车辆半主动悬架非线性特性与控制算法研究
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摘要
车辆悬架系统是保证车辆行驶平顺性和稳定性的关键部件,半主动悬架形式是悬架发展的一大方向,也是近年来研究的重点热点之一。本文主要就随机路面谱模型、磁流变减振器非线性建模、半主动悬架非线性特性和半主动非线性悬架控制策略这四个半主动悬架研究中的关键问题进行理论与实验研究,取得了如下一些进展：
提出一种能同时表征路面不平度和轮迹激励相干性的三维路面谱建模方法。基于二维路面谱模型,深入研究时间域内路面不平度的谐波叠加方法的原理,将其拓展到三维空间内,提出三维路面谱的建模方法,并对其进行数值仿真研究。频谱特性分析表明,该三维路面模型能够很好地模拟实际路面不平度并能有效描述车辆行驶中轮迹激励之间的相干性关系。
提出一种新的改进的磁流变减振器Bouc-Wen参数化模型。该模型解决已有的Bouc-Wen模型在低速下滞回环描述不准确,在高速下缺少滞回特性,并无法表述蓄能器造成阻尼力偏置的现象。并将最终的控制变量励磁电流引入了模型,通过实验数据的拟合和验证,表明改进的Bouc-Wen减振器模型能够更准确地磁流变减振器的滞环现象和阻尼外特性。
研究使用磁流变减振器的半主动悬架的非线性特性。根据得到的改进Bouc-Wen磁流变减振器模型,建立了四分之一改进Bouc-Wen悬架模型。对比了该非线性悬架与线性悬架的不同点,分析簧载质量、簧下质量、弹簧刚度、悬架阻尼等对非线性悬架整体动力学特性的影响。用混沌理论分析非线性悬架的振动特性,揭示其复杂多变的振动形式。而后通过相空间重构等手段,验证悬架系统在随机路面下存在混沌振动过程,为下一步的半主动悬架控制提供理论依据。
提出半主动最优天棚地棚混合控制策略。分析理想天棚阻尼、主动天棚阻尼、主动天棚地棚混合控制、半主动天棚地棚混合控制策略的控制特性,通过反馈线性化的方法,结合混沌VFC控制,设计出半主动悬架控制器,并在自主搭建的四分之一车辆悬架实验台架系统上验证了该控制策略的可实现性和有效性。经过正弦激励扫频试验和随机路面试验,结果表明该控制策略能很好地抑制振动对车身加速度和轮胎动位移的影响。
Vehicle suspension system is the key component for riding comfort and stability. Semi-active suspension is the development direction of suspension, but also a key research hotspot in recent years. In this paper, random surface model, damping nonlinear modeling, semi-active suspension nonlinear characteristics of semi-active suspension and nonlinear control strategy are studied in theoretical and experimental research and made some progress as follows:
A new approach to simulate three-dimensional road spectrum model, which could represent road surface roughness and coherence of wheelpath excitation, was put forward. The model was obtained by the further study on the sinusoid superposition method, based on two-dimensional road surface spectrum model. It was expanded to three-dimensional space, and was studied by numerical simulation. The spectrum characteristics analysis shows that, the new model reconstructed the time domain model of road surface spectrum and included the coherent relationship between wheelpaths of vehicle driving.
A modificatory Bouc-Wen parametric model is proposed, aiming at the nonlinear modeling of MRD. The new model can describe the hysteretic loop in low speed exactly, introduces hysteretic characteristics in high speed and contains the bias of damping force caused by accumulator of single-out-rod damper. The force-velocity and force-displacement curves are obtained by indicator experiment on self-designed large scaled MRD. The modificatory Bouc-Wen model parameters are identified with the test data, and correspond to the practical physical quantities. Then excitation current parameter is introduced to the model. The modificatory Bouc-Wen model is verified by experiment data finally.
The nonlinear characteristics of semi-active suspension including modificatory Bouc-Wen model are researched. It analyzed the influence on the varible sprung mass, unsprung mass, spring stiffness and dampering to the nonlinear suspension characteristics. Then it judged the vibration forms of nonlinear suspension on various frequency and amplitude, and studied the path of the suspension vibration to chaos with variety of pavement, by phase portrait, Poincare diagram and bifurcate diagram. Finally, the suspension response under stochastic road irregularities is simulated, and analyzes the time series. It proved that the suspension vibration is chaotic motion. The research ultimately indicates the chaotic behavior under variable situations, and provides the basis for the dynamic design of ground vehicle.
The semi-active control strategy of nonlinear suspension is studied based on analyzing the nonlinear force component of MRD. The optimal semi-active sky-ground hook hybrid control method is gain by layer progression from ideal sky-hook control method. The semi-active suspension controller is designed by feedback linearization method. The simulation result shows that the optimal semi-active sky-ground hook hybrid control method can inhibit vehicle body acceleration and dynamic tyre load. Then a quarter suspension vehicle lab system is established. And the effect of optimal semi-active sky-ground hook hybrid control method is verified by experiment.
提出一种能同时表征路面不平度和轮迹激励相干性的三维路面谱建模方法。基于二维路面谱模型,深入研究时间域内路面不平度的谐波叠加方法的原理,将其拓展到三维空间内,提出三维路面谱的建模方法,并对其进行数值仿真研究。频谱特性分析表明,该三维路面模型能够很好地模拟实际路面不平度并能有效描述车辆行驶中轮迹激励之间的相干性关系。
提出一种新的改进的磁流变减振器Bouc-Wen参数化模型。该模型解决已有的Bouc-Wen模型在低速下滞回环描述不准确,在高速下缺少滞回特性,并无法表述蓄能器造成阻尼力偏置的现象。并将最终的控制变量励磁电流引入了模型,通过实验数据的拟合和验证,表明改进的Bouc-Wen减振器模型能够更准确地磁流变减振器的滞环现象和阻尼外特性。
研究使用磁流变减振器的半主动悬架的非线性特性。根据得到的改进Bouc-Wen磁流变减振器模型,建立了四分之一改进Bouc-Wen悬架模型。对比了该非线性悬架与线性悬架的不同点,分析簧载质量、簧下质量、弹簧刚度、悬架阻尼等对非线性悬架整体动力学特性的影响。用混沌理论分析非线性悬架的振动特性,揭示其复杂多变的振动形式。而后通过相空间重构等手段,验证悬架系统在随机路面下存在混沌振动过程,为下一步的半主动悬架控制提供理论依据。
提出半主动最优天棚地棚混合控制策略。分析理想天棚阻尼、主动天棚阻尼、主动天棚地棚混合控制、半主动天棚地棚混合控制策略的控制特性,通过反馈线性化的方法,结合混沌VFC控制,设计出半主动悬架控制器,并在自主搭建的四分之一车辆悬架实验台架系统上验证了该控制策略的可实现性和有效性。经过正弦激励扫频试验和随机路面试验,结果表明该控制策略能很好地抑制振动对车身加速度和轮胎动位移的影响。
Vehicle suspension system is the key component for riding comfort and stability. Semi-active suspension is the development direction of suspension, but also a key research hotspot in recent years. In this paper, random surface model, damping nonlinear modeling, semi-active suspension nonlinear characteristics of semi-active suspension and nonlinear control strategy are studied in theoretical and experimental research and made some progress as follows:
A new approach to simulate three-dimensional road spectrum model, which could represent road surface roughness and coherence of wheelpath excitation, was put forward. The model was obtained by the further study on the sinusoid superposition method, based on two-dimensional road surface spectrum model. It was expanded to three-dimensional space, and was studied by numerical simulation. The spectrum characteristics analysis shows that, the new model reconstructed the time domain model of road surface spectrum and included the coherent relationship between wheelpaths of vehicle driving.
