摘要
光纤Bragg光栅(FBG)传感器具有传、感一体的独特优点,可以在同一根光纤上布置许多传感点,构成分布式传感系统,适合于制作结构的健康监测网络,因此,光纤Bragg光栅在智能结构健康监测领域具有非常广阔的应用前景。本文对光纤Bragg光栅应用于智能结构的动态信号进行监测。研究了动态信号的采集方法、信号特征量提取及定位算法,构建了一个具有冲击载荷自诊断功能的光纤智能结构系统。同时,对光纤Bragg光栅传感器应用车架结构健康监测进行了初步研究。
文中主要研究工作内容有以下几个方面:
(1)对光纤Bragg光栅的光谱进行了仿真,研究了光栅长度与折射率调制周期改变情况下,FBG的反射、透射光谱。对光纤Bragg光栅的应变传感特性进行了实验研究,得到了光纤Bragg光栅中心波长的变化量与应变成线性关系的结果,所以可以通过监测光纤Bragg光栅中心波长的变化来监测结构的应变。
(2)为对光纤Bragg光栅动态信号进行监测,提出了一种基于双长周期光栅的光纤Bragg光栅的高速解调系统。双长周期光栅是由两个中心波长一致的长周期光栅构成,利用长周期光栅的带阻滤波特性,获得光纤Bragg光栅反射光经双长周期光栅调制后的出射光,通过光电探测器监测光强的改变量来反推光纤Bragg光栅中心波长的变化。解调系统采用全光纤技术,结构紧凑、精度高,具有较好的线性输出。
(3)对基于光纤Bragg光栅网络的振动、冲击监测方法进行了研究。多个光纤Bragg光栅传感器复用构成分布式光纤传感网络作为光纤智能结构的神经系统,通过对光纤Bragg光栅中心波长的分析,实现了该结构的振动、冲击响应监测。对不同冲击点,传感器监测的冲击响应信号进行了分析。
(4)提出一种冲击载荷定位算法,对传感器采集的冲击响应信号进行特征提取,采用小波包分析方法提取冲击响应不同频段内的信号能量特征指标。将模态频率对应的能量值作为样本,采用支持向量回归机对有限样本数据建立回归模型,实现了复合材料试件的冲击载荷定位。
(5)将光纤Bragg光栅应用于汽车车架结构健康监测领域,研究在不同工况下,车架受到的动态载荷情况。通过车架振动实验、整车瞬态冲击实验和路面实验对车架振动情况进行分析。
Fiber Bragg grating (FBG) sensors have been expected to candidates for distributed sensoring system by arrangement many sensors in a single fiber because of their transmission and Sensing property. Besides these advantages, FBG sensors are Suitable for manufacturing network of structural health monitoring, FBG sensors have extensive potential applications in smart structure and materials health monitoring field. FBG sensors are applied for the dynamic signal monitoring of smart structure in the paper. In order to built a impact loading self-diagnosing system, Acquisition methods of dynamic signal, feature extraction and loading location algorithm are researched. Meanwhile, a preliminary study of vehicle frame health monitoring based on Fiber Bragg grating sensors is proposed in the paper.
The main achievements are described as follows:
(1) Spectrum numerical simulationof FBG is studied in the paper. In order to study sensing properties of FBG, reflectivity and transmission spectrum of FBG is analyzed under the condition of grating length and refractive index change. Because the wavelength change of FBG and strain is linear, structural strain is monitored by wavelength change of FBG monitoring.
(2) High speed demodulation system based on double long period grating is studied in order to research dynamic signal monitored by FBG sensor. Double LPFG is consisted of two LPFGS whose center wavelengths are same. Reflection light of FBG modulated by double LPFG is obtained and studied by use of band-hider filter characteristics for double LPFG, and wavelength change of FBG is deduced by light intensity achieved by photodetector.Demodulation system using total fiber technology has the property sunch as compact structure, high precision,linear output.
(3) Vibration and impact monitoring method based on FBG network is proposed. Many FBG sensors are used to set up sensing network, which is nervous system of optical fiber smart structure. Impact response signal monitoring is achieved by detecting wavelength change of FBG. Impact different location of structure, impact response signal monitored by FBG is studied.
(4)Impact loading localization algorithm is proposed. Feature extraction of acquisition impact response signal is realized with signal energy of different frequency segment using wavelet packet analysis used as characteristic index. Energy corresponding to modal frequency reguarded as sample is imput to Support Vector Machine to set up regression model and impact loading localization of composite speciment is realizated.
