车辆减振系统原理与仿真分析
|
摘要
车辆舒适性及碰撞安全性能与减振器密切相关,目前国产减振器的开发、设计多停留在模仿设计、经验设计和试验修正上,缺乏减振器的先进设计理论,导致国产减振器故障问题多、成本高、开发周期长。因此,通过理论、试验和仿真手段深入研究减振器的工作原理和故障机理,完善减振器的设计理念,优化减振器结构,具有重要的理论意义和工程价值。
本文从理论上建立了阻尼力和油液压强的换算公式、减振器节流计算的公式、三种受力形式下阀片变形的计算公式,并通过Java编程进行迭代计算获得了阀片和弹簧座的分离点位于环形槽内(d≤a)时阀片径向线变化的过程曲线。发现常通孔节流是平行平面缝隙节流,开阀后的节流为平行平板间径向节流。在二类节流分析中均考虑了局部节流损失、沿程节流损失；在第二类节流中对起始段被活塞部分填充后的节流内径、考虑常通孔存在后的节流高度作了等效处理。由节流公式获得的油液压强与由换算公式获得的油液压强具有很好的一致性。研究了阀片与弹簧座的三种接触方式：集中接触,分布接触(未接触区域全部受油液压强作用),分布接触(未接触区域部分受油液压强作用)。在假定分布载荷下,基于板壳理论的阀片变形计算与由有限元计算结果吻合很好。
从理论上分析了示功图(F-S曲线图)偏斜的原因、示功图上各曲线相互穿透的原因、及影响示功图饱满的因素。阀系灵敏度不足会导致阻尼力变化滞后于活塞速度变化,从而形成“残余力”(激励速度为零而阻尼力不为零),并使示功图偏斜、阻尼力-速度过程图(F-V曲线图)复原或压缩行程前半段曲线与后半段曲线分离。当高速度点曲线的分离过大时,示功图上该曲线会穿透低速度点曲线。速度点(Vmax)和开阀速度对示功图饱满的影响可忽略；当开阀阻尼力(Fo)和阻尼力-速度特性曲线第二段的斜率(k2)确定,开阀后的饱满情况确定；当F0确定,适当减小k2时,减振器总做功减小；阻尼力迟滞则示功图不饱满现象严重。
通过系列试验发现,阻尼力异常波动与加工质量、设计分析有对应关系,减振器的异响与开阀状态(F0/V0)有对应关系。质量问题主要有漏油、气压抗力降低、阻尼力偏离设计值和松退力矩不合格等。摩擦力换向、螺母松动、换向空程、损伤、开阀、阀片与阀门盖碰撞、补偿阀阀片被卡住和阀片翘曲等造成的阻尼力异常波动在示功图、F-V图及解析结果上有不同特点。通过172型减振器咔咔声异响的试验分析发现,异响件加速度、阻尼力信号的时频特征都普遍比正常件大；异响件的阻尼力异常由开阀引起,其开阀状态普遍比正常件大。
提出了两种阻尼力-速度特性曲线(F-Vmax曲线)仿真预测的方法；开发了筒式减振器瞬态双向流固耦合仿真系统并完成了相应预测方式下阻尼力的预测；建立了减振器流固耦合冲击响应仿真系统,并联合活塞杆固定环压装仿真完成了活塞杆冲击破坏仿真分析。F-Vmax曲线仿真预测的方法为：①使用准稳态方式获得各个速度点的阻尼力值；②获得F-V图中Vmax=1500mm/s的曲线。通过瞬态双向流固耦合仿真获得了阻尼力、阀片应力和位移分布及变化的特点,筒内流场分布及变化的特点,并验证了理论方法的合理性,探讨了降低仿真计算规模和提高计算精度的方法。
完成了某特种车辆空投降落的碰撞仿真。发现其最薄弱的部位是车轴,其次为发动机附近区域；车辆与地面接触碰撞的时间与地面的刚度密切相关。当地面为混凝土材料时,碰撞时间最短,车辆的动态应力及其波动幅度也最大。这为进一步研究减振器对车辆空投降落的影响及减振器自身的冲击破坏提供了基础。
Vehicle comfort and collision safety performance is closely related with the shock absorber. At present, the development and the design of shock absorber stay in imitation of design, experience design and experimental correction. The lack of advanced design theory of shock absorber leads to problems of failure, high cost and long development cycle. In hence, study on the working principles, failure mechanism theories, perfect design concepts, optimizations of damper structure by experiment and simulation have important theoretical significance and engineering value.
Based on the theoretic research, this paper established the conversion formula of damping force and oil hydraulic pressure, throttling formulas, valve deformation formulas under three different equilibrium models of forces. Further, through the Java iterative calculation, we obtained the change history of valve radial line when the separation point between valve disc and spring basement was out of the ring groove(d≤a). We found that it was a parallel flow during the period the valve wasn't open and it was a radial flow between two parallel flat planes during the period the valve was open. In the analysis of the two throtting calculation, the local head loss and the frictional head loss were considered. The rod padding effect to the inner radius and the throttle orifice flow effect to the throtting thickness were considered in the second throttling calculation. Oil pressure obtained by the throttle formula and obtained by the conversion formula had a good consistency. The contact types between valve disc and spring seat were circumference line contact, circumference surface contact (the untouched section is entirely subjected to the hydraulic pressure) and circumference surface contact (the untouched section is partially subjected to the hydraulic pressure). Under the assumed distribution load, valve disc deformation calculation based on the theory of shells and the finite element showed a good agreement.
Based on the theoretic research, we pointed out the causation of the indicator diagram (F-S diagram) deviation, the causation of the curve penetrating, the factors which influenced the indicator diagram plumpness. The valve system sensitivity deficiency would lead to the variation of damping force behinds the piston speed change, and to form a "residual force"(the incentive speed was zero but damping force wasn't zero), and the indicator diagram deviation. On the damping force vs. velocity diagram (F-V diagram), the first half of the recovery curve or the compression curve would separate from the second half. When the separation of a high speed curve was too large, this curve would pass through a low speed curve on the indictor diagram. Effects of the velocity point (Vmax) and the open gate velocity to the indicator diagram plumpness were neglectable; when the open gate damping force and the slope of the second segment of the F-Vmax curve (k2) were determined, the indicator diagram plumpness was certain; when Fo was certain and k2reduced, work would decline; the damping force hysteresis would induce serious un-plumpness of the indicator diagram.
Through tests and anatomizations, we pointed out that abnormal fluctuations of damping force were corresponding to the processing quality and the design analysis, there was a correspondence between the abnormal noise and valve opening state (Fo/Vo)-The main quality problems were the oil leak, the gas pressure resistance loss, the aberrancy of damping force and the pine twisting moment loss. Friction direction swerve, lack of valve sensitivity, loss of pine twisting moment, irrational design and valve disc wrap had different features in the anatomization results and the F-S curves and the F-V curves. The acceleration time characteristics and the acceleration frequency characteristics of withdraws with noisy problem were generally bigger than the normal ones', so were the damping force time characteristics and the damping force frequency characteristics of withdraws with noisy problem; those abnormities were caused by opening the valve, and their open status were generally bigger than the normal ones.
