汽车后扭力梁振动疲劳数值分析与研究
|
摘要
工程上，受到模态频率相近的动态载荷的作用，结构表面产生的应力水平虽然低于静态疲劳极限值，但是仍可能由于疲劳损伤的累积而产生疲劳破坏，而且结构的实际疲劳寿命远低于依据传统普通疲劳计算而得的预测结果。至今为止，这仍是传统的疲劳寿命分析理论无法清楚阐述的难题之一。
本文介绍了振动疲劳与传统普通疲劳之间的基本概念，提出了振动疲劳与传统的普通疲劳的主要区别在于激励频率是否涵盖了结构的工作模态频率。通过对某后扭力梁结构在服役状态下容易出现疲劳破坏的分析，提出了一种解决汽车底盘结构振动疲劳的办法，即运用多体动力学、有限元法和应变工作模态试验与分析相结合的手段，从载荷识别、工作模态分析、动应力数值估算与试验验证、激励频率对结构动应力影响分析等方面进行研究。在此基础上，阐述振动疲劳分析的若干关键技术，本文完成的主要工作如下：
1、创建了后扭力梁结构的有限元模型，分析获得了结构固有模态频率，并应用模态试验验证了结构有限元模型的准确性。根据后扭力梁结构实际工作状态下的装配关系，确定了后扭力梁结构的3种可能的边界条件，并运用随机子空间法识别得到了不同边界条件下后扭力梁的工作模态参数，研究表明结构在服役状态下其边界条件较为复杂。
2、为解决大规模应变测试中可能面临的数据采集通道不足的问题，采用二向应变片代替应变花测试结构表面的应变信号，并推导了薄壁结构件的主应力计算公式。为验证推导的主应力公式的正确性，设计和加工了U型薄壁结构试件，开展应变测试。研究表明基于二向应变片计算的薄壁件主应力能够反映结构的真实应力水平，为后续工程上的应用提供参考。将研究结果应用于后扭力梁结构应力分析，通过实车道路试验验证了该推导方法的正确性和精度。
3、考虑后扭力梁结构轴头处橡胶衬管内的衬垫非线性特性，应用ADAMS和Matlab/Simulink模块建立了后扭力梁结构刚柔耦合多体动力学模型，基于样车道路试验采集的悬架弹簧的位移信号，通过迭代仿真获得了后扭力梁左、右轴头载荷。为了验证其准确性，基于整车台架试验对仿真结果进行了验证。试验表明联合ADAMS和Matlab/Simulink对后扭力梁结构左、右轴头载荷迭代仿真具有较高的准确性，误差控制在10%。
4、采用准静态、直接积分和模态叠加法分析后扭力梁结构的动应力，重点研究了关键部位横梁的动应力变化。通过分析各方法对振动疲劳动应力计算精度，对比了三种方法的优缺点和适用性。最后，通过整车台架应变试验对数值分析结果进行验证。试验表明准静态法难以直观表达结构的实际动应力，而模态叠加和直接积分法能较准确描述结构动应力。
5、考虑了结构尺寸和加工工艺等对材料疲劳特性曲线S-N的影响，经修正获得了部件的S-N曲线。基于准静态、直接积分和模态叠加法在时域范畴内对后扭力梁结构在不同路段的疲劳寿命进行数值仿真分析，找到对应路况下结构疲劳寿命薄弱区域，并通过台架应变试验对结果进行了验证。试验表明这三种方法均能精确定位结构疲劳薄弱区域，但准静态法不能准确预测结构振动疲劳寿命，而直接积分和模态叠加法可较为准确预测结构振动疲劳寿命。
6、对后扭力梁结构的轴头载荷进行频谱分析，获得了轴头载荷的频域范围和能量分布信息。在频域内运用Dirlik方法预测结构疲劳寿命，获得了结构在全路段、共振三路段、石块路段工况下的疲劳寿命。为研究加载频率对结构动应力和疲劳寿命的影响，提出了采用放大因子来评价共振频率激励对结构动应力的贡献的研究方法。结果表明，等能量的共振频率激励使得结构产生的疲劳损伤约为非共振激励的4倍。
When structure is suffering from dynamic load which is close to the naturalfrequency, stress level is lower than the static fatigue stress limit in the project. But itmay produce crack. In other words, the actual life of the structure is lower thanprediction results on the basis of the static fatigue analysis method. It is one ofproblems difficulty resolved by the traditional theory of fatigue life analysis so far.