(5)FBG sensors are applied for health monitoring field of vehicle frame to detect dynamic load states under different conditions. Vibration Conditions of vehicle frame are analysed by experiments of vibration, transient impact and pavement.
引文
[1]Jan D, Achenbach. Structural health monitoring– What is the prescription. Mechanics Research Communications, 2009, 36(2): 137~138.
[2]董晓马.智能结构的损伤诊断及传感器优化配置研究,[博士学位论文].南京:东南大学2006.
[3]陈长征,罗跃纲,白秉三等.结构损伤监测与智能诊断.北京:科学出版社,2001: 5~6.
[4]姜德生,Richard O.Claus(美国),智能材料器件结构与应用.武汉:武汉工业大学出版社,2000:2~3.
[5]杨大智.智能材料与智能系统.天津:天津大学出版社,2000:15~40.
[6]涂亚庆,刘兴长.光纤智能结构.重庆:重庆出版社,2001:9~12.
[7]Rosalie C, Chan A, Chiu W K et al.Structural health monitoring of composite structures using stress wave methods.Composite Structures,2005,67(2):157~158.
[8]姜德生,何伟.光纤光栅传感器的应用概况.光电子.激光,2002,13(4):420~430.
[9]Sauro L, Jason L, Speyer. Application of a fault detection filter to structural health monitoring.Automatica, 2006, 42(7): 1199~1209.
[10]Tmickens, Schulz M, Sundaresan M et al. Structural health monitoring of an aircraft joint. Mechanical Systems and Signal Processing, 2003, 17(2): 285~303.
[11]Liebowitz H, Sandhu J S, Menandro F C M etal.Smart computational fracture of materials and structures. Engineering Fracture Mechanics, 1995, 50(5): 639~645.
[12]Kagai T T. A concept of intelligent materials. US一Jpana Workshop on Smart/intelligent Materials Systems,Technmic Publishing ComPally Inc,1990,3~10.
[13]Rogers C A. Intelligent materials systems-the dawn of a new materials age. Jounral of Intelligent Material Systems and Sturcutre,1993,4(1):1~8.
[14]谢建宏,张为公.智能材料结构的研究与发展.传感技术学报,2004,(1期):164~167.
[15]Liang DaKai. Research on some problems about optic fiber embedded in carbon fiber smart structure.Proceedings of and International Workshop on structure health monitoring, USA,1999:680~689.
[16]梁大开,李东升.基于法珀腔光纤传感器的光纤智能夹层的研究.仪器仪表学报,2005,26(8): 225~228.
[17]Wood K, Brown T, Rogowski R et al.Fiber Optic Sensors for Health Monitoring of Morphing Airframes:Ⅰ. Bragg Grating Strain and Temperature Sensor. Smart Materials and Structures,2000, 9(2): 163~169.
[18]Wood K, Brown T, Rogowski R et al.Fiber Optic Sensors for Health Monitoring of Morphing Airframes:Ⅱ. Bragg Grating Strain and Temperature Sensor. Smart Materials and Structures, 2000, 9(2): 170~174.
[19]Siogren A, Lindstrom B.Connection of Optical Fibers Embedded in Aircraft Composite Components.SPIE,2000,3985:533~542.
[20]Giurgiutiu V, Redmond J, Roach D et al. Active Sensors for Health Monitoring of Aging Aerospace Structures.Proceedings of SPIE, 2000, 3(985):294~305.
[21]Kabashima S, Ozaki T, Takeda N.Damage Detection of Satellite Structures by Optical Fiber with Optical Fiber with Small Diameter. Proceedings of SPIE, 2000, 3(985):343~351.
[22]Manson G, Worden K, Allman D. Experimental Validation of A Structural Health Monitoring Methodology: Part III. Damage Location on An Aircraft Wing. Journal of sound and Vibration, 2003, 259 ( 2) :365~385.
[23]杜设亮,傅建中,居冰峰等.光纤智能结构及其在制造工程中的应用.机电工程,1999(5): 214 ~217.
[24]李尚俊.光纤智能结构/蒙皮在航空上的应用.中国民航飞行学院学报, 2000(2):29~30.
[25]刘兴长,涂亚庆.军用航空器的光纤智能结构分析.压电与声光,2002,24(2):97~100.
[26]Alan Baker, Nik Rajic, Claire Davis.Towards a practical structural health monitoring technology for patched cracks in aircraft structure. Composites Part A: Applied Science and Manufacturing, 2008:6~12.