Two simulation methods for forecasting the damping force characteristics, a dynamic fluid-structure interaction (FSI) finite element system and a dynamic fluid-structure interaction finite element impact system were promoted. The predicting methods of F-Vmax curve were:①aining the damping force at each velocity point by using quasi-statics method;②Gaining the F-V curve of Vmax=1500mm/s. Through a series of simulations, we gained the damping force vs. velocity characteristics, the distribution and the history of the valve disc stress and the fluid field. Meanwhile, simulation results had verified the rationality of the theoretic method. Also, we probed into ways, such as sub cycling, to promote the computation speed and the computation precision.
Also, this paper had accomplished an airdrop landing simulation of a vehicle for special services. We pointed out that the axle was the weakest part; the contact time and the ground stiffness were closely related. When the ground was a concrete material, the contact time was the shortest, vehicle dynamic stress and its fluctuation was the biggest. For further understanding the effects of the shock absorber to the vehicle safety and its damage, this part has a good help.
本文从理论上建立了阻尼力和油液压强的换算公式、减振器节流计算的公式、三种受力形式下阀片变形的计算公式,并通过Java编程进行迭代计算获得了阀片和弹簧座的分离点位于环形槽内(d≤a)时阀片径向线变化的过程曲线。发现常通孔节流是平行平面缝隙节流,开阀后的节流为平行平板间径向节流。在二类节流分析中均考虑了局部节流损失、沿程节流损失；在第二类节流中对起始段被活塞部分填充后的节流内径、考虑常通孔存在后的节流高度作了等效处理。由节流公式获得的油液压强与由换算公式获得的油液压强具有很好的一致性。研究了阀片与弹簧座的三种接触方式：集中接触,分布接触(未接触区域全部受油液压强作用),分布接触(未接触区域部分受油液压强作用)。在假定分布载荷下,基于板壳理论的阀片变形计算与由有限元计算结果吻合很好。
从理论上分析了示功图(F-S曲线图)偏斜的原因、示功图上各曲线相互穿透的原因、及影响示功图饱满的因素。阀系灵敏度不足会导致阻尼力变化滞后于活塞速度变化,从而形成“残余力”(激励速度为零而阻尼力不为零),并使示功图偏斜、阻尼力-速度过程图(F-V曲线图)复原或压缩行程前半段曲线与后半段曲线分离。当高速度点曲线的分离过大时,示功图上该曲线会穿透低速度点曲线。速度点(Vmax)和开阀速度对示功图饱满的影响可忽略；当开阀阻尼力(Fo)和阻尼力-速度特性曲线第二段的斜率(k2)确定,开阀后的饱满情况确定；当F0确定,适当减小k2时,减振器总做功减小；阻尼力迟滞则示功图不饱满现象严重。
通过系列试验发现,阻尼力异常波动与加工质量、设计分析有对应关系,减振器的异响与开阀状态(F0/V0)有对应关系。质量问题主要有漏油、气压抗力降低、阻尼力偏离设计值和松退力矩不合格等。摩擦力换向、螺母松动、换向空程、损伤、开阀、阀片与阀门盖碰撞、补偿阀阀片被卡住和阀片翘曲等造成的阻尼力异常波动在示功图、F-V图及解析结果上有不同特点。通过172型减振器咔咔声异响的试验分析发现,异响件加速度、阻尼力信号的时频特征都普遍比正常件大；异响件的阻尼力异常由开阀引起,其开阀状态普遍比正常件大。
提出了两种阻尼力-速度特性曲线(F-Vmax曲线)仿真预测的方法；开发了筒式减振器瞬态双向流固耦合仿真系统并完成了相应预测方式下阻尼力的预测；建立了减振器流固耦合冲击响应仿真系统,并联合活塞杆固定环压装仿真完成了活塞杆冲击破坏仿真分析。F-Vmax曲线仿真预测的方法为：①使用准稳态方式获得各个速度点的阻尼力值；②获得F-V图中Vmax=1500mm/s的曲线。通过瞬态双向流固耦合仿真获得了阻尼力、阀片应力和位移分布及变化的特点,筒内流场分布及变化的特点,并验证了理论方法的合理性,探讨了降低仿真计算规模和提高计算精度的方法。
完成了某特种车辆空投降落的碰撞仿真。发现其最薄弱的部位是车轴,其次为发动机附近区域；车辆与地面接触碰撞的时间与地面的刚度密切相关。当地面为混凝土材料时,碰撞时间最短,车辆的动态应力及其波动幅度也最大。这为进一步研究减振器对车辆空投降落的影响及减振器自身的冲击破坏提供了基础。
Vehicle comfort and collision safety performance is closely related with the shock absorber. At present, the development and the design of shock absorber stay in imitation of design, experience design and experimental correction. The lack of advanced design theory of shock absorber leads to problems of failure, high cost and long development cycle. In hence, study on the working principles, failure mechanism theories, perfect design concepts, optimizations of damper structure by experiment and simulation have important theoretical significance and engineering value.
Based on the theoretic research, this paper established the conversion formula of damping force and oil hydraulic pressure, throttling formulas, valve deformation formulas under three different equilibrium models of forces. Further, through the Java iterative calculation, we obtained the change history of valve radial line when the separation point between valve disc and spring basement was out of the ring groove(d≤a). We found that it was a parallel flow during the period the valve wasn't open and it was a radial flow between two parallel flat planes during the period the valve was open. In the analysis of the two throtting calculation, the local head loss and the frictional head loss were considered. The rod padding effect to the inner radius and the throttle orifice flow effect to the throtting thickness were considered in the second throttling calculation. Oil pressure obtained by the throttle formula and obtained by the conversion formula had a good consistency. The contact types between valve disc and spring seat were circumference line contact, circumference surface contact (the untouched section is entirely subjected to the hydraulic pressure) and circumference surface contact (the untouched section is partially subjected to the hydraulic pressure). Under the assumed distribution load, valve disc deformation calculation based on the theory of shells and the finite element showed a good agreement.
Based on the theoretic research, we pointed out the causation of the indicator diagram (F-S diagram) deviation, the causation of the curve penetrating, the factors which influenced the indicator diagram plumpness. The valve system sensitivity deficiency would lead to the variation of damping force behinds the piston speed change, and to form a "residual force"(the incentive speed was zero but damping force wasn't zero), and the indicator diagram deviation. On the damping force vs. velocity diagram (F-V diagram), the first half of the recovery curve or the compression curve would separate from the second half. When the separation of a high speed curve was too large, this curve would pass through a low speed curve on the indictor diagram. Effects of the velocity point (Vmax) and the open gate velocity to the indicator diagram plumpness were neglectable; when the open gate damping force and the slope of the second segment of the F-Vmax curve (k2) were determined, the indicator diagram plumpness was certain; when Fo was certain and k2reduced, work would decline; the damping force hysteresis would induce serious un-plumpness of the indicator diagram.