This paper has introduced the basic concept between vibration fatigue and thetraditional ordinary fatigue, and pointed out the primary difference whether theexcitation frequency covers work modal frequency between vibration fatigue and thetraditional ordinary fatigue. Aiming at vibration fatigue damage problem on reartorsion beam when a certain type of vehicle with rear torsion beam suspension is inservice condition, a method used to predict vibration fatigue life of complex structurewith rigid-flexible coupled was proposed in the paper. Based on vibration fatigueanalysis of a rear torsion beam which was a typical chassis component in a passengervehicle, key techniques for vibration fatigue analysis were described by usingmulti-body dynamics, finite element method and the strain operational modal test andanalysis, including load identification, operational modal analysis, numericalprediction method of dynamic stress and the influence analysis of dynamic stressfrom excitation frequency.
1、The finite model of rear torsion beam was established and its free modalfrequencies were acquired. The three possible boundary conditions were studiedaccording to assembly relationship of rear torsion beam in working status. Theoperational modal parameters of rear torsion beam were identified by using thestochastic subspace method based on the strain modal test platform. Studies haveshown that the boundary condition of structure in the state of serving is morecomplicated.
2、In order to solve the problem of insufficient data acquisition channel in largescale testing, the strain signals on structure surface were tested by two-direction straingauge instead of three-direction strain gauge. The principal stress calculation formula of thin-walled structure was conducted based on the strain gauge. The U-shapedthin-walled structure specimen was designed and processed. The numerical principalstress was verified by surface strain testing system of the thin-walled structure. Thestudy has shown the principal stress of thin-walled structure calculated based on thestrain gauge can reflect the real stress level, and provide reference for subsequentengineering application. Then the research result was applied into stress analysis ofrear torsion beam, and the correctness and precision of the method was validatedthrough the real vehicle road test.
3、In the dynamic analysis of rear torsion beam, the nonlinear characteristics ofrubber lining tube in spindle head were considered. Based on displacement signal ofthe suspension spring on the real vehicle road test and multi-body dynamic model ofthe torsion beam with rigid-flexible coupled via the ADAMS of dynamic simulationsoftware, the load of left and right spindle noses of rear torsion beam were simulatedvia iterate. In order to verify the accuracy of the method, the load of spindle nose wasverified based on the test bench. Experiment has shown that the simulation resultshad high accuracy and the error was in10%.
4、The quasi-static method, the direct-integral method and modal-superpositionmethod used to analyze the dynamic stress of structure were presented. And thedynamic stress of the key parts of transom was paid much attention. In the analysis ofdynamic stress, the relation between load frequency and the operational modalfrequency of structure was especially studied. The applicability of the method ofvibration fatigue analysis was analyzed. Finally the calculation results ware verifiedon the bench test of whole vehicle. Tests has showed that the quasi-static method isdifficult to directly express the actual dynamic stress of structure, but the modalsuperposition method and direct integration method can accurately describe thestructure dynamic stress.
5、 Considering with the influence of material fatigue characteristic fromstructure size and processing technology, the S-N curve of part was obtained byamendment. The fatigue life analysis of rear torsion beam in time domain method ondifferent road was calculated by using the quasi-static method, the direct-integralmethod and modal-iteration method. And analysis results were verified by bench strain test. Test has showed that the quasi-static method can not accurately predictvibration fatigue life of structures, but the direct integral method and modalsuperposition method can accurately predict vibration fatigue life of structure.
6、The frequency range and energy distribution information of load spectrum ofspindle nose was given through spectrum analysis of load of spindle nose. In order toget the frequency response characteristics of structure, a method used to impel the teststructure on spindle nose by way of sine sweep method in indoor test bench ispresented. Based on method of Dirlik, the fatigue life of rear torsion beam waspredicted by using fatigue frequency domain analysis method. The fatigue life of reartorsion beam was analyzed in the whole road, resonance-three section and therock-road. In order to study the influence of the dynamic stress and fatigue life fromload frequency, the zoom factor is presented, which is used to the contribution of thedynamic stress from resonance excitation frequency. The results have shown that thefatigue damage of structure from resonance excitation is about four times from thesame energy non-resonant incentive.