[27]Mickens T, Schulz M, Sundaresan M et al. Structural Health Monitoring of an Aircraft Joint. Mechanical Systems and Signal Processing, 2003, 17(2): 285~303.
[28]Kim H S, Ghoshal A. Development of embedded sensor models in composite laminates for structure health monitoring.Proceedings of SPIE-THE International Society for Optical Engineering, 2003, 5056:99~110.
[29]Tzou H S, Lee H J, Arnold S M.Smart materials precision sensors/actuators and structronic systems. Mechanics of Advanced Materials and Structures, 2004, 11(4):367~393.
[30]李川,张以谟,赵永贵,等.光纤光栅原理、技术与传感应用.北京:科学出版社, 2005: 200~205.
[31]Michael N Trutzel, Karsten Wauer, Daniel Betz, et al. Smart sensing of aviation structures with fiber-optic Bragg grating sensors. Richard O. Claus, Smart Structures and Materials 2000:Sensory phenomena and measurement instrument for smart structures and materials,Newport Beach, Proc. SPIE 3986, 2000:134~143.
[32]Takeda Y, Aoki T, Ishikawa. Structural health monitoring of composite wing structure during durability test. Composite Structures,2007,(1):133-139.
[33]Wayne Baker, Iain McKenzie, Rhys Jones. Development of life extension strategies for Australian military aircraft, using structural health monitoring of composite repairs and joint. Composite Structures,2004,66(4):133-143.
[34]Takeda S, Aoki Y, Ishikawa T et al. Structural health monitoring of composite wing structure during durability test. Composite Structures, 2007, 79(1): 133~139.
[35]Casanova N,Inaudi D. Structural monitoring with embedded and surface mounted fiber optic sensors.ISMES, International Colloquium Seriate.1997:325~332.
[36]Chan T H T, Yu L, Tam H Y et al.Fiber Bragg grating sensors for structural health monitoring of Tsing Ma bridge: Background and experimental observation. Engineering Structures, 2006,28(5): 648~659.
[37]Ko J M, Ni Y Q.Technology developments in structural health monitoringof large-scale bridges .Engineering Structures, 2005, 27(12): 1715~1725.
[38]黄方林,王学敏.大型桥梁健康监测研究进.中国铁道科学,2005, 26(2): 1~7.
[39]Kister G, Winter D, Badcock R A et al. Monitoring of an all-composite bridge using Bragg grating sensors. Construction and Building Materials,2007,21(7): 1599~1604.
[40]Kerrouche A,. Boyle W.J.O, Gebremichael Y. et al.Field tests of fibre Bragg grating sensors incorporated into CFRP for railway bridge strengthening condition monitoring. Sensors and Actuators A: Physical, 2008,148(1): 68~74.
[41]芦吉云,梁大开,潘晓文.基于分布式光纤光栅传感器的机翼盒段载荷监测研究.南京航空航天大学学报,2009,41(2),217~221.
[42]符晶华.光纤光栅智能材料、结构的应用与研究,[博士学位论文].武汉:武汉理工大学2006.
[43]梁磊.光纤光栅智能材料与结构理论和应用研究,[博士学位论文].武汉:武汉理工大学2006.
[44]John Zeleznikow, James K.Nolan.Using soft computing to build real world intelligent decision support systems in uncertain domains.Decision Support Systems, 2001,31:263~285.
[45]边肇祺,张学工.模式识别.北京:清华大学出版社,2000:10～28.
[46]彭鸽,袁慎芳.复合材料结构损伤的小波神经网络辨识研究.宇航学报,2005,26(5): 625~629.
[47]刘浩吾,吴永红.光纤应变传感的非线性有限元分析.光电子·激光,2003,14(5):526~528.
[48]廖延彪.用于智能材料和结构的光纤传感技术.激光与红外,1999,29(1):14~16.
[49]Butter C D, Hocker G B. Fiber optics strain gauge. Appl Opt, 1978, 17(18):2867~2869.
[50]Childers B A, EFroggatt M, GAllison S et al. Use of Brgag grating srtain sensors distributed on four eight meter optical fibers during static load tests of a composite structure. Smart structure and Materials Conefernce, SPIE, 2001:133~ 142.
[51]Hill K O, Fujii Y, Johnson D C et al. Photosensitivity in Optical Waveguides Application to Refle -ction Filter Fabrication. Applied Physics Letters,1978,32 (10): 647~649.
[52]Kawasaki B S, Hill K O, Jonhnson D C et al.Narrow-Band Bragg Reflectors in Optical Fibers. Optics Letters, 1978, 3:66~68.