Through tests and anatomizations, we pointed out that abnormal fluctuations of damping force were corresponding to the processing quality and the design analysis, there was a correspondence between the abnormal noise and valve opening state (Fo/Vo)-The main quality problems were the oil leak, the gas pressure resistance loss, the aberrancy of damping force and the pine twisting moment loss. Friction direction swerve, lack of valve sensitivity, loss of pine twisting moment, irrational design and valve disc wrap had different features in the anatomization results and the F-S curves and the F-V curves. The acceleration time characteristics and the acceleration frequency characteristics of withdraws with noisy problem were generally bigger than the normal ones', so were the damping force time characteristics and the damping force frequency characteristics of withdraws with noisy problem; those abnormities were caused by opening the valve, and their open status were generally bigger than the normal ones.
Two simulation methods for forecasting the damping force characteristics, a dynamic fluid-structure interaction (FSI) finite element system and a dynamic fluid-structure interaction finite element impact system were promoted. The predicting methods of F-Vmax curve were:①aining the damping force at each velocity point by using quasi-statics method;②Gaining the F-V curve of Vmax=1500mm/s. Through a series of simulations, we gained the damping force vs. velocity characteristics, the distribution and the history of the valve disc stress and the fluid field. Meanwhile, simulation results had verified the rationality of the theoretic method. Also, we probed into ways, such as sub cycling, to promote the computation speed and the computation precision.
Also, this paper had accomplished an airdrop landing simulation of a vehicle for special services. We pointed out that the axle was the weakest part; the contact time and the ground stiffness were closely related. When the ground was a concrete material, the contact time was the shortest, vehicle dynamic stress and its fluctuation was the biggest. For further understanding the effects of the shock absorber to the vehicle safety and its damage, this part has a good help.
引文
[1]约森.赖姆帕尔.汽车底盘基础[M].吉林科学技术出版社.1991,15-171.
[2]耶尔森.赖姆帕尔.汽车底盘基础[M].科学普及出版社.1992,1-10.
[3]宇野高明[著].汽车行驶性能和底盘机构[M].郝长文等[译].第一汽车集团公司技术中心.1994.
[4]郭孔辉.操纵系统动力学[M].吉林科学技术出版社.1992,20-180.
[5]喻凡,林逸.汽车系统动力学[M].机械工业出版社.2005,20-30.
[6]Dave C.,喻凡.车辆动力学及其控制[M].人民交通出版社.2004,200-210.
[7]俞德孚.悬架减振器的理论和实践[M].中国兵工业出版社.2003.
[8]John D. The Shoek Absorber Handbook[M].2nd Edition. John Wiley & Sons. 2007,0-432.
[9]吕振华,李世民.筒式液阻减振器动态特性模拟分析技术的发展[J].清华大学学报.2002,42(11)：1532-1536.
[10]Lee K. Numerical modelling for the hydraulic performance prediction of automotive monotube dampers[J]. Vehicle System Dynamics.1997,28:25-39.
[11]Herr F. A CFD investigation of control force changes due to manufacturing variations inside piston port/pot area[J]. Tenneco Automotive.1998.
[12]Herr F., Mallin T., Lane J. A shock absorber model using CFD analysis and Easy5[C]. SAE Paper.1999-01-1322.
[13]Tallec P.L., Mouro J. Fluid structure interaction with large structural displacements [J]. Computer Methods in Applied Mechanics and Engineering.2001,190:3039-3067.
[14]李世民,吕振华.汽车减振器液-固耦合动力学特性的分步间接耦合模拟分析[J].汽车技术.2005,(2)：12-16.
[15]李世民,吕振华,伍卓安.减振器节流阀非线性特性的有限元模拟分析[J].机械强度.2003,25(6)：614-620.
[16]冯雪梅,刘佐民.减振器内部油压行为分布特征有限元分析[J].武汉理工大学学报.2002,24(5)：121-124.
[17]冯雪梅,刘佐民,魏东.减振器双节流孔闭式油路稳态行为特征有限元分析[J].机械设计与研究.2003,19(1)：66-69.
[18]李小波,沈季胜,宁晓斌.基于流固耦合分析方法的减振器复原阀节流特性研究[J].机械制造和研究.2010.20(4)：20-22.
[19]Lau K., Diaz Z.V., Scambler P., etc. Mitral valve dynamics in structural and fluid-structure interaction models[J]. Medical Engineering & Physics.2010. (32):1057-1064.
[20]Pereira G.J., Lienhart H. Time-Phase Resolved Optical Measurements on Two-Dimensional FSI Problems [J]. Physics Procedia.2010, (5):679-688.
[21]Bernhard G, Miriam M., Tobias N. A coupling environment for partitioned multiphysics simulations applied to fluid-structure interaction scenarios[J]. Procedia Computer Science.2010, (1):681-689.
[22]Seyyed A.A., Lotfi V. Computing mode shapes of fluid-structure systems using subspace iteration methods[J]. Scientia Iranica.2011,18 (6):1159-1169.
[23]Wang X. Analytical and computational approaches for some fluid-structure interaction analysis[J]. Computer and Structure.1999,72:423-433.
[24]Bathe K.J., Zhang H., Ji S. Finite element analysis of fluid flows fully coupled with structural interactions[J]. Computer and Structure.1999,72:1-16.
[25]Le T.P., Mouro J. Fluid structure interaction with large structural displacements[J]. Computer Methods in Applied Mechanics and Engineering.2001,190:3039-3067.
[26]Lang H.H. A study of the characteristics of automotive hydraulic dampers at high stroking frequencies[D]. The University of Michigan Doctor Degree Dissertation. 1977.
[27]Karadayi R., Masada G.Y. A Nonlinear Shock Absorber model[J]. American Society of Mechanical Engineers, Applied Mechanics Division.1986,80:149-165.
[28]Besinger F.H., Cebon D., Cole D.J. Damper model for Heavy vehicle Ride dynamics[J]. Vehicle System Dynamics.1995, (24):35-64.
[29]Duym S.W., Stiens R., Baron G.V., etc. Physical modelling of the hysteretic behaviour of automotive shock absorbers[C]. SAE Paper.1997,125-138.
[30]Duym S., Reybrouck K. Physical characterization of nonlinear shock absorber dynamics[J]. European Journal of Mechanical and Environmental Engineering. 1998,43:181-188.
[31]Reybrouck K. A nonlinear parametric model of an automotive shock absorber[C]. SAE Paper.1994-08-69.
[32]Richard V.K., Wang C.G., etc. A new shock absorber model with an application in vehicle dynamics studies[J]. SAE Paper.2003-01-3411.
[33]陈耀钧.轿车油液压强减振器阻力特性模拟预测预测结果分析[J].汽车技术.2001,8(12)：8-11.