本文介绍了振动疲劳与传统普通疲劳之间的基本概念，提出了振动疲劳与传统的普通疲劳的主要区别在于激励频率是否涵盖了结构的工作模态频率。通过对某后扭力梁结构在服役状态下容易出现疲劳破坏的分析，提出了一种解决汽车底盘结构振动疲劳的办法，即运用多体动力学、有限元法和应变工作模态试验与分析相结合的手段，从载荷识别、工作模态分析、动应力数值估算与试验验证、激励频率对结构动应力影响分析等方面进行研究。在此基础上，阐述振动疲劳分析的若干关键技术，本文完成的主要工作如下：
1、创建了后扭力梁结构的有限元模型，分析获得了结构固有模态频率，并应用模态试验验证了结构有限元模型的准确性。根据后扭力梁结构实际工作状态下的装配关系，确定了后扭力梁结构的3种可能的边界条件，并运用随机子空间法识别得到了不同边界条件下后扭力梁的工作模态参数，研究表明结构在服役状态下其边界条件较为复杂。
2、为解决大规模应变测试中可能面临的数据采集通道不足的问题，采用二向应变片代替应变花测试结构表面的应变信号，并推导了薄壁结构件的主应力计算公式。为验证推导的主应力公式的正确性，设计和加工了U型薄壁结构试件，开展应变测试。研究表明基于二向应变片计算的薄壁件主应力能够反映结构的真实应力水平，为后续工程上的应用提供参考。将研究结果应用于后扭力梁结构应力分析，通过实车道路试验验证了该推导方法的正确性和精度。
3、考虑后扭力梁结构轴头处橡胶衬管内的衬垫非线性特性，应用ADAMS和Matlab/Simulink模块建立了后扭力梁结构刚柔耦合多体动力学模型，基于样车道路试验采集的悬架弹簧的位移信号，通过迭代仿真获得了后扭力梁左、右轴头载荷。为了验证其准确性，基于整车台架试验对仿真结果进行了验证。试验表明联合ADAMS和Matlab/Simulink对后扭力梁结构左、右轴头载荷迭代仿真具有较高的准确性，误差控制在10%。
4、采用准静态、直接积分和模态叠加法分析后扭力梁结构的动应力，重点研究了关键部位横梁的动应力变化。通过分析各方法对振动疲劳动应力计算精度，对比了三种方法的优缺点和适用性。最后，通过整车台架应变试验对数值分析结果进行验证。试验表明准静态法难以直观表达结构的实际动应力，而模态叠加和直接积分法能较准确描述结构动应力。
5、考虑了结构尺寸和加工工艺等对材料疲劳特性曲线S-N的影响，经修正获得了部件的S-N曲线。基于准静态、直接积分和模态叠加法在时域范畴内对后扭力梁结构在不同路段的疲劳寿命进行数值仿真分析，找到对应路况下结构疲劳寿命薄弱区域，并通过台架应变试验对结果进行了验证。试验表明这三种方法均能精确定位结构疲劳薄弱区域，但准静态法不能准确预测结构振动疲劳寿命，而直接积分和模态叠加法可较为准确预测结构振动疲劳寿命。
6、对后扭力梁结构的轴头载荷进行频谱分析，获得了轴头载荷的频域范围和能量分布信息。在频域内运用Dirlik方法预测结构疲劳寿命，获得了结构在全路段、共振三路段、石块路段工况下的疲劳寿命。为研究加载频率对结构动应力和疲劳寿命的影响，提出了采用放大因子来评价共振频率激励对结构动应力的贡献的研究方法。结果表明，等能量的共振频率激励使得结构产生的疲劳损伤约为非共振激励的4倍。
When structure is suffering from dynamic load which is close to the naturalfrequency, stress level is lower than the static fatigue stress limit in the project. But itmay produce crack. In other words, the actual life of the structure is lower thanprediction results on the basis of the static fatigue analysis method. It is one ofproblems difficulty resolved by the traditional theory of fatigue life analysis so far.
