofer A. Response Spectrum Method for Multi-Support Seismic Excitations. Earthquake Eng. and Struct. Dyn.,1992,21:713～740
[216]Ernesto H Z, Vanmarcke E H. Seismic Random Vibration Analysis of Multi-Support Structural Systems. ASCE, Journal of Engineering Mechanics,1994,120:1107～1128
[217]姚卫星.结构疲劳寿命分析.北京：国防工业出版社,2003.
[218]张志超,赵岩,林家浩.车桥耦合系统非平稳随机振动分析.振动工程学报.2007,20(5)：439-446.
[219]张志超,张亚辉,林家浩.车桥耦合系统非平稳随机振动分析的虚拟激励-精细积分法.工程力学.2008.25(11)：197-204.
[220]蔡坤.基于骨重建理论的连续体结构拓扑优化方法.(博士学术论文),大连：大连理工大学,2008