A modificatory Bouc-Wen parametric model is proposed, aiming at the nonlinear modeling of MRD. The new model can describe the hysteretic loop in low speed exactly, introduces hysteretic characteristics in high speed and contains the bias of damping force caused by accumulator of single-out-rod damper. The force-velocity and force-displacement curves are obtained by indicator experiment on self-designed large scaled MRD. The modificatory Bouc-Wen model parameters are identified with the test data, and correspond to the practical physical quantities. Then excitation current parameter is introduced to the model. The modificatory Bouc-Wen model is verified by experiment data finally.
The nonlinear characteristics of semi-active suspension including modificatory Bouc-Wen model are researched. It analyzed the influence on the varible sprung mass, unsprung mass, spring stiffness and dampering to the nonlinear suspension characteristics. Then it judged the vibration forms of nonlinear suspension on various frequency and amplitude, and studied the path of the suspension vibration to chaos with variety of pavement, by phase portrait, Poincare diagram and bifurcate diagram. Finally, the suspension response under stochastic road irregularities is simulated, and analyzes the time series. It proved that the suspension vibration is chaotic motion. The research ultimately indicates the chaotic behavior under variable situations, and provides the basis for the dynamic design of ground vehicle.
The semi-active control strategy of nonlinear suspension is studied based on analyzing the nonlinear force component of MRD. The optimal semi-active sky-ground hook hybrid control method is gain by layer progression from ideal sky-hook control method. The semi-active suspension controller is designed by feedback linearization method. The simulation result shows that the optimal semi-active sky-ground hook hybrid control method can inhibit vehicle body acceleration and dynamic tyre load. Then a quarter suspension vehicle lab system is established. And the effect of optimal semi-active sky-ground hook hybrid control method is verified by experiment.
引文
[1]顾伯良等.BOSCH汽车工程手册[M].北京理工大学出版社,北京,2004
[2]杨国桢,王福天.机车车辆液压减振器[M].中国铁道出版社.北京,2003.
[3]Priyandoko G, Mailah M, Jamaluddin H. Vehicle active suspension system using skyhook adaptive neuro active force control[J]. Mechanical Systems and Signal Processing,2009,23(3):855-868
[4]Huang C J, Lin J S, Chen C C. Road-adaptive algorithm design of half-car active suspension system[J]. Expert Systems with Applications,2010,37(6):4392-4402
[5]Jones M. Investigation of fraudulent arson involving a racing car [J]. Science & Justice,2002,42(4):231-234
[6]http://www.daimler.com. The Mercedes-Benz R-Class:spacious, prestigious and exceptionally comfortable
[7]http://www.citroen.com.cn/Models/Newcarselector/C6/Presentation东风雪铁龙公司雪铁龙C6介绍
[8]Yokoya K,Kizu R, Kawaguchi H,Ohashi K. Integrated control system between active control suspension and four wheel steering for the 1989 Celica[C]. Passenger Car Conference & Exposition, Dearborn, 1990.
[9]Grosby M J, Karnopp D C. The Active Damper-A New Concept for Shock and Vibration Control [J]. The Shock and Vibration Bull,1973,43(4): 119-133.
[10]Deprez K, Moshou D, Anthonis J, Baerdemaeker J, Ramon H. Improvement of vibrational comfort on agricultural vehicles by passive and semi-active cabin suspensions [J]. Computers and Electronics in Agriculture,2005,49(3):431-440
[11]Tanifuji K, Koizumi S, Shimamune R. Mechatronics in Japanese rail vehicles:active and semi-active suspensions [J]. Control Engineering Practice,2002,10(9):999-1004
[12]Schonfield K H, Geiger H, Hesse K H. Electronically controlled air suspensions (ECAS) for commercial vehicles [C]. International Truck & Bus Meeting & Exposition, Chicago,1991
[13]Log W D. An Improvement Research of Under body platform at midsize sedan-YF sonata Development Instances in Center[C]. SAE World Congress & Exhibition,2010.
[14]Sturesson P, Svensson C, Johansson P, Sohr P. Powertrain and Driveline Integration Using Transfer Path Analysis in the New Saab 9-5[C].6th International Styrian Noise, Vibration & Harshness Congress-Sustainable NVH solutions inspired by ecology and economy, 2010.
[15]Gregory W D. Development of a Flexible Fueled Snowmobile Operating on Ethanol Blended Gasoline for the 2010 SAE Clean Snowmobile Challenge[C]. Small Engine Technology Conference & Exposition, 2010.
[16]Yokoyama M, Hedrick J K, Toyama S. A Model Following Sliding-Mode Controller for Semi-active Suspensi on Systems with MR Dampers [C]. Proceedings of the American Control Conference, Arlington,2001.
[17]喻凡,林逸.汽车系统动力学.北京：机械工业出版社,2005
[18]Choi S B, Lee H K, Chang E G. Field Test Results of a Semi-active ER Suspension System Associated with Skyhook Controller [J]. Mechatronics,2001,11(1):345-353.
[19]Rabinow J..The Magnetic Fluid Clutch. The Science News-Letter, 1949,55(7):1308-1315
[20]Carlson J D. Magnetorheological Fluid Damper. U. S. Patent5277281, 1994
[21]Carlson J D. Magnetorheological Materials Based on Alloy Particles. U. S. Patent5382373,1995
[22]王维锐车辆悬架系统关键技术研究[D].杭州：浙江大学机械设计研究所,2006
[23]Jason E Lindler, Glen, A-Dimock and Norman M-Wereley, Design of A Magnetorheological Automotive Shock Absorber [C], Proc of SPIE, 2000,3985(385):426-437
[24]http://www.lord.com, Lord Corporation Magnetorheological (MR) Fluid for Automotive Damping Systems.
[25]Breese D G, Gordaninejad F. Heating of Magneto-Rheological Fluid Dampers:A Theoretical Study[C], SPIE Conference on Smart Systems for Bridges, Structures, and Highways,2007,221(1):265-278
[26]Gavin H, Hoagg J. Optimal design of MR Dampers[C]. Proc. U. S. -Japan Workshop on Smart Structures for Improved Seismic Performance in Urban Regions,Seattle,2001.