This paper has introduced the basic concept between vibration fatigue and thetraditional ordinary fatigue, and pointed out the primary difference whether theexcitation frequency covers work modal frequency between vibration fatigue and thetraditional ordinary fatigue. Aiming at vibration fatigue damage problem on reartorsion beam when a certain type of vehicle with rear torsion beam suspension is inservice condition, a method used to predict vibration fatigue life of complex structurewith rigid-flexible coupled was proposed in the paper. Based on vibration fatigueanalysis of a rear torsion beam which was a typical chassis component in a passengervehicle, key techniques for vibration fatigue analysis were described by usingmulti-body dynamics, finite element method and the strain operational modal test andanalysis, including load identification, operational modal analysis, numericalprediction method of dynamic stress and the influence analysis of dynamic stressfrom excitation frequency.
1、The finite model of rear torsion beam was established and its free modalfrequencies were acquired. The three possible boundary conditions were studiedaccording to assembly relationship of rear torsion beam in working status. Theoperational modal parameters of rear torsion beam were identified by using thestochastic subspace method based on the strain modal test platform. Studies haveshown that the boundary condition of structure in the state of serving is morecomplicated.
2、In order to solve the problem of insufficient data acquisition channel in largescale testing, the strain signals on structure surface were tested by two-direction straingauge instead of three-direction strain gauge. The principal stress calculation formula of thin-walled structure was conducted based on the strain gauge. The U-shapedthin-walled structure specimen was designed and processed. The numerical principalstress was verified by surface strain testing system of the thin-walled structure. Thestudy has shown the principal stress of thin-walled structure calculated based on thestrain gauge can reflect the real stress level, and provide reference for subsequentengineering application. Then the research result was applied into stress analysis ofrear torsion beam, and the correctness and precision of the method was validatedthrough the real vehicle road test.
3、In the dynamic analysis of rear torsion beam, the nonlinear characteristics ofrubber lining tube in spindle head were considered. Based on displacement signal ofthe suspension spring on the real vehicle road test and multi-body dynamic model ofthe torsion beam with rigid-flexible coupled via the ADAMS of dynamic simulationsoftware, the load of left and right spindle noses of rear torsion beam were simulatedvia iterate. In order to verify the accuracy of the method, the load of spindle nose wasverified based on the test bench. Experiment has shown that the simulation resultshad high accuracy and the error was in10%.
4、The quasi-static method, the direct-integral method and modal-superpositionmethod used to analyze the dynamic stress of structure were presented. And thedynamic stress of the key parts of transom was paid much attention. In the analysis ofdynamic stress, the relation between load frequency and the operational modalfrequency of structure was especially studied. The applicability of the method ofvibration fatigue analysis was analyzed. Finally the calculation results ware verifiedon the bench test of whole vehicle. Tests has showed that the quasi-static method isdifficult to directly express the actual dynamic stress of structure, but the modalsuperposition method and direct integration method can accurately describe thestructure dynamic stress.
5、 Considering with the influence of material fatigue characteristic fromstructure size and processing technology, the S-N curve of part was obtained byamendment. The fatigue life analysis of rear torsion beam in time domain method ondifferent road was calculated by using the quasi-static method, the direct-integralmethod and modal-iteration method. And analysis results were verified by bench strain test. Test has showed that the quasi-static method can not accurately predictvibration fatigue life of structures, but the direct integral method and modalsuperposition method can accurately predict vibration fatigue life of structure.
6、The frequency range and energy distribution information of load spectrum ofspindle nose was given through spectrum analysis of load of spindle nose. In order toget the frequency response characteristics of structure, a method used to impel the teststructure on spindle nose by way of sine sweep method in indoor test bench ispresented. Based on method of Dirlik, the fatigue life of rear torsion beam waspredicted by using fatigue frequency domain analysis method. The fatigue life of reartorsion beam was analyzed in the whole road, resonance-three section and therock-road. In order to study the influence of the dynamic stress and fatigue life fromload frequency, the zoom factor is presented, which is used to the contribution of thedynamic stress from resonance excitation frequency. The results have shown that thefatigue damage of structure from resonance excitation is about four times from thesame energy non-resonant incentive.
引文
[l]余建星,郭振邦,徐慧编著.船舶与海洋结构物可靠性原理[M].天津:天津大学出版社.2001.