[53]Torben Storgaard-Larsen, Siebe Bouwstra, Otto Leistiko.Opto-mechanical accelerometer based on strain sensing by a Bragg grating in a planar waveguide. Sensors and Actuators A: Physical, 1996, 52(3): 25~32.
[54]Dong L, Cruz J L, EekieLR et al. Chirped Fiber Bragg Gratings Fabricated Using Etched Tapers. Optical Fiber Technology, 1995, 1(4):363~368.
[55]Xie W X, Douay M, Bernage P et al. Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres. Optics Communications, 1993,101(1-2): 85~91.
[56]Brady G P, Hope S, Lobo Ribeiro A B et al. Demultiplexing of fibre Bragg grating temperature and strain sensors. Optics Communications,1994,111(1): 51~54.
[57]梁大开,陶宝祺.智能复合材料结构中偏振式光纤传感器系统的研究.航空学报,1998,19(3):335~337.
[58]梁大开,黄明双,陶宝祺等.光纤埋人碳纤维复合材料结构的实验研究.材料工程,2000(2): 16~18.
[59]Farries M C, Ragdale C M, Reid D C.Broadband chirped fiber Bragg filter for pump rejection and recycling in erbium doped fiber amplifiers. Electronics Letters, 1992, 28(5): 487~489.
[60]廖帮全.光纤光栅理论、传感应用及全光纤声光调制研究,(博士学位论文).天津:南开大学,2002.
[61]梁磊,姜德生,孙东亚.光纤传感器在混凝土结构中的相容性研究.武汉工业大学学报,2000,22(2):11~14.
[62]梁大开,李东升,潘晓文.智能结构中光纤智能夹层力学特性的实验研究[J].应用力学学报,2006,23(1):150-153.
[63]Hill K O.Photosensitivity in Optical Fiber Waveguides: Application to Reflection Filter Fabrication.Applied Physics Letters, 1978, 32(10): 647~649.
[64]Meltz G.Formation of Bragg gratings in optical fibers by a transversal holographic method. Optics Letters, 1989, 15(14): 823~825.
[65]Yariv A.Coupled-Mode Theory for Guided-wave Optics.IEEE Journal of Quantum Electronics, 1973,9:919~933.
[66]Kogelnik H.Filter Response of Nonuniform Almost-Periodic Structures.Bell System Technical Journal, 1976,55:109~126.
[67]Winick K A.Effective-Index Method and Coupled-Mode Theory for Almost Periodic Waveguide Gratings:A Comparison.Applied Optics,1987,26:.3474~3478.
[68]Fang Xie, Shulian Zhang, Yan Li et al.Multiple in-fiber Bragg gratings sensor with a grating scale. Measurement, 2002,31(2): 139~142.
[69]Shi Hongsheng,Zhang Ge,Shen Hongyuan.Measurement of principal refractive indices and the thermal refractive index coefficients of yttrium vanadate.Journal of Synthetic Crystals,2001,30(1):85-88.
[70]Fang Xie, Shulian Zhang, Yan Li et al.Multiple in-fiber Bragg gratings sensor with a grating scale. Measurement, 2002,31(2): 139~142.
[71]Haus H A, Huang W.Coupled-mode theory. Proceedings of the IEEE.1991,79: 1505~1518.
[72]王惠文.光纤传感技术及应用,国防工业出版社,2001:86~88.
[73]贾宏志.光纤光栅传感器的理论和技术研究, (博士学位论文).西安:西安光学精密机械研究所,2000.
[74]Akhavan F.Measurement and analysis of impact-induced strain using extrinsic Fabry-Perot fiber optic sensors.Smart Mater Struct,1999,7:745-751.
[75]Kin-tak Lau, Libo Yuan, Li-min Zhou et al. Strainmonitoring in FRP laminates and concrete beams using FBG sensors. Composite Structures, 2001,51(1): 9~20.
[76]Yu Fan, Mojtaba Kahrizi. Characterization of a FBG strain gage array embedded in composite structure.Sensors and Actuators A: Physical, 2005,121(2): 297~305.
[77]Othonos A, Lee X, Measure R M.Superimposed Multiple Bragg Gratings.Electronics Letters, 1994, 30(23):1972~1973.
[78]文庆珍,苑秉成,黄俊斌.光纤光栅压力传感器封装增敏技术.海军工程大学学报,2005,17(3):1~4.
[79]毕卫红,李卫,傅广为.分布式光纤光栅实现应变和温度的同时测量.光电子·激光,2003,14(8):827~834.