[27]Jeong-Hoi Koo, Fernando D. Goncalves, Mehdi Ahmadian, Investigation of the response time of magnetorheological fluid dampers [C], Proc. of SPIE,2004,5386(573):63-71
[28]欧进萍,关新春磁流变耗能器性能的试验研究[J]地震工程与工程振动.1999,19(4)：76-81
[29]欧进萍,关新春.磁流变耗能器及其性能[J].地震工程与工程振动.1998,18(3)：74-81
[30]邓志党,高峰,刘献栋等。汽车磁流变减振器阻尼特性理论计算与试验[J]。机械工程学报.2008,44(8)：202-207
[31]Stanway R, Sproston J L, Stevens N G. Nonlinear modeling of an electrorheological vibration damper [J]. Journal of Electrostatics, 1997,20(2):167-184
[32]Occhiuzzi A, Spizzuoco M and Serino G. Experimental analysis of magnetorheological dampers for structural control [J]. Smart Materials & Structures,2003(10):703-711
[33]翁建生,胡海岩。磁流变阻尼器的实验建模[J]振动工程学报,2000,13(4)：616-621
[34]Wereley N M, Pang L. Nondimensional analysis of semi-active electrorheological and magnetorheological dampers using approximate parallel plate models[J]. Smart Material and Structures,1998,7(5):97-105
[35]Spencer Jr B F, Dyke S J, Sain M K, et al. Phenomenological model for magnetorheologieal damper [J]. Journal of Engineering Mechanics, 1997,123(8):249-272
[36]关新春 磁流变液及其智能结构减振驱动器的理论与试验研究[D]哈尔滨工业大学,2000
[37]杨礼康,潘双夏,王维锐等.磁流变减振器滞环特性试验及建模方法[J].机械工程学报,2006,42(11):138-143
[38]徐赵东,李爱群,程文瀼等。磁流变阻尼器带质量元素的温度唯象模型[J].工程力学,2005,22(2)：144-148
[39]郭孔辉,孙胜利,邢云明,高仕猛.行程相关减振器的建模与试验[J].吉林大学学报：工学版。2008,38(2)：32-36
[40]Gavin H P, Hanson R D, Filisko F E. Electrorheological damper part I:analysis and design[J]. Transactions of the ASME Journal Applied Mechanic,1996,63(3):669-675
[41]廖昌荣 余淼 杨建春 陈伟民 黄尚廉 汽车磁流变减振器神经网络模型研究[J].中国公路学报。2003,16(4)：94-97
[42]汪小华 张培强 磁流变液阻尼器的模糊逻辑非参数建模[J]中国科学技术大学学报.2002,30(2)：218-222
[43]Choi S B, Lee S K. A hysteresis model for the field-dependent damping force of a magnetorheological damper [J]. Journal of Sound and Vibration,2001,245(2):375-383
[44]何亚东,黄金枝,何玉敖。智能磁流变(MR)阻尼器半主动控制的研究[J]。振动工程学报,2003,16(2)：198-202
[45]Zhu Q, Ishitobi M. Chaos and bifurcations in a nonlinear vehicle model [J]. Journal of Sound and Vibration,2004,275 (10):1136-1146
[46]Zhu Q, Ishitobi M. Chaotic vibration of a nonlinear full-vehicle model[J]. International Journal of Solids and Structures,2006, 43(2):747-759
[47]Grzegorz L, Marek B, Michael I F, et al. Chaotic vibration of a quarter-car model excited by the road surface profile[J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(5):1373-1383
[48]Grzegorz L, Marek B, Michael I F, et al. Chaotic response of a quarter car model forced by a road profile with a stochastic component [J]. Chaos, Solitons and Fractals,2007,39(5):2448-2456
[49]Zhu W Q, Huang Z L. Stochastic Hopf bifurcation of quasi non integrable Hamiltonian systems. International Journal of Non-Linear Mechanics,2005,34 (3):437-447
[50]Zhu W Q, Huang Z L. Lyapunov exponent and Stochastic stability of quasi integrable Hamiltonian systems [J]. Journal of Applied Mechanics,2005,66(1):211-217
[51]Zhu W Q, Ying Z G, Soong T T. An Optimal Nonlinear Stochastic Control Strategy for Randomly Excited Structural Systems[J]. Nonlinear Dynamics,2001,24(2):31-51.
[52]Zhu W Q, Ying Z G,Ni Y Q, et al. Optimal Nonlinear Stochastic Control of Hyst-eretic Systems [J]. Journal of Engineering Mechanics,2000, 126(25):1027-1032
[53]李鸿光,何旭,孟光.Bouc-Wen滞回系统动力学特性的仿真研究[J].系统仿真学报,2004,16(9)：2009-2011
[54]李韶华,杨绍普.具有滞后非线性的汽车悬架中的混沌[J].振动、测试与诊断,2003,23(2)：86-89
[55]杨绍普,李韶华,郭文武.随机激励滞后非线性汽车悬架系统的混沌运[J].振动、测试与诊断,2005,25(1)：22-25
[56]罗仁,曾京.列车系统蛇行运动稳定性分析及其与单车模型的比较[J].机械工程学报,2008,44(4)：184-188
[57]Sammier D, sename 0, dugard L. Skyhook and H ∞ Control of Semi-active Suspensions Some Practical Aspects [J]. Vehicle system dynamics,2003.39(4):279-308
[58]Simon D E. An Investigation of the Effectiveness of Skyhook Suspensions for Controlling Roll Dynamics of Sport Utility Vehicles Using Magneto-Rheological Dampers[D]. Blacksburg, Virginia Polytechnic Institute and State University,2001.
[59]Wang W L, Xu G X. Fluid formulae for damping changeability conceptual design of railway semi-active hydraulic dampers [J]. International Journal of Non-Linear Mechanics,2009,44(7):809-819
[60]Fernando D, Goncalve S, Mehdi A. A Hybrid Control Policy for Semi-active Vehicle Suspensions [J].Shock and Vibration,2003, 10(2):59-69.
[61]Brogan W L. Modern conteol theory[M], Prentice Hall, New Jersey, 1991
[62]Leitmann G. Semiactive control for vibration attenuation [J]. Journal of Intelligent Material Systems and Structures,1994,5(6): 841-846
[63]Woosoon Y, Sahjendra N S, Semi-active Control of Magnetorheological Damper System:A Lyapunov Design[C], Proceedings of SPIE,2004, 5383(289):289-297
[64]Dyke S J, Spencer B F Jr, Sain M K, et al. Modeling and control of magnetorheological dampers for seismic response reduction[J]. Smart Materials and Structures,2003,5(5):565-584
[65]Jansen L M, Dyke S J. Semi-active control strategies for the MR damper:a comparative study[J]. Journal of Engineering Mechanics, 2001,127(11):1129-1159
[66]Yoshida 0, Dyke S J. Seismic control of a nonlinear benchmark building using smart dampers [J]. Journal of Engineering Mechanics, 2004,130(4):386-392
[67]Uwe R, Oskar V S. Optimal and robust damping control for semi-active vehicle suspension[C]. Pro.5th EUROMECH Nonlinear Dynamics Conference,2005:125-136
[68]McClamroch N H, Gavin H P. Closed loop structural control using electrorheological dampers[C]. Proc. of the American Control Conference, Seattle, Washington,1995.