[2] Ridnou, James Andrew.Methodology for evaluating vehicle fatigue life and durability. PhDthesis, The University of Tennessee, Knoxville,2003,12.
[3]姚起杭,姚军.结构振动疲劳问题的特点与分析方法[J].机械科学与技术,2000,19(s):56-58.
[4]姚起杭,姚军.工程结构的振动疲劳研究[J].飞机工程,2005,3:5-8.
[5]姚起杭,姚军.工程结构的振动疲劳问题[J].应用力学学报,2006,23(1):12-15.
[6]刘艳华.轿车扭力梁后悬架的开发研究[J].沈阳大学学报,2006,18(4):5-9.
[7]肖寿庭,杜修德.飞机结构振动疲劳问题[C].第六届全国疲劳学术会议论文集(下),厦门,1993.
[8]军用飞机强度和刚度规范(振动)[S].北京:航空工业部630研究所,1985.
[9]美国军用规范飞机强度和刚度MIL-A-8860B(AS)系列[S].北京:航空航天工业部飞行试验研究中心飞机强度规范研究室,1988.
[10] Osgood C C. Fatigue design [M]. Oxford: Pergamon press,1982.
[11] Crandall S H. Random vibration [M]. New York: Technology Press of MIT and John WileyandSons,1958.
[12] Crandall S H, Mark W D. Random Vibration in Mechanical Systems [M].Academic Press,1963.
[13]姚起杭.谈谈加速振动试验问题[J].航空标准与质量,1975.06:7-18.
[14] M. Nagode, M. Fajdiga. An improved algorithm for parameter estimation suitable for mixedWeibull distributions [J]. International Journal Fatigue,2000,22(1):75~80.
[15]姚起杭,姚军.结构振动疲劳问题的特点与分析方法[J].机械科学与技术,2000,19(S):56-58.
[16]何泽夏.振动与疲劳[J].火箭推进,1994,3:14-20.
[17] C.格林.振动手册[M].北京:《强度与环境》编辑部,1982.
[18]刘光文.结构共振疲劳试验及裂纹构件的振动疲劳耦合分析[D].南京:南京航空航天大学,2010.
[19] M.Haiba, D.c. Barton,P.c.Brooks. Review of life assessment techniques applied todynamically loaded automotive components[J].Computers and structures.2002(80):481-494.
[20] S. D. Downing, D.F. Socie. Simple rainflow counting algorithms [J]. International Journal ofFatigue,1982,4(1):31-40.
[21] R.J. Anthes. Modified rainflow counting keeping the load sequence[J]. International Journalof Fatigue,1997,19(7):529-535.
[22] M. P. Repetto. Cycle counting methods for bi-modal stationary Gaussian processes[J]Probabilistic Engineering Mechanics,2005,20:229-238.
[23] M. Grigoriu. A spectral representation based modal for Monte Carlo simulation[J].Probabilistic Engineering Mechanics,2000,15:365-370.
[24]侯传亮,张永林.工程平稳随机过程的数值模拟研究[J].武汉工业学院学报,2003,22(3):27-29.
[25]刘献栋,邓志党,高峰.基于逆变换的路面不平度仿真研究[J].中国公路学报,2005,18(1):122~126.
[26]陈春俊,李华超.频域采样三角级数法模拟轨道不平顺信号[J].铁道学报,2006,28(3):38-42.
[27]刘寅华,李芾,黄运华.轨道不平顺数值模拟方法[J].交通运输工程学报,2006,6(1):29-33.
[28]安刚,龚鑫茂.随机振动环境下结构的疲劳失效分析[J].机械科学与技术,2000,19(s):40-42.
[29]徐菲,肖寿庭.结构声疲劳寿命估算的功率谱密度法[J].机械强度,1996,18(4):38-42.
[30] P. H. Wirsching. Fatigue under wide band random stress[J]. Journal of the Structural Division,1980,1593-1606.
[31] G. Chaudhury. Spectral fatigue of broad-band stress spectrum with one or more peaks[J].OTC5333,1986,387-396.
[32] L. D. Lutes, S. Sarkani. Stochastic analysis of structural and mechanical vibrations [J]. NewJersey: Prentice-Hall,1997.
[33] Andrew Halfpenny.基于功率谱密度信号的疲劳寿命分析[J].中国机械工程,1998,9(11):16-19.