[34]吴云飞,雷雨成.双筒液压减振器的阻力特性的仿真模拟计算[J].上海汽车.2000,4：14-17.
[35]Wallaschek J. Dynamics of nonlinear automobile shock absorbers[J]. International Journal of Nonlinear Mechanics.1990, (25):299-308.
[36]Surace C., Storer D., Tomlinson G.R. Characterising an automotive shock absorber and the dependency on the temperature[C]. Proceedings of 10th International Modal Analysis Conferene, San Diego.1992,1317-1326.
[37]Worden K., Tomlinson G.R. Parametric and nonparametric identification of automotive shock absorbers[C]. Proceedings of 10th International Modal Analysis Conferene, San Diego.1992,764-771.
[38]Rao M.D., Gruenberg S., Torab H., etc. Vibration testing and dynamic modelling of automotive shock absorbers[C]. The International Society for Optical Engineering, Smart Structures and Materials, Bellingham.2000,423-429.
[39]Rao M.D., Gruenberg S., Torab H. Measurement of dynamic properties of automotive shock absorbers for NVH[C]. SAE Paper.1999-01-1840.
[40]Weigell M., Mack W., Riepl. A. Nonparametric shock absorber modeling based on standard test data[J]. Vehicle System Dynamics.2002, (38):415-432.
[41]Duym S., Stiens R., Reybrouck K. Evaluation of shock absorber models[J]. Vehicle System Dynamics.1997,27:109-127.
[42]Audenino A.L., Belingardi G. A new and effective characterization method for automotive shock absorbers[C]. Proceedings of Second Polish-Italian Seminar, Torino. 1993,237-244.
[43]Liu Y., Zhang J., Yu F., etc. Test and simulation of nonlinear dynamic response for the twin-tube hydraulic shock absorber[J]. Society of Automotive Engineers.2002,91-98.
[44]Duym S.W.R. Nonparametric identification of nonlinear mechanical systems[D]. Vrije University Brussel Doctor Degree Dissertation.1998.
[45]Duym S.W.R. Simulation tools, modeling and identification for an automotive shock absorber in the context of vehicle dynamics[J]. Vehicle System Dynamics. 2000,33:263-285.
[46]Morman K. A modelling and identification procedure for the analysis and simulation of hydraulic shock absorber performance[J]. Vehicle Research Laboratory.1984.
[47]Morman K., Lin Y, Kubis J. A Model for the analysis and simulation of hydraulic shock absorber performance-Part II parameter identification and model validation studies[J]. Ford Motor Company Research Staff Reports.1986:86-61.
[48]Alonso M., Comas A. Modelling a Twin Tube Cavitating Shock Absorber[J]. Proceedings of the Institution Mechanical Engineers.2006,220:1031-1040.
[49]Worden K. Data processing and experiment design for the restoring force surface method, part I:Integration and differentiation of measured time data[J]. Mechanical Systems and Signal Processing.1990,4(4):295-319.
[50]Audenino A., Belingardi G, Garibaldi L. An application of the restoring force mapping method for the diagnostic of vehicular shock absorbers dynamic simulation behaviour[C]. Dipartimento di Meccanica del Politecnico di, Torino.1990.
[51]Cafferty S., Worden K., Tomlinson G. Characterization of automotive shock absorbers using random excitation [J]. Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering.1995,209:239-248.
[52]Schiehlen W., Hu B. Spectral simulation and shock absorber identification[J]. International Journal of Non-Linear Mechanics.2003,38:161-171.
[53]Tsai C.S., Chen K.C., Lin S.B., etc. Analytic model of fluid viscous damper under seismic loadings[J]. Seismic Engineering.2000,1:175-182.
[54]刘延庆,张建武.车用双筒液压减振器动态响应的试验与仿真[J].上海交通大学学报.2002,36(8)：1095-1099.
[55]王一兵,徐明龙,邱阳.汽车液压阻尼器的四段线性化模型[J].应用力学学报.2003,20(2)：60-63.
[56]俞德孚,陈庆东,方大雨.悬架减振器外特性平安比的设计研究[J].车辆与动力技术.2002,87(3)：11-17.
[57]SahinY, Ibrahim U. Neuralnetwork application to vehicle's vibration analysis[J]. Mechanism and Machine Theory.2003,38:27-41.
[58]Yildirim S. Vibration Control of Suspension Systems Using a Proposed Neural Network[J]. Journal of Sound and Vibration.2004,277(4):1059-1069.
[59]Szygula M. Development of the computer simulation method on energy absorbing device[C]. Komag Testing Laboratory.2002.
[60]Rakheja M.D., Su H., Sankar T.S. Analysis of a passive sequential hydraulic damper for vehicle suspension[J]. Vehicle System Dynamics.1999,19:289-295.
[61]Fukushima N, Hidaka K, Iwata K. Optimum Characteristics of Automotive Shock Absorbers under Various Driving Conditions and Road Surfaces [J]. International Journal of Vehicle Design.1983,4(5):15-19.
[62]Gobbi M., Mastinu G. Analytical description and optimization of the dynamic behaviour of passively suspended road vehieles[J]. Journal of Sound and Vibration. 2001,245(3):457-481.
[63]李莉.基于ADAMS/Car的某轿车平顺性仿真、分析与改进[D].吉林大学博士毕业论文.2007.
[64]David C. The influence of damper properties on vehicle dynamic behavior[J]. SAE Paper.2002-01-0319.
[65]Etman, L.F.P., Vernmeulen, R.C.N, etc. Design of a stroke dependent damper for the front axle suspension of a truck using multibody system dynamics and numerical optimization[J]. Vehicle System Dynamics.2002,38(2):85-101.
[66]William F.M., Douglas L.M. Race car vehicle dynamics[C]. SAE Paper.1999-792.
[67]Holen P., Thorvald B. Aspects on roll and bounce damping for heavy vehicles[C]. SAE Paper 2002-01-3060.
[68]MSC software corporation. MSC. Dytran Workshop Examples[M]. USA.2010.
[69]MSC software corporation. MSC. Documentation Library[M]. USA.2010.
[70]Horst G, Stanislaw S., Krzysztof M. Use of the finite elements method for modelling the dynamic load impact on hydraulic leg[J]. Sbornik Vedecky Chpracivy Sokeskoly Banske.2007, (1):61-72.
[71]杨基忠.车辆筒式减振器高频畸变特性研究[J].兵工学报.1999,75(3)：12-18.
[72]俞德孚,马彪.悬架减振器外特性畸变及其对车辆运行的有害影响[J].兵工学报坦克装甲车与发动机分册.1990,(1)：32-39.
[73]俞德孚,刘晓璞,李晓雷.车辆悬架减振器外特性的高频畸变与高频设计[J].北京工业学院学报.1988,8(3)：82-89.
[74]鲁明俊.冲击载荷下Xcxy-1型减振器动态特性分析[J].石油矿场机械.2007,36(11)：11-13.