[69]Yang J N, Agrawal A K, Chen S. Optimal polynomial control for seismically excited nonlinear and hysteretic structures [J]. Earthquake Engineering and Structural Dynamics,1998,25(11): 1211-1230
[70]Swevers J, Lauwerys C, Vandersmissen B, et al. A model-free control structure for the on-line tuning of the semi-active suspension of a passenger car[C]. Mechanical Systems and Signal Processing,2007, 21(3):1422-1436
[71]Du H P, Kam Y S, James L. Semi-active H ∞ control of vehicle suspension with magneto-rheological dampers[J]. Journal of Sound and Vibration,2005,283(3-5):981-996
[72]杨礼康.基于磁流变技术的车辆半主动悬挂系统理论与试验研究[D].杭州：浙江大学机械设计研究所,2003
[73]Yahaya M S, Johari H S O, Ghani M R A. A class of proportional-integral sliding mode control with application to active suspension system[J]. Systems & Control Letters,2004,51(3-4):217-223
[74]Liu H, Nonami K, Hagiwara T. Active following fuzzy output feedback sliding mode control of real-vehicle semi-active suspensions[J]. Journal of Sound and Vibration,2008,314(1-2):39-52
[75]Byeonghwa K, Roschke P N. Linearization of Magnetorheological Behavior Using a Neural Network[C], Proceedings of the American Control Conference,1999
[76]陈无畏,王其东.汽车半主动悬架的非线性神经网络自适应控制研究[J].机械工程学报,2000,36(1)：75-78
[77]汪若尘,陈龙,江浩斌.时滞半主动悬架模糊神经网络控制[J].农业机械 学报,2007,38(7)：10-12,48
[78]Rao M V C, Prahlad V. A tunable fuzzy logic controller for vehicle-active suspension systems [J]. Fuzzy Sets and Systems,1997, 85(1):11-21
[79]来飞,邓兆祥,董红亮.考虑悬架几何特性及作动器延时的整车模糊控制[J].系统仿真学报,2008,20(20)：5695-5699
[80]陈兵,曾鸣,尹忠俊.车辆半主动悬架的模糊控制策略设计与仿真研究[J].系统仿真学报,2008,20(2)：420-424
[81]Song X B, Ahmadian M, Southward S, et al. An Adaptive Semiactive Control Algorithm for Magnetorheological Suspension Systems. Journal of Vibration and Acoustics,2005,127(5):493-502.
[82]余淼.汽车磁流变半主动悬架控制系统研究[D].重庆：重庆大学,2003
[83]孙鹏远,陈虹,康健等.汽车主动悬架的约束预测控制[J].吉林大学学报：信息科学版,2002,20(2)：47-53
[84]宋晓琳,殷智宏,郭孔辉等.基于免疫算法的汽车主动悬架控制研究[J].汽车工程,2006,28(5)：465-467,470
[85]LAUWERYS C, SWEVERS J, SAS P. Robust linear control of an active suspension on a quarter car test-rig. [J] Control Engineering Practice,2005,13(5):577-586
[86]Zhang Y L, Zhang J F. Numerical simulation of stochastic road process using white noise filtration. [J] Mechanical Systems and Signal Processing,2006,20(2):363-372
[87]余志生.汽车理论.[M]北京：机械工业出版社,2000：173-180
[88]卢文祥,杜润生机械工程测试.信息.信号分析(第二版)[M].武汉：华中科技大学出版社,1999：189-200
[89]黄志宇,刘保华,陈高平等随机信号的功率谱估计及Matlab的实现[J]现代电子技术2002,143(3)：21-23
[90]米奇克 M.汽车动力学(B卷).[M]陈萌三译.北京：人民交通出版社,1994：195-200
[91]张永林,胡志刚,陈立平时空相关车辆道路的高效数值仿真[J]农业机械 学报2005.36(9)：13-15
[92]张莉洁,王炅,钱林方.冲击载荷下磁流变阻尼器动态特性分析及模型参数识别[J].机械工程学报,2009,45(1)：211-217
[93]刘伟,刘大维,陈焕明,等.基于联合仿真的半主动悬架车辆行驶平顺性研究[J].农业机械学报,2009,40(6)：16-22
[94]Gavin H P, Hanson R D, Filisko F E. Electrorheological Dampers, Part Ⅰ:Analysis and Design[J]. Journal of Applied Mechanics. 1996,63(3):669-675.
[95]Kamath G M, Hurt M K, Wereley N M. Analysis and testing of Bingham plastic behavior in semi-active electrorheological fluid dampers [J]. Smart Materials and Structures,1996,5:576-90
[96]周云,谭平.磁流变阻尼控制理论与技术[M].北京：科学出版社,2007.
[97]杨礼康,潘双夏,王维锐等.磁流变减振器滞环特性试验及建模方法[J].机械工程学报,2006,42(11)：138-143
[98]Boada M J L, Calvo J A, Boada B L, et al. Modeling of a magnetorheological damper by recursive lazy learning [J]. International Journal of Non-Linear Mechanics, Available online 13 December 2008.
[99]Kwok N M, Ha Q P, Nguyen T H, et al. A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization[J]. Sensors and Actuators A: Physical,2006,132(2):441-451
[100]Metered H, Bonello P, Oyadiji S 0. The experimental identification of magnetorheological dampers and evaluation of their controllers [J]. Mechanical Systems and Signal Processing, Available online 16 September 2009.