[34]伍义生.随机载荷下疲劳损伤计算[J].机械科学与技术.1996,11:879-882.
[35]李超.基于功率谱密度的疲劳寿命估算[J].机械设计与研究,2005,21(2):6-8.
[36]王琳,倪樵,张强,刘攀.随机激励下高压管道的疲劳寿命分析[J].华中科技大学学报(自然科学版),2003,31(12):100-102.
[37]吴启鹤,叶笃毅.一种估算结构件随机疲劳寿命的新方法[J].工程力学,1995,12(2):87-94.
[38]骆红云,陈志刚,张卫波,梁淑卿.窄带随机应力下机械构件寿命预测法[J].吉林工学院学报,2000,21(4):32-34.
[39] S. D. Downing, D.F. Socie. Simple rainflow counting algorithms[J]. International Journal ofJournal of Fatigue,2002,24:1137-1147.
[40] Bishop N W M. The use of frequency domain parameters to predict structural fatigue,[Ph.D.Dissertation]. Coventry: University of Warwick,1988.
[41] D. P. Kihl, S. Sarkani, J. E. Beach. Stochastic fatigue damage accumulation under broadbandloadings[J]. International Journal of Fatigue,1995,17(5):321-329.
[42] D. Benasciutti, R. Tovo. Comparison of spectral methods for fatigue analysis of broad-bandGaussian random processes[J]. Probabilistic Engineering Mechanics,2005,1:1-13.
[43] D. Benasciutti, R. Tovo. Spectral method for lifetime prediction under wide-band stationaryrandom processes[J]. International Journal of Fatigue,2005,27:867-877.
[44] M. Frendhal, I. Rychlik. Rainflow analysis: Markov method[J]. InternationalJournal of Fatigue,1993,15:265~273.
[45] M. Nagode, M. Fajdiga. On a new method for prediction of the scatter of loading spectra[J].International Journal of Fatigue,1998,20(4):271-277.
[46] M. Nagode, M. Fajdiga. An improved algorithm for parameter estimation suitable for mixedWeibull distributions[J]. International Journal Fatigue,2000,22(1):75-80.
[47] R. Tovo. A damage-based evaluation of probability density distribution for rain-flow rangesfrom random processes[J]. International Journal of Fatigue,2000,22:425-429.
[48]吕澎民.宽带随机载荷谱下结构疲劳寿命估算[J].长安大学学报.2004,24(1):76-78.
[49]阳光武,肖守讷,金鼑昌.基于分段S-N曲线的频域疲劳损伤估计[J].机械强度,2005,27(4):544-548.
[50] Pengmin Lu, Banghua Zhao, Junmao Yan. Efficient algorithm for fatigue life calculationsunder broad band loading based on peak approximation[J]. Journal Engineering Mechanics,1998,5:233~236.
[51] C. L. Chow, D. L. Li. An analytical solution for fast fatigue assessment under wide-bandrandom loading[J]. International Journal of Fatigue,1991,13(5):395~404.
[52] J. C. P. Kam. Recent development in the fast corrosion fatigue analysis of offshore structuresunder random wave loading [J]. International Journal of Fatigue,1990,12(6):458~468.
[53]吕澎民,赵邦华,严隽耄.宽带随机谱下一种实用的等效应力计算模型[J].甘肃工业大学学报.1996,22(5):76~82.
[54]屠海明,邓洪渊.桅杆结构风振疲劳分析[J].四川建筑科学研究,2001,27(2):6~8.
[55] S. Sakai, H. Okamura. On the distribution of rainflow range for Gaussian random processeswith bimodal PSD[J]. JSME International Journal, Series A,1995,38(4):440~445.
[56] T.-T. Fu, D. Cebon. Prediction fatigue lives for bi-modal stress spectral densities[J].International Journal of Fatigue,2000,22:11~21.
[57] C. Braccesi, F. Cianetti, G. Lori, D. Pioli. Fatigue behaviour analysis of mechanicalcomponents subject to random bimodal stress process: frequency domain approach[J].International Journal of Fatigue,2005,27:335~345.
[58] T. Lagoda, E. Macha, R. Pawliczek. The influence of the mean stress on fatigue life of10HNAP steel