[75]景晓华.垂直冲击减振器的实验研究[J].机械研究与应用.2005,18(1)：14-15.
[76]谭波.锤击法测量减振器冲击刚度[J].噪声与振动控制.2003,(4)：43-45.
[77]周长城,减振器液压气穴与气体反弹现象的研究[J].液压与气动.2007,(8)：3-7.
[78]王侃.某轻型车辆液力减震器活塞杆断裂失效分析[J].兵器材料科学与工程.2008,32(1)：82-85.
[79]陈轶杰,顾亮.减振器节流阀片对阀门水击力的影响研究[J].振动与冲击.2008,27(2)：103-106.
[80]Bourel B. Handling contact in multi-domain simulation of automobile crashes[J]. Finite Elements in Analysis and Design.2006,42:766-779.
[81]Mei L.Q., Thole C.A. Data analysis for parallel car-crash simulation results and model optimization[J]. Simulation Modeling Practice and Theory.2008,16:329-337.
[82]Surendra K. Use of unsymmetric finite element method in impact analysis of composite laminates[J]. Finite Element in Analysis and Design.2011,47:373-377.
[83]Lynn K.M., Isobe D. Structural collapse analysis of framed structures under Impact loads using ASI-Gauss finite element method[J]. International Journal of Impact Engineering.2007,34:1500-1516.
[84]Peter I. On the simulation of failure mechanisms in steel structures [J]. Advances in Engineering Software.2009,40:871-882.
[85]Deb A, M.S. Mahendrakumar, C. Chavan, J. Karve, etc. Design of an aluminium-based vehicle platform for front impact safety[J]. International Journal of Impact Engineering.2004,30:1055-1079.
[86]Stijn D, Brughmansa M, Hermansa L. The robustness of dynamic vehicle performance to spot weld failures[J]. Finite Elements in Analysis and Design. 2006,42:670-682.
[87]Cheng Z.Q. Experiences in reverse-engineering of a finite element automobile crash model[J]. Finite Elements in Analysis and Design.2001,37:68-74.
[88]Dario V. Simplified method for evaluating energy loss in vehicle collisions[J]. Accident Analysis and Prevention.2009,41:633-641.
[89]Gary R. Impact simulation and full scale crash testing of a low profile concrete work zone barrier[J]. Computers and Structures.2003,81:1359-1374.
[90]Bossak M., Jakub K. Global/local analysis of composite light aircraft crash landing[J]. Computers and Structures.2003,81:503-514.
[91]雷正保,龙建强.汽车碰撞CAE技术中几个尚未解决的问题.长沙交通学院学报.2003,19(3)：415-417.
[92]赵广耀,樊新华,邸建卫,付东宇等.车辆碰撞计算机模拟分析与评价[J].东北大学学报(自然科学版).2008,7：42-45.
[93]赵欣超,朱平.基于两种正面碰撞的轿车耐撞性能仿真与改进研究[J].汽车工程.2007,29(10)：842-846.
[94]王大志.基于乘员保护的汽车正面碰撞结构设计与变形控制研究[D].清华大学博士毕业论文.2001,18-78.
[95]李碧浩,杜汉斌,卓鹏等.轿车侧面碰撞安全性能改进措施探讨[J].汽车工程.2008,30(11)：23-26.
[96]William A. Numerical simulation of AM50A magnesium alloy under large deformation [J]. International Journal of Impact Engineering.2004,30:117-142.
[97]Javad M. Design and analysis of an automotive bumper beam in low-speed frontal crashes[J]. Thin-Walled Structures.2009,47:902-911.
[98]Mohamed S.N., Guptab N.K., Velmurugan R. Optimization of thin conical frusta for impact energy absorption[J]. Thin-Walled Structures.2009,46:653-666.
[99]Herzl C. On optimizing crash energy and load-bearing capacity in cellular structures [J]. International Journal of Solids and Structures.2008,45:528-539.
[100]Rajendran R., Moorthi A., Basu S. Numerical simulation of drop weight impact behavior of closed cell aluminium foam[J]. Materials and Design. 2009,30(8):2823-2830.
[101]Zarei H.R., Kroger M. Bending behavior of empty and foam-filled beams:structural optimization[J]. International Journal of Impact Engineering.2008,35:521-529.
[102]Zarei H.R., Kroger M. Optimization of the foam-filled aluminum tubes for crush box application[J]. Thin-Walled Structures.2008,48:214-221.
[103]李素霞,雷正保.面向中级轿车的低成本螺纹剪切吸能结构优化设计[J].长沙理工大学学报.2009,6(2)：51-55.
[104]Lee D.W. FOA(first-order analysis)model of a granule-filled tube for vehicle crash energy absorption[J]. Mechanics of Materials.2009,41:684-690.
[105]Chen D.H., Ozaki S. Numerical study of axially crushed cylindrical tubes with corrugated surface[J]. Thin-Walled Structures.2009,47:1387-1396.
[106]Rossi A. Numerical simulation of the axial collapse of thin-walled polygonal section tubes[J]. Thin-Walled Structures,2005,43:1646-1661.
[107]Nagel G.M., Thambiratnam D.P. A numerical study on the impact response and energy absorption of tapered thin-walled tubes[J]. International Journal of Mechanical Sciences.2004,46:201-216.
[108]Mamalis A.G., Manolakos D.E., Ioannidis M.B. On the crashworthiness of composite rectangular thin-walled tubes internally reinforced with aluminium or polymeric foams:Experimental and numerical simulation[J]. Composite Structures. 2009,89(3):416-423.
[109]陈懋章.粘性流体力学[M].高等教育出版社.2002,1-72.
[110]夏泰淳.工程流体力学[M].上海交通大学出版社.2006,15-213.
[111]陈卓如,金朝铭,王成敏等.工程流体力学[M].高等教育出版社.1992,280-425.
[112]机械设计手册编委会.机械设计手册[M].机械工业出版社.2006,23-19.
[113]郭金基.平行平板间径向气流的Navier-Stokes方程的近似解[J].力学学报.1980,(3)：306-310.
[114]袁锰吾.平行平板间径向气流的Navier-stokes方程的新的近似解[J].上海力学.1985,(2)：1-9.
[115]黄德成,膝克利,江体乾.两固定平行圆盘间幂律流体径向流动的摄动解法[J].华东化工学院学报.1992,12(6)：798-807.
[116]王致清,刘震北.在液压工程中两平行圆板间径向层流的压力损失与流量的计算问题[J].液压气动与密封.1982,5-11.
[117]金朝铭,王致清.在液压工程中两平行圆板间径向层流的压力损失与流量的计算问题(续)[J].液压气动与密封.1984,(04)：14-16.
[118]刘震北,王致清.两平行圆板间径向层流进口段效应分析[J].应用数学和力学.1984,5(1)：77-89.
[119]丁忠满,王致清.幂律流体两平行圆板间径向扩散层流进口段流动阻力的分析[J].力学学报.1994,26(3)：368-373.