[101]周燕.基于磁流变阻尼器的汽车半主动悬架的神经模糊控制[J].南京理工大学学报：自然科学版,2008,32(6)：715-718
[102]Alexander N A, Schilder F. Exploring the performance of a nonlinear tuned mass damper. Journal of Sound and Vibration,2009,319(1-2): 445-462
[103]Yang Y, Ren W Q, Chen L P, Jiang M, Yang Y L. Study on ride comfort of tractor with tandem suspension based on multi-body system dynamics. Applied Mathematical Modelling,2009,33(1):11-33
[104]Bai Y Q, Grigoriadis K M. Damping parameter design optimization in structural systems using an explicit Hoo norm bound. Journal of Sound and Vibration,2009,319 (3-5):117-132
[105]Awrejcewicza J, Dzyubakb L P. Evolution of chaotic regions in control parameter planes depending on hysteretic dissipation. Nonlinear Analysis,2005,63(5-7):155-164
[106]Charalampakis A E, Koumousis V K. Identification of Bouc-Wen hysteretic systems by a hybrid evolutionary algorithm [J]. Journal of Sound and Vibration,2008,314(5):571-585
[107]Ahmadian M, Norris J A. Experimental analysis of magnetorheological dampers when subjected to impact and shock loading [J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(2):1978-1985
[108]王良曦,王红岩.车辆动力学[M].北京：国防工业出版社,2008
[109]Thomas D G.车辆动力学基础[M].北京：清华大学出版社,2006
[110]冯纯伯,张侃健.非线性系统的鲁棒控制[M].北京：科学出版社,2004
[111]Sung K.J., Han Y.M., Cho J.W., Choi S.B.,2008. Vibration control of vehicle ER suspension system using fuzzy moving sliding mode controller. Journal of Sound and Vibration,311 (3-5):1004-1019
[112]刘小河非线性系统分析与控制引论.北京：清华大学出版社,2008
[113]吕金虎.一个统一混沌系统及其研究[D].中国科学院,2002
[114]Li Z J, Cai G W, Huang Q B, et al. Analysis of nonlinear vibration of a motor-linkage mechanism system with composite links[J]. Journal of Sound and Vibration,2008,311(7):924-940
[115]Cai W, Chang J N, Chao K. Bifurcation analysis of flexible rotor supported by couple-stress fluid film bearings with non-linear suspension systems[J]. Tribology International,2008,41(15): 367-386
[116]Albert C J L. On Global Transversality and Chaos in Two-Dimensional Nonlinear Dynamical Systems[J]. Journal of computational and nonlinear dynamics,2007,2 (3):242-248
[117]罗冠炜,张艳龙,谢建华.多自由度含间隙振动系统周期运动的二重Hopf分岔[J].工程力学,2006,23(3)：37-43
[118]Yamapi R, Aziz-Alaoui M A. Vibration analysis and bifurcations in the self-sustained electromechanical system with multiple functions [J]. Communications in Nonlinear Science and Numerical Simulation,2007,12(8):1534-1549
[119]Charalampakis A E, Koumousis V K. On the response and dissipated energy of Bouc-Wen hysteretic model [J]. Journal of Sound and Vibration,2008,309(143):887-895
[120]王艳群.Duffing振子混沌动力学研究[J].衡阳师范学院学报,2007,28(3)：33-35
[121]吕金虎,陆君安,陈士华.混沌时间序列及其应用[M].武汉大学出版社,2002.
[122]Cao L Y. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D,1997,110(20): 43-50
[123]王海燕,卢山.非线性时间序列分析及其应用.科学出版社,2006
[124]Takens F. On the numerical determination of the dimension of an attractor[J]. Dynamical Systems and Turbulence.1981,898:366-381
[125]Mane R. On the dimension of the compact invariant sets of certain nonlinear maps.1981,898:230
[126]SUNG K J, HAN Y M, CHO J W, et al. Vibration control of vehicle ER suspension system using fuzzy moving sliding mode controller[J]. Journal of Sound and Vibration,2008,311 (3-5):1004-1019
[127]王维锐,吴参,潘双夏等.车辆半主动悬架负刚度控制策略研究[J].浙 江大学学报：工学版,2009,43(6)：1129-1133
[128]YAGIZ N, HACIOGLU Y. Backstepping control of a vehicle with active suspensions [J]. Control Engineering Practice,2008,16(12): 1457-1467
[129]YU M, DONG X M, CHOI S B, et al. Human simulated intelligent control of vehicle suspension system with MR dampers [J]. Journal of Sound and Vibration,2009,319(3-5):753-767
[130]汪若尘,江浩斌,张效良等.阻尼非线性半主动悬架的建模与控制[J].农业机械学报,2008,39(12)：14-17
[131]GRZEGORZ L, MAREK B, MICHEAL I F, et al. Chaotic vibration of a quarter-car model excited by the road surface profile[J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(5):1373-1383
[132]Yagiz N, Hacioglu Y. Backstepping control of a vehicle with active suspensions [J]. Control Engineering Practice,2008,16(12): 1457-1467
[133]Zapateiro M, Luo N, Karimi H R, et al. Vibration control of a class of semi-active suspension system using neural network and backstepping techniques [J]. Mechanical Systems and Signal Processing, In Press, Accepted Manuscript, Available online 31 October 2008
[134]Yu M, Dong X M, Choi S B, et al. Human simulated intelligent control of vehicle suspension system with MR dampers [J]. Journal of Sound and Vibration,2009,319(3-5):753-767
[135]Wan C, Jian C, Chen C K. Chaotic response and bifurcation analysis of a flexible rotor supported by porous and non-porous bearings with nonlinear suspension[J]. Nonlinear Analysis:Real World Applications,2009,10(2):1114-1138
[136]Dekker H. Vibrational resonances of nonrigid vehicles: Polygonization and ripple patterns [J]. Applied Mathematical Modelling,2009,33(3):1349-1355
[2]杨国桢,王福天.机车车辆液压减振器[M].中国铁道出版社.北京,2003.
[3]Priyandoko G, Mailah M, Jamaluddin H. Vehicle active suspension system using skyhook adaptive neuro active force control[J]. Mechanical Systems and Signal Processing,2009,23(3):855-868
[4]Huang C J, Lin J S, Chen C C. Road-adaptive algorithm design of half-car active suspension system[J]. Expert Systems with Applications,2010,37(6):4392-4402
[5]Jones M. Investigation of fraudulent arson involving a racing car [J]. Science & Justice,2002,42(4):231-234
[6]http://www.daimler.com. The Mercedes-Benz R-Class:spacious, prestigious and exceptionally comfortable
[7]http://www.citroen.com.cn/Models/Newcarselector/C6/Presentation东风雪铁龙公司雪铁龙C6介绍
[8]Yokoya K,Kizu R, Kawaguchi H,Ohashi K. Integrated control system between active control suspension and four wheel steering for the 1989 Celica[C]. Passenger Car Conference & Exposition, Dearborn, 1990.
[9]Grosby M J, Karnopp D C. The Active Damper-A New Concept for Shock and Vibration Control [J]. The Shock and Vibration Bull,1973,43(4): 119-133.
[10]Deprez K, Moshou D, Anthonis J, Baerdemaeker J, Ramon H. Improvement of vibrational comfort on agricultural vehicles by passive and semi-active cabin suspensions [J]. Computers and Electronics in Agriculture,2005,49(3):431-440
[11]Tanifuji K, Koizumi S, Shimamune R. Mechatronics in Japanese rail vehicles:active and semi-active suspensions [J]. Control Engineering Practice,2002,10(9):999-1004
[12]Schonfield K H, Geiger H, Hesse K H. Electronically controlled air suspensions (ECAS) for commercial vehicles [C]. International Truck & Bus Meeting & Exposition, Chicago,1991
[13]Log W D. An Improvement Research of Under body platform at midsize sedan-YF sonata Development Instances in Center[C]. SAE World Congress & Exhibition,2010.