[80]郭凤珍,于长泰.光纤传感技术与应用.杭州:浙江大学出版社,1992:116～117.
[81]张双寅,刘济庆,于晓霞.复合材料结构的力学性能.北京:北京理工大学出版社, 1992: 124~125.
[82]Zeng-Ling Ran,Yun-Jiang Rao.A FBG sensor system with cascaded LPFGs and Music Algorithm for dynamic strain measurement. Sensors and Actuators, 2007,15(2):415~419.
[83]Jian Y, Yong Zh, Bao-Jin P,et al. Temperature-compensated high pressure FBG sensor with a bulk-modulus and self-demodulation method. Sensors and Actuators, 2005,25(2):254~258.
[84]Yong Zhao,Yanbiao Liao. Discrimination methods and demodulation techniques for fiber Bragg grating sensors. Optics and Lasers in Engineering,2005,1 (41):1~18.
[85]Jung-Ryul Lee, Hiroshi Tsuda, Nobuyuki Toyama.Impact wave and damage detections using a strain-free fiber Bragg grating ultrasonic receiver.NDT&E International, 2007, 40: 85~93.
[86]宋剑飞,邵理阳,张阿平等.一种新型FBG动态应变解调系统.光电子?激光, 2007, 8(11): 924~926.
[87]余有龙,谭华耀.基于干涉解调技术的光纤光栅传感系统.光学学报,2001,21(8): 987~989.
[88]Jackson D A, Ribeiro A B L, Reekie L et a1.Simple Multiplexing Scheme for a Fiber -optic Grating Sensor Network.0pt.Lett.,1993,18〔14):1192~1194.
[89]Kersey A D, Berkoff T A, Morey W W.High-resolution fiber-grating based strain sensor with interferometric wavelength-shift detection. Electron Lett, 1992,28(3):236~238.
[90]KerseyA D, Berkoff T A. Dual wavelength fiber interferometer with wavelength selection via fiber Bragg grating elements .Electron Lett,1992, 28(13):1215~l216.
[91]Davis M A, Keysey A D.All-fiber Bragg grating strain sensor demodulation technique using a wavelength-division coupler. Electron Lett., 1994, 30(1):76~78.
[92]Patrick H J, Kersey A D.Fiber Bragg grating sensor demodulation system using in fiber long period grating fibers.Proc.SPIE., 1996, 2838: 60~65.
[93]Kersey A D.Multiplexed Fiber Bragg Grating Strain-sensor System with a Fiber Fabry-Perot wavelength Filter. Optics Letters, 1993,18(16):1370~1371.
[94]Ning Y N, Meldrum A, Shi W J et al.Bragg Grating Sensing Instrument Using a Tunable Febry-Perot Filter to Detect Wavelength Variations. Meas Sci. & Technol,1998,9(6):599~606.
[95]Agrawal G, Radic S.Phase-shifted fiber Bragg gratings and their applications for wavelength demultiplexing. IEEE Photon. Technol. Lett., 1994, 6(8):995~997
[96]Bhatia V, Vengsarkar A M. Optical fiber long-period grating sensors. Opt. Lett ,1996,(21): 692~694.
[97]王义平,饶云江,冉曾令.一种新颖的长周期光纤光栅可调增益均衡器.光学学报,2003,23(8):970～973.
[98]廖延彪,黎敏,田芊.长周期光栅-新兴的光纤光栅传感器.激光与红外,1997,27(6): 371~374.
[99]Gwandu B, Zhang W, Ghafouri Shiraz H.The co-measurement of curvature and temperature using a single LPG in a standard single mode fibre.Proceedings of the IEEE sensors, 2004, 13:1349~1352
[100]孔梅.长周期光纤光栅的理论和应用研究,[博士学位论文].杭州:浙江大学,1999.
[101]胡海岩,孙久厚,陈怀海等.机械振动与冲击.北京:航空工业出版社,2002:3~4.
[102]郑兆昌主编.机械振动(上册).北京:机械工业出版社,1980:5~15.
[103]王跃科,叶湘滨,黄芝平等.现代动态测试技术.北京:国防工业出版社,2003: 1~16.
[104]孙玉声.振动传感器.西安:西安交通大学出版社,1991: 11~13.
[105]付宝连,弯曲矩形板的广义位移理论,北京,科学出版社,2006:12~22. [ 106 ]Srinivasan R S, Chellapandi P. Dynamic stability of rectangular laminated composite plates.Computers and Structures,1986,24(2):232~238.