[120]周长城,顾亮.筒式减振器叠加节流阀片开度与特性试验[J].机械工程学报.2007,43(6)：210-215.
[121]铁摩辛科S.,沃诺斯基S.板壳理论[M].科学出版社.1977,1-75.
[122]刘鸿文,林建兴,曹曼玲.板壳理论[M].浙江大学出版社.1992,1-141.
[123]谭刚,李华译KYB SL20减震器验算书[Z].山川机械厂.1998,6-17.
[124]田茹会,王钟羡.改进的遗传算法在减振器优化中的应用[J].机械工程师.2006,(3)：99-101.
[125]马振来.汽车液压减震器参数优化设计[D].哈尔滨工业大学博士毕业论文.2002.
[126]Kruse A. Characterizing and reducing structural noises of vehicle shock absorber systems[C]. SAE Paper.2002-01-1234.
[127]刘延庆.车用液压减振器的异常噪声及动力学特性研究[D].上海交通大学博士毕业论文.2002.
[2]耶尔森.赖姆帕尔.汽车底盘基础[M].科学普及出版社.1992,1-10.
[3]宇野高明[著].汽车行驶性能和底盘机构[M].郝长文等[译].第一汽车集团公司技术中心.1994.
[4]郭孔辉.操纵系统动力学[M].吉林科学技术出版社.1992,20-180.
[5]喻凡,林逸.汽车系统动力学[M].机械工业出版社.2005,20-30.
[6]Dave C.,喻凡.车辆动力学及其控制[M].人民交通出版社.2004,200-210.
[7]俞德孚.悬架减振器的理论和实践[M].中国兵工业出版社.2003.
[8]John D. The Shoek Absorber Handbook[M].2nd Edition. John Wiley & Sons. 2007,0-432.
[9]吕振华,李世民.筒式液阻减振器动态特性模拟分析技术的发展[J].清华大学学报.2002,42(11)：1532-1536.
[10]Lee K. Numerical modelling for the hydraulic performance prediction of automotive monotube dampers[J]. Vehicle System Dynamics.1997,28:25-39.
[11]Herr F. A CFD investigation of control force changes due to manufacturing variations inside piston port/pot area[J]. Tenneco Automotive.1998.
[12]Herr F., Mallin T., Lane J. A shock absorber model using CFD analysis and Easy5[C]. SAE Paper.1999-01-1322.
[13]Tallec P.L., Mouro J. Fluid structure interaction with large structural displacements [J]. Computer Methods in Applied Mechanics and Engineering.2001,190:3039-3067.
[14]李世民,吕振华.汽车减振器液-固耦合动力学特性的分步间接耦合模拟分析[J].汽车技术.2005,(2)：12-16.
[15]李世民,吕振华,伍卓安.减振器节流阀非线性特性的有限元模拟分析[J].机械强度.2003,25(6)：614-620.
[16]冯雪梅,刘佐民.减振器内部油压行为分布特征有限元分析[J].武汉理工大学学报.2002,24(5)：121-124.
[17]冯雪梅,刘佐民,魏东.减振器双节流孔闭式油路稳态行为特征有限元分析[J].机械设计与研究.2003,19(1)：66-69.
[18]李小波,沈季胜,宁晓斌.基于流固耦合分析方法的减振器复原阀节流特性研究[J].机械制造和研究.2010.20(4)：20-22.
[19]Lau K., Diaz Z.V., Scambler P., etc. Mitral valve dynamics in structural and fluid-structure interaction models[J]. Medical Engineering & Physics.2010. (32):1057-1064.
[20]Pereira G.J., Lienhart H. Time-Phase Resolved Optical Measurements on Two-Dimensional FSI Problems [J]. Physics Procedia.2010, (5):679-688.
[21]Bernhard G, Miriam M., Tobias N. A coupling environment for partitioned multiphysics simulations applied to fluid-structure interaction scenarios[J]. Procedia Computer Science.2010, (1):681-689.
[22]Seyyed A.A., Lotfi V. Computing mode shapes of fluid-structure systems using subspace iteration methods[J]. Scientia Iranica.2011,18 (6):1159-1169.
[23]Wang X. Analytical and computational approaches for some fluid-structure interaction analysis[J]. Computer and Structure.1999,72:423-433.
[24]Bathe K.J., Zhang H., Ji S. Finite element analysis of fluid flows fully coupled with structural interactions[J]. Computer and Structure.1999,72:1-16.
[25]Le T.P., Mouro J. Fluid structure interaction with large structural displacements[J]. Computer Methods in Applied Mechanics and Engineering.2001,190:3039-3067.
[26]Lang H.H. A study of the characteristics of automotive hydraulic dampers at high stroking frequencies[D]. The University of Michigan Doctor Degree Dissertation. 1977.
[27]Karadayi R., Masada G.Y. A Nonlinear Shock Absorber model[J]. American Society of Mechanical Engineers, Applied Mechanics Division.1986,80:149-165.
[28]Besinger F.H., Cebon D., Cole D.J. Damper model for Heavy vehicle Ride dynamics[J]. Vehicle System Dynamics.1995, (24):35-64.
[29]Duym S.W., Stiens R., Baron G.V., etc. Physical modelling of the hysteretic behaviour of automotive shock absorbers[C]. SAE Paper.1997,125-138.
[30]Duym S., Reybrouck K. Physical characterization of nonlinear shock absorber dynamics[J]. European Journal of Mechanical and Environmental Engineering. 1998,43:181-188.
[31]Reybrouck K. A nonlinear parametric model of an automotive shock absorber[C]. SAE Paper.1994-08-69.
[32]Richard V.K., Wang C.G., etc. A new shock absorber model with an application in vehicle dynamics studies[J]. SAE Paper.2003-01-3411.
[33]陈耀钧.轿车油液压强减振器阻力特性模拟预测预测结果分析[J].汽车技术.2001,8(12)：8-11.
[34]吴云飞,雷雨成.双筒液压减振器的阻力特性的仿真模拟计算[J].上海汽车.2000,4：14-17.
[35]Wallaschek J. Dynamics of nonlinear automobile shock absorbers[J]. International Journal of Nonlinear Mechanics.1990, (25):299-308.
[36]Surace C., Storer D., Tomlinson G.R. Characterising an automotive shock absorber and the dependency on the temperature[C]. Proceedings of 10th International Modal Analysis Conferene, San Diego.1992,1317-1326.
[37]Worden K., Tomlinson G.R. Parametric and nonparametric identification of automotive shock absorbers[C]. Proceedings of 10th International Modal Analysis Conferene, San Diego.1992,764-771.
[38]Rao M.D., Gruenberg S., Torab H., etc. Vibration testing and dynamic modelling of automotive shock absorbers[C]. The International Society for Optical Engineering, Smart Structures and Materials, Bellingham.2000,423-429.