[14]Sturesson P, Svensson C, Johansson P, Sohr P. Powertrain and Driveline Integration Using Transfer Path Analysis in the New Saab 9-5[C].6th International Styrian Noise, Vibration & Harshness Congress-Sustainable NVH solutions inspired by ecology and economy, 2010.
[15]Gregory W D. Development of a Flexible Fueled Snowmobile Operating on Ethanol Blended Gasoline for the 2010 SAE Clean Snowmobile Challenge[C]. Small Engine Technology Conference & Exposition, 2010.
[16]Yokoyama M, Hedrick J K, Toyama S. A Model Following Sliding-Mode Controller for Semi-active Suspensi on Systems with MR Dampers [C]. Proceedings of the American Control Conference, Arlington,2001.
[17]喻凡,林逸.汽车系统动力学.北京：机械工业出版社,2005
[18]Choi S B, Lee H K, Chang E G. Field Test Results of a Semi-active ER Suspension System Associated with Skyhook Controller [J]. Mechatronics,2001,11(1):345-353.
[19]Rabinow J..The Magnetic Fluid Clutch. The Science News-Letter, 1949,55(7):1308-1315
[20]Carlson J D. Magnetorheological Fluid Damper. U. S. Patent5277281, 1994
[21]Carlson J D. Magnetorheological Materials Based on Alloy Particles. U. S. Patent5382373,1995
[22]王维锐车辆悬架系统关键技术研究[D].杭州：浙江大学机械设计研究所,2006
[23]Jason E Lindler, Glen, A-Dimock and Norman M-Wereley, Design of A Magnetorheological Automotive Shock Absorber [C], Proc of SPIE, 2000,3985(385):426-437
[24]http://www.lord.com, Lord Corporation Magnetorheological (MR) Fluid for Automotive Damping Systems.
[25]Breese D G, Gordaninejad F. Heating of Magneto-Rheological Fluid Dampers:A Theoretical Study[C], SPIE Conference on Smart Systems for Bridges, Structures, and Highways,2007,221(1):265-278
[26]Gavin H, Hoagg J. Optimal design of MR Dampers[C]. Proc. U. S. -Japan Workshop on Smart Structures for Improved Seismic Performance in Urban Regions,Seattle,2001.
[27]Jeong-Hoi Koo, Fernando D. Goncalves, Mehdi Ahmadian, Investigation of the response time of magnetorheological fluid dampers [C], Proc. of SPIE,2004,5386(573):63-71
[28]欧进萍,关新春磁流变耗能器性能的试验研究[J]地震工程与工程振动.1999,19(4)：76-81
[29]欧进萍,关新春.磁流变耗能器及其性能[J].地震工程与工程振动.1998,18(3)：74-81
[30]邓志党,高峰,刘献栋等。汽车磁流变减振器阻尼特性理论计算与试验[J]。机械工程学报.2008,44(8)：202-207
[31]Stanway R, Sproston J L, Stevens N G. Nonlinear modeling of an electrorheological vibration damper [J]. Journal of Electrostatics, 1997,20(2):167-184
[32]Occhiuzzi A, Spizzuoco M and Serino G. Experimental analysis of magnetorheological dampers for structural control [J]. Smart Materials & Structures,2003(10):703-711
[33]翁建生,胡海岩。磁流变阻尼器的实验建模[J]振动工程学报,2000,13(4)：616-621
[34]Wereley N M, Pang L. Nondimensional analysis of semi-active electrorheological and magnetorheological dampers using approximate parallel plate models[J]. Smart Material and Structures,1998,7(5):97-105
[35]Spencer Jr B F, Dyke S J, Sain M K, et al. Phenomenological model for magnetorheologieal damper [J]. Journal of Engineering Mechanics, 1997,123(8):249-272
[36]关新春 磁流变液及其智能结构减振驱动器的理论与试验研究[D]哈尔滨工业大学,2000
[37]杨礼康,潘双夏,王维锐等.磁流变减振器滞环特性试验及建模方法[J].机械工程学报,2006,42(11):138-143
[38]徐赵东,李爱群,程文瀼等。磁流变阻尼器带质量元素的温度唯象模型[J].工程力学,2005,22(2)：144-148
[39]郭孔辉,孙胜利,邢云明,高仕猛.行程相关减振器的建模与试验[J].吉林大学学报：工学版。2008,38(2)：32-36
[40]Gavin H P, Hanson R D, Filisko F E. Electrorheological damper part I:analysis and design[J]. Transactions of the ASME Journal Applied Mechanic,1996,63(3):669-675
[41]廖昌荣 余淼 杨建春 陈伟民 黄尚廉 汽车磁流变减振器神经网络模型研究[J].中国公路学报。2003,16(4)：94-97
[42]汪小华 张培强 磁流变液阻尼器的模糊逻辑非参数建模[J]中国科学技术大学学报.2002,30(2)：218-222
[43]Choi S B, Lee S K. A hysteresis model for the field-dependent damping force of a magnetorheological damper [J]. Journal of Sound and Vibration,2001,245(2):375-383
[44]何亚东,黄金枝,何玉敖。智能磁流变(MR)阻尼器半主动控制的研究[J]。振动工程学报,2003,16(2)：198-202
[45]Zhu Q, Ishitobi M. Chaos and bifurcations in a nonlinear vehicle model [J]. Journal of Sound and Vibration,2004,275 (10):1136-1146
[46]Zhu Q, Ishitobi M. Chaotic vibration of a nonlinear full-vehicle model[J]. International Journal of Solids and Structures,2006, 43(2):747-759
[47]Grzegorz L, Marek B, Michael I F, et al. Chaotic vibration of a quarter-car model excited by the road surface profile[J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(5):1373-1383
[48]Grzegorz L, Marek B, Michael I F, et al. Chaotic response of a quarter car model forced by a road profile with a stochastic component [J]. Chaos, Solitons and Fractals,2007,39(5):2448-2456
[49]Zhu W Q, Huang Z L. Stochastic Hopf bifurcation of quasi non integrable Hamiltonian systems. International Journal of Non-Linear Mechanics,2005,34 (3):437-447
[50]Zhu W Q, Huang Z L. Lyapunov exponent and Stochastic stability of quasi integrable Hamiltonian systems [J]. Journal of Applied Mechanics,2005,66(1):211-217
[51]Zhu W Q, Ying Z G, Soong T T. An Optimal Nonlinear Stochastic Control Strategy for Randomly Excited Structural Systems[J]. Nonlinear Dynamics,2001,24(2):31-51.