[107]董杰.复杂结构在冲击和振动加载下动态响应分析,[博士学位论文].合肥:中国科学技术大学,2006.
[108]Hutt J M, Salam A E. Dynamic instability of plates by finite element method. American Society of Civil Engineers Journal of Engineering Mechanics, 1971, 3:879~899.
[109]C T Sun. An analytical method for evaluation of impact damage energy of laminated composites . Composite Materials,Testing and Design, 1977, 617(1):427~440.
[110]Greszczuk L B. Impact dynamics . New York: John Wiley and Sons Inc, 1982: 55-94.
[111]Christoforou A P, Swanson S R. Analysis of impact response in composite plates. International Journal of Solids and Structure,1991, 27(2): 161~170.
[112]Yigit A S, Christoforou A P. Impact dynamics of compositebeams. Composite Structures, 1995, 32(1): 187-195.
[113]Abrate S. Impact on composite structures. New York: Cambridge University Press, 1998: 1~30.
[114]Allix O.A composite damage meso-model for impact problems. Composites Science andTechnology, 2001, 61(15):2193~2205.
[115]Zhou D W, Stronge W J. Low velocity impact denting of HSSA lightweight sandwich panel . Int J Mech Sci, 2006,48(10): 1031~1045.
[116]Soula M, Nasri R, Ghazel A et al.The effects of kinematic model approximations on natural frequencies and modal damping of laminated composite plates. Journal of Soundand Vibration, 2006, 297(1): 315~328.
[117]Alix O, Ladeveze P. Interlaminar interface modeling for theprediction of delamination . Composite Structures, 1992,22(4): 235-242.
[118]张思进,陆启韶,傅衣铭.对称角铺设矩形复合材料叠层板受低速冲击时的应力波传及解层破坏分析.复合材料学报,2008,5(25:181~183.
[119]Sun H, Pan N. Mechanical characterization of interfaces in laminated composites. Composite structures, 2006,74(1): 25-29.
[120]徐长发,李国宽,实用小波方法(第二版),武汉:华中科技大学出版社,2003:15~39.
[121]信思金,基于光纤光栅和小波包分析的智能材料与结构损伤识别研究,[博士学位论文],武汉,武汉理工大学,2004.
[122]董长虹,高志,余啸海等,Matlab小波分析工具箱原理与应用,北京:国防工业出版社,2004:17~34.
[123]Spillman W B, Sirkis J S, Gardiner P T. Smart materials and structures,What are they? Smart Struct, 1996,5:245~254.
[124]Burges J C. Atutorial on support vectormachines for pattern recognition. DataMining and Knowledge Discovery.1998,2(2):955~974.
[125]Dirk T, Andreas S. A Modified General Regression Neural Network (MGRNN) with new, efficient training algorithms as a robust‘black box’-tool for data analysis. Neural Networks,2001,8(14): 1023~1034.
[126]张学工.统计学习理论的本质.北京:清华大学出版社,2000:96~116.
[127]芦吉云,梁大开,张晓丽等.基于支持向量回归机的机翼盒段结构健康监测研究.仪器仪表学报,2009,30(3):486-491.
[128]谢建宏.压电智能结构损伤检测及其传感器优化配置的研究,[博士学位论文].南京:东南大学,2005.
[129]喻凡,林逸.汽车系统动力学.北京:机械工业出版社,2005:15~25.
[130]张立军,曾庆东,梁海林.减振器联接弹性对阻尼特性的影响及其确定.机械设计与制造,1999(6):31~33.
[131]朱海涛.轻型货车动态性能仿真分析及结构优化,硕士学位论文.吉林:吉林大学,2006.
[132]苏庆,孙凌玉,刘福保.运用CAE技术进行某微型客车车架结构的分析与优化设计.农业装备与车辆工程,2005,4(173):26~32.
[133]尹辉俊,韦志林,沈光烈.货车车架的有限元分析.机械设计,2005, 22(11):26~28.
[134]张庆灵.广义系统结构稳定性判别的李雅普诺夫方法.系统科学与数学,1994,14(2): 117~120.
[135]熊永华,杜发荣,高峰等.轻型载货汽车车架动态特性分析与研究.机械设计,2007, 24 (4):60 ~62.
[136]Boehm F. Models for the radial tire for high frequent rolling contact. The Dynamics of Vehicles on Roads and on Tracks, 1991,27(2):24~31.
[137]Gim G, Nikravesh P E. A three dimensional tire model for steady-state simulations of vehicles. SAE paper, 1993,102(2):150~159.