[39]Rao M.D., Gruenberg S., Torab H. Measurement of dynamic properties of automotive shock absorbers for NVH[C]. SAE Paper.1999-01-1840.
[40]Weigell M., Mack W., Riepl. A. Nonparametric shock absorber modeling based on standard test data[J]. Vehicle System Dynamics.2002, (38):415-432.
[41]Duym S., Stiens R., Reybrouck K. Evaluation of shock absorber models[J]. Vehicle System Dynamics.1997,27:109-127.
[42]Audenino A.L., Belingardi G. A new and effective characterization method for automotive shock absorbers[C]. Proceedings of Second Polish-Italian Seminar, Torino. 1993,237-244.
[43]Liu Y., Zhang J., Yu F., etc. Test and simulation of nonlinear dynamic response for the twin-tube hydraulic shock absorber[J]. Society of Automotive Engineers.2002,91-98.
[44]Duym S.W.R. Nonparametric identification of nonlinear mechanical systems[D]. Vrije University Brussel Doctor Degree Dissertation.1998.
[45]Duym S.W.R. Simulation tools, modeling and identification for an automotive shock absorber in the context of vehicle dynamics[J]. Vehicle System Dynamics. 2000,33:263-285.
[46]Morman K. A modelling and identification procedure for the analysis and simulation of hydraulic shock absorber performance[J]. Vehicle Research Laboratory.1984.
[47]Morman K., Lin Y, Kubis J. A Model for the analysis and simulation of hydraulic shock absorber performance-Part II parameter identification and model validation studies[J]. Ford Motor Company Research Staff Reports.1986:86-61.
[48]Alonso M., Comas A. Modelling a Twin Tube Cavitating Shock Absorber[J]. Proceedings of the Institution Mechanical Engineers.2006,220:1031-1040.
[49]Worden K. Data processing and experiment design for the restoring force surface method, part I:Integration and differentiation of measured time data[J]. Mechanical Systems and Signal Processing.1990,4(4):295-319.
[50]Audenino A., Belingardi G, Garibaldi L. An application of the restoring force mapping method for the diagnostic of vehicular shock absorbers dynamic simulation behaviour[C]. Dipartimento di Meccanica del Politecnico di, Torino.1990.
[51]Cafferty S., Worden K., Tomlinson G. Characterization of automotive shock absorbers using random excitation [J]. Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering.1995,209:239-248.
[52]Schiehlen W., Hu B. Spectral simulation and shock absorber identification[J]. International Journal of Non-Linear Mechanics.2003,38:161-171.
[53]Tsai C.S., Chen K.C., Lin S.B., etc. Analytic model of fluid viscous damper under seismic loadings[J]. Seismic Engineering.2000,1:175-182.
[54]刘延庆,张建武.车用双筒液压减振器动态响应的试验与仿真[J].上海交通大学学报.2002,36(8)：1095-1099.
[55]王一兵,徐明龙,邱阳.汽车液压阻尼器的四段线性化模型[J].应用力学学报.2003,20(2)：60-63.
[56]俞德孚,陈庆东,方大雨.悬架减振器外特性平安比的设计研究[J].车辆与动力技术.2002,87(3)：11-17.
[57]SahinY, Ibrahim U. Neuralnetwork application to vehicle's vibration analysis[J]. Mechanism and Machine Theory.2003,38:27-41.
[58]Yildirim S. Vibration Control of Suspension Systems Using a Proposed Neural Network[J]. Journal of Sound and Vibration.2004,277(4):1059-1069.
[59]Szygula M. Development of the computer simulation method on energy absorbing device[C]. Komag Testing Laboratory.2002.
[60]Rakheja M.D., Su H., Sankar T.S. Analysis of a passive sequential hydraulic damper for vehicle suspension[J]. Vehicle System Dynamics.1999,19:289-295.
[61]Fukushima N, Hidaka K, Iwata K. Optimum Characteristics of Automotive Shock Absorbers under Various Driving Conditions and Road Surfaces [J]. International Journal of Vehicle Design.1983,4(5):15-19.
[62]Gobbi M., Mastinu G. Analytical description and optimization of the dynamic behaviour of passively suspended road vehieles[J]. Journal of Sound and Vibration. 2001,245(3):457-481.
[63]李莉.基于ADAMS/Car的某轿车平顺性仿真、分析与改进[D].吉林大学博士毕业论文.2007.
[64]David C. The influence of damper properties on vehicle dynamic behavior[J]. SAE Paper.2002-01-0319.
[65]Etman, L.F.P., Vernmeulen, R.C.N, etc. Design of a stroke dependent damper for the front axle suspension of a truck using multibody system dynamics and numerical optimization[J]. Vehicle System Dynamics.2002,38(2):85-101.
[66]William F.M., Douglas L.M. Race car vehicle dynamics[C]. SAE Paper.1999-792.
[67]Holen P., Thorvald B. Aspects on roll and bounce damping for heavy vehicles[C]. SAE Paper 2002-01-3060.
[68]MSC software corporation. MSC. Dytran Workshop Examples[M]. USA.2010.
[69]MSC software corporation. MSC. Documentation Library[M]. USA.2010.
[70]Horst G, Stanislaw S., Krzysztof M. Use of the finite elements method for modelling the dynamic load impact on hydraulic leg[J]. Sbornik Vedecky Chpracivy Sokeskoly Banske.2007, (1):61-72.
[71]杨基忠.车辆筒式减振器高频畸变特性研究[J].兵工学报.1999,75(3)：12-18.
[72]俞德孚,马彪.悬架减振器外特性畸变及其对车辆运行的有害影响[J].兵工学报坦克装甲车与发动机分册.1990,(1)：32-39.
[73]俞德孚,刘晓璞,李晓雷.车辆悬架减振器外特性的高频畸变与高频设计[J].北京工业学院学报.1988,8(3)：82-89.
[74]鲁明俊.冲击载荷下Xcxy-1型减振器动态特性分析[J].石油矿场机械.2007,36(11)：11-13.
[75]景晓华.垂直冲击减振器的实验研究[J].机械研究与应用.2005,18(1)：14-15.
[76]谭波.锤击法测量减振器冲击刚度[J].噪声与振动控制.2003,(4)：43-45.
[77]周长城,减振器液压气穴与气体反弹现象的研究[J].液压与气动.2007,(8)：3-7.
[78]王侃.某轻型车辆液力减震器活塞杆断裂失效分析[J].兵器材料科学与工程.2008,32(1)：82-85.
[79]陈轶杰,顾亮.减振器节流阀片对阀门水击力的影响研究[J].振动与冲击.2008,27(2)：103-106.
[80]Bourel B. Handling contact in multi-domain simulation of automobile crashes[J]. Finite Elements in Analysis and Design.2006,42:766-779.
[81]Mei L.Q., Thole C.A. Data analysis for parallel car-crash simulation results and model optimization[J]. Simulation Modeling Practice and Theory.2008,16:329-337.