[52]Zhu W Q, Ying Z G,Ni Y Q, et al. Optimal Nonlinear Stochastic Control of Hyst-eretic Systems [J]. Journal of Engineering Mechanics,2000, 126(25):1027-1032
[53]李鸿光,何旭,孟光.Bouc-Wen滞回系统动力学特性的仿真研究[J].系统仿真学报,2004,16(9)：2009-2011
[54]李韶华,杨绍普.具有滞后非线性的汽车悬架中的混沌[J].振动、测试与诊断,2003,23(2)：86-89
[55]杨绍普,李韶华,郭文武.随机激励滞后非线性汽车悬架系统的混沌运[J].振动、测试与诊断,2005,25(1)：22-25
[56]罗仁,曾京.列车系统蛇行运动稳定性分析及其与单车模型的比较[J].机械工程学报,2008,44(4)：184-188
[57]Sammier D, sename 0, dugard L. Skyhook and H ∞ Control of Semi-active Suspensions Some Practical Aspects [J]. Vehicle system dynamics,2003.39(4):279-308
[58]Simon D E. An Investigation of the Effectiveness of Skyhook Suspensions for Controlling Roll Dynamics of Sport Utility Vehicles Using Magneto-Rheological Dampers[D]. Blacksburg, Virginia Polytechnic Institute and State University,2001.
[59]Wang W L, Xu G X. Fluid formulae for damping changeability conceptual design of railway semi-active hydraulic dampers [J]. International Journal of Non-Linear Mechanics,2009,44(7):809-819
[60]Fernando D, Goncalve S, Mehdi A. A Hybrid Control Policy for Semi-active Vehicle Suspensions [J].Shock and Vibration,2003, 10(2):59-69.
[61]Brogan W L. Modern conteol theory[M], Prentice Hall, New Jersey, 1991
[62]Leitmann G. Semiactive control for vibration attenuation [J]. Journal of Intelligent Material Systems and Structures,1994,5(6): 841-846
[63]Woosoon Y, Sahjendra N S, Semi-active Control of Magnetorheological Damper System:A Lyapunov Design[C], Proceedings of SPIE,2004, 5383(289):289-297
[64]Dyke S J, Spencer B F Jr, Sain M K, et al. Modeling and control of magnetorheological dampers for seismic response reduction[J]. Smart Materials and Structures,2003,5(5):565-584
[65]Jansen L M, Dyke S J. Semi-active control strategies for the MR damper:a comparative study[J]. Journal of Engineering Mechanics, 2001,127(11):1129-1159
[66]Yoshida 0, Dyke S J. Seismic control of a nonlinear benchmark building using smart dampers [J]. Journal of Engineering Mechanics, 2004,130(4):386-392
[67]Uwe R, Oskar V S. Optimal and robust damping control for semi-active vehicle suspension[C]. Pro.5th EUROMECH Nonlinear Dynamics Conference,2005:125-136
[68]McClamroch N H, Gavin H P. Closed loop structural control using electrorheological dampers[C]. Proc. of the American Control Conference, Seattle, Washington,1995.
[69]Yang J N, Agrawal A K, Chen S. Optimal polynomial control for seismically excited nonlinear and hysteretic structures [J]. Earthquake Engineering and Structural Dynamics,1998,25(11): 1211-1230
[70]Swevers J, Lauwerys C, Vandersmissen B, et al. A model-free control structure for the on-line tuning of the semi-active suspension of a passenger car[C]. Mechanical Systems and Signal Processing,2007, 21(3):1422-1436
[71]Du H P, Kam Y S, James L. Semi-active H ∞ control of vehicle suspension with magneto-rheological dampers[J]. Journal of Sound and Vibration,2005,283(3-5):981-996
[72]杨礼康.基于磁流变技术的车辆半主动悬挂系统理论与试验研究[D].杭州：浙江大学机械设计研究所,2003
[73]Yahaya M S, Johari H S O, Ghani M R A. A class of proportional-integral sliding mode control with application to active suspension system[J]. Systems & Control Letters,2004,51(3-4):217-223
[74]Liu H, Nonami K, Hagiwara T. Active following fuzzy output feedback sliding mode control of real-vehicle semi-active suspensions[J]. Journal of Sound and Vibration,2008,314(1-2):39-52
[75]Byeonghwa K, Roschke P N. Linearization of Magnetorheological Behavior Using a Neural Network[C], Proceedings of the American Control Conference,1999
[76]陈无畏,王其东.汽车半主动悬架的非线性神经网络自适应控制研究[J].机械工程学报,2000,36(1)：75-78
[77]汪若尘,陈龙,江浩斌.时滞半主动悬架模糊神经网络控制[J].农业机械 学报,2007,38(7)：10-12,48
[78]Rao M V C, Prahlad V. A tunable fuzzy logic controller for vehicle-active suspension systems [J]. Fuzzy Sets and Systems,1997, 85(1):11-21
[79]来飞,邓兆祥,董红亮.考虑悬架几何特性及作动器延时的整车模糊控制[J].系统仿真学报,2008,20(20)：5695-5699
[80]陈兵,曾鸣,尹忠俊.车辆半主动悬架的模糊控制策略设计与仿真研究[J].系统仿真学报,2008,20(2)：420-424
[81]Song X B, Ahmadian M, Southward S, et al. An Adaptive Semiactive Control Algorithm for Magnetorheological Suspension Systems. Journal of Vibration and Acoustics,2005,127(5):493-502.
[82]余淼.汽车磁流变半主动悬架控制系统研究[D].重庆：重庆大学,2003
[83]孙鹏远,陈虹,康健等.汽车主动悬架的约束预测控制[J].吉林大学学报：信息科学版,2002,20(2)：47-53
[84]宋晓琳,殷智宏,郭孔辉等.基于免疫算法的汽车主动悬架控制研究[J].汽车工程,2006,28(5)：465-467,470
[85]LAUWERYS C, SWEVERS J, SAS P. Robust linear control of an active suspension on a quarter car test-rig. [J] Control Engineering Practice,2005,13(5):577-586
[86]Zhang Y L, Zhang J F. Numerical simulation of stochastic road process using white noise filtration. [J] Mechanical Systems and Signal Processing,2006,20(2):363-372
[87]余志生.汽车理论.[M]北京：机械工业出版社,2000：173-180
[88]卢文祥,杜润生机械工程测试.信息.信号分析(第二版)[M].武汉：华中科技大学出版社,1999：189-200
[89]黄志宇,刘保华,陈高平等随机信号的功率谱估计及Matlab的实现[J]现代电子技术2002,143(3)：21-23
[90]米奇克 M.汽车动力学(B卷).[M]陈萌三译.北京：人民交通出版社,1994：195-200
[91]张永林,胡志刚,陈立平时空相关车辆道路的高效数值仿真[J]农业机械 学报2005.36(9)：13-15
[92]张莉洁,王炅,钱林方.冲击载荷下磁流变阻尼器动态特性分析及模型参数识别[J].机械工程学报,2009,45(1)：211-217
[93]刘伟,刘大维,陈焕明,等.基于联合仿真的半主动悬架车辆行驶平顺性研究[J].农业机械学报,2009,40(6)：16-22
[94]Gavin H P, Hanson R D, Filisko F E. Electrorheological Dampers, Part Ⅰ:Analysis and Design[J]. Journal of Applied Mechanics. 1996,63(3):669-675.