[82]Surendra K. Use of unsymmetric finite element method in impact analysis of composite laminates[J]. Finite Element in Analysis and Design.2011,47:373-377.
[83]Lynn K.M., Isobe D. Structural collapse analysis of framed structures under Impact loads using ASI-Gauss finite element method[J]. International Journal of Impact Engineering.2007,34:1500-1516.
[84]Peter I. On the simulation of failure mechanisms in steel structures [J]. Advances in Engineering Software.2009,40:871-882.
[85]Deb A, M.S. Mahendrakumar, C. Chavan, J. Karve, etc. Design of an aluminium-based vehicle platform for front impact safety[J]. International Journal of Impact Engineering.2004,30:1055-1079.
[86]Stijn D, Brughmansa M, Hermansa L. The robustness of dynamic vehicle performance to spot weld failures[J]. Finite Elements in Analysis and Design. 2006,42:670-682.
[87]Cheng Z.Q. Experiences in reverse-engineering of a finite element automobile crash model[J]. Finite Elements in Analysis and Design.2001,37:68-74.
[88]Dario V. Simplified method for evaluating energy loss in vehicle collisions[J]. Accident Analysis and Prevention.2009,41:633-641.
[89]Gary R. Impact simulation and full scale crash testing of a low profile concrete work zone barrier[J]. Computers and Structures.2003,81:1359-1374.
[90]Bossak M., Jakub K. Global/local analysis of composite light aircraft crash landing[J]. Computers and Structures.2003,81:503-514.
[91]雷正保,龙建强.汽车碰撞CAE技术中几个尚未解决的问题.长沙交通学院学报.2003,19(3)：415-417.
[92]赵广耀,樊新华,邸建卫,付东宇等.车辆碰撞计算机模拟分析与评价[J].东北大学学报(自然科学版).2008,7：42-45.
[93]赵欣超,朱平.基于两种正面碰撞的轿车耐撞性能仿真与改进研究[J].汽车工程.2007,29(10)：842-846.
[94]王大志.基于乘员保护的汽车正面碰撞结构设计与变形控制研究[D].清华大学博士毕业论文.2001,18-78.
[95]李碧浩,杜汉斌,卓鹏等.轿车侧面碰撞安全性能改进措施探讨[J].汽车工程.2008,30(11)：23-26.
[96]William A. Numerical simulation of AM50A magnesium alloy under large deformation [J]. International Journal of Impact Engineering.2004,30:117-142.
[97]Javad M. Design and analysis of an automotive bumper beam in low-speed frontal crashes[J]. Thin-Walled Structures.2009,47:902-911.
[98]Mohamed S.N., Guptab N.K., Velmurugan R. Optimization of thin conical frusta for impact energy absorption[J]. Thin-Walled Structures.2009,46:653-666.
[99]Herzl C. On optimizing crash energy and load-bearing capacity in cellular structures [J]. International Journal of Solids and Structures.2008,45:528-539.
[100]Rajendran R., Moorthi A., Basu S. Numerical simulation of drop weight impact behavior of closed cell aluminium foam[J]. Materials and Design. 2009,30(8):2823-2830.
[101]Zarei H.R., Kroger M. Bending behavior of empty and foam-filled beams:structural optimization[J]. International Journal of Impact Engineering.2008,35:521-529.
[102]Zarei H.R., Kroger M. Optimization of the foam-filled aluminum tubes for crush box application[J]. Thin-Walled Structures.2008,48:214-221.
[103]李素霞,雷正保.面向中级轿车的低成本螺纹剪切吸能结构优化设计[J].长沙理工大学学报.2009,6(2)：51-55.
[104]Lee D.W. FOA(first-order analysis)model of a granule-filled tube for vehicle crash energy absorption[J]. Mechanics of Materials.2009,41:684-690.
[105]Chen D.H., Ozaki S. Numerical study of axially crushed cylindrical tubes with corrugated surface[J]. Thin-Walled Structures.2009,47:1387-1396.
[106]Rossi A. Numerical simulation of the axial collapse of thin-walled polygonal section tubes[J]. Thin-Walled Structures,2005,43:1646-1661.
[107]Nagel G.M., Thambiratnam D.P. A numerical study on the impact response and energy absorption of tapered thin-walled tubes[J]. International Journal of Mechanical Sciences.2004,46:201-216.
[108]Mamalis A.G., Manolakos D.E., Ioannidis M.B. On the crashworthiness of composite rectangular thin-walled tubes internally reinforced with aluminium or polymeric foams:Experimental and numerical simulation[J]. Composite Structures. 2009,89(3):416-423.
[109]陈懋章.粘性流体力学[M].高等教育出版社.2002,1-72.
[110]夏泰淳.工程流体力学[M].上海交通大学出版社.2006,15-213.
[111]陈卓如,金朝铭,王成敏等.工程流体力学[M].高等教育出版社.1992,280-425.
[112]机械设计手册编委会.机械设计手册[M].机械工业出版社.2006,23-19.
[113]郭金基.平行平板间径向气流的Navier-Stokes方程的近似解[J].力学学报.1980,(3)：306-310.
[114]袁锰吾.平行平板间径向气流的Navier-stokes方程的新的近似解[J].上海力学.1985,(2)：1-9.
[115]黄德成,膝克利,江体乾.两固定平行圆盘间幂律流体径向流动的摄动解法[J].华东化工学院学报.1992,12(6)：798-807.
[116]王致清,刘震北.在液压工程中两平行圆板间径向层流的压力损失与流量的计算问题[J].液压气动与密封.1982,5-11.
[117]金朝铭,王致清.在液压工程中两平行圆板间径向层流的压力损失与流量的计算问题(续)[J].液压气动与密封.1984,(04)：14-16.
[118]刘震北,王致清.两平行圆板间径向层流进口段效应分析[J].应用数学和力学.1984,5(1)：77-89.
[119]丁忠满,王致清.幂律流体两平行圆板间径向扩散层流进口段流动阻力的分析[J].力学学报.1994,26(3)：368-373.
[120]周长城,顾亮.筒式减振器叠加节流阀片开度与特性试验[J].机械工程学报.2007,43(6)：210-215.
[121]铁摩辛科S.,沃诺斯基S.板壳理论[M].科学出版社.1977,1-75.
[122]刘鸿文,林建兴,曹曼玲.板壳理论[M].浙江大学出版社.1992,1-141.
[123]谭刚,李华译KYB SL20减震器验算书[Z].山川机械厂.1998,6-17.
[124]田茹会,王钟羡.改进的遗传算法在减振器优化中的应用[J].机械工程师.2006,(3)：99-101.
[125]马振来.汽车液压减震器参数优化设计[D].哈尔滨工业大学博士毕业论文.2002.
[126]Kruse A. Characterizing and reducing structural noises of vehicle shock absorber systems[C]. SAE Paper.2002-01-1234.
[127]刘延庆.车用液压减振器的异常噪声及动力学特性研究[D].上海交通大学博士毕业论文.2002.