[95]Kamath G M, Hurt M K, Wereley N M. Analysis and testing of Bingham plastic behavior in semi-active electrorheological fluid dampers [J]. Smart Materials and Structures,1996,5:576-90
[96]周云,谭平.磁流变阻尼控制理论与技术[M].北京：科学出版社,2007.
[97]杨礼康,潘双夏,王维锐等.磁流变减振器滞环特性试验及建模方法[J].机械工程学报,2006,42(11)：138-143
[98]Boada M J L, Calvo J A, Boada B L, et al. Modeling of a magnetorheological damper by recursive lazy learning [J]. International Journal of Non-Linear Mechanics, Available online 13 December 2008.
[99]Kwok N M, Ha Q P, Nguyen T H, et al. A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization[J]. Sensors and Actuators A: Physical,2006,132(2):441-451
[100]Metered H, Bonello P, Oyadiji S 0. The experimental identification of magnetorheological dampers and evaluation of their controllers [J]. Mechanical Systems and Signal Processing, Available online 16 September 2009.
[101]周燕.基于磁流变阻尼器的汽车半主动悬架的神经模糊控制[J].南京理工大学学报：自然科学版,2008,32(6)：715-718
[102]Alexander N A, Schilder F. Exploring the performance of a nonlinear tuned mass damper. Journal of Sound and Vibration,2009,319(1-2): 445-462
[103]Yang Y, Ren W Q, Chen L P, Jiang M, Yang Y L. Study on ride comfort of tractor with tandem suspension based on multi-body system dynamics. Applied Mathematical Modelling,2009,33(1):11-33
[104]Bai Y Q, Grigoriadis K M. Damping parameter design optimization in structural systems using an explicit Hoo norm bound. Journal of Sound and Vibration,2009,319 (3-5):117-132
[105]Awrejcewicza J, Dzyubakb L P. Evolution of chaotic regions in control parameter planes depending on hysteretic dissipation. Nonlinear Analysis,2005,63(5-7):155-164
[106]Charalampakis A E, Koumousis V K. Identification of Bouc-Wen hysteretic systems by a hybrid evolutionary algorithm [J]. Journal of Sound and Vibration,2008,314(5):571-585
[107]Ahmadian M, Norris J A. Experimental analysis of magnetorheological dampers when subjected to impact and shock loading [J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(2):1978-1985
[108]王良曦,王红岩.车辆动力学[M].北京：国防工业出版社,2008
[109]Thomas D G.车辆动力学基础[M].北京：清华大学出版社,2006
[110]冯纯伯,张侃健.非线性系统的鲁棒控制[M].北京：科学出版社,2004
[111]Sung K.J., Han Y.M., Cho J.W., Choi S.B.,2008. Vibration control of vehicle ER suspension system using fuzzy moving sliding mode controller. Journal of Sound and Vibration,311 (3-5):1004-1019
[112]刘小河非线性系统分析与控制引论.北京：清华大学出版社,2008
[113]吕金虎.一个统一混沌系统及其研究[D].中国科学院,2002
[114]Li Z J, Cai G W, Huang Q B, et al. Analysis of nonlinear vibration of a motor-linkage mechanism system with composite links[J]. Journal of Sound and Vibration,2008,311(7):924-940
[115]Cai W, Chang J N, Chao K. Bifurcation analysis of flexible rotor supported by couple-stress fluid film bearings with non-linear suspension systems[J]. Tribology International,2008,41(15): 367-386
[116]Albert C J L. On Global Transversality and Chaos in Two-Dimensional Nonlinear Dynamical Systems[J]. Journal of computational and nonlinear dynamics,2007,2 (3):242-248
[117]罗冠炜,张艳龙,谢建华.多自由度含间隙振动系统周期运动的二重Hopf分岔[J].工程力学,2006,23(3)：37-43
[118]Yamapi R, Aziz-Alaoui M A. Vibration analysis and bifurcations in the self-sustained electromechanical system with multiple functions [J]. Communications in Nonlinear Science and Numerical Simulation,2007,12(8):1534-1549
[119]Charalampakis A E, Koumousis V K. On the response and dissipated energy of Bouc-Wen hysteretic model [J]. Journal of Sound and Vibration,2008,309(143):887-895
[120]王艳群.Duffing振子混沌动力学研究[J].衡阳师范学院学报,2007,28(3)：33-35
[121]吕金虎,陆君安,陈士华.混沌时间序列及其应用[M].武汉大学出版社,2002.
[122]Cao L Y. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D,1997,110(20): 43-50
[123]王海燕,卢山.非线性时间序列分析及其应用.科学出版社,2006
[124]Takens F. On the numerical determination of the dimension of an attractor[J]. Dynamical Systems and Turbulence.1981,898:366-381
[125]Mane R. On the dimension of the compact invariant sets of certain nonlinear maps.1981,898:230
[126]SUNG K J, HAN Y M, CHO J W, et al. Vibration control of vehicle ER suspension system using fuzzy moving sliding mode controller[J]. Journal of Sound and Vibration,2008,311 (3-5):1004-1019
[127]王维锐,吴参,潘双夏等.车辆半主动悬架负刚度控制策略研究[J].浙 江大学学报：工学版,2009,43(6)：1129-1133
[128]YAGIZ N, HACIOGLU Y. Backstepping control of a vehicle with active suspensions [J]. Control Engineering Practice,2008,16(12): 1457-1467
[129]YU M, DONG X M, CHOI S B, et al. Human simulated intelligent control of vehicle suspension system with MR dampers [J]. Journal of Sound and Vibration,2009,319(3-5):753-767
[130]汪若尘,江浩斌,张效良等.阻尼非线性半主动悬架的建模与控制[J].农业机械学报,2008,39(12)：14-17
[131]GRZEGORZ L, MAREK B, MICHEAL I F, et al. Chaotic vibration of a quarter-car model excited by the road surface profile[J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(5):1373-1383
[132]Yagiz N, Hacioglu Y. Backstepping control of a vehicle with active suspensions [J]. Control Engineering Practice,2008,16(12): 1457-1467
[133]Zapateiro M, Luo N, Karimi H R, et al. Vibration control of a class of semi-active suspension system using neural network and backstepping techniques [J]. Mechanical Systems and Signal Processing, In Press, Accepted Manuscript, Available online 31 October 2008
[134]Yu M, Dong X M, Choi S B, et al. Human simulated intelligent control of vehicle suspension system with MR dampers [J]. Journal of Sound and Vibration,2009,319(3-5):753-767
[135]Wan C, Jian C, Chen C K. Chaotic response and bifurcation analysis of a flexible rotor supported by porous and non-porous bearings with nonlinear suspension[J]. Nonlinear Analysis:Real World Applications,2009,10(2):1114-1138
[136]Dekker H. Vibrational resonances of nonrigid vehicles: Polygonization and ripple patterns [J]. Applied Mathematical Modelling,2009,33(3):1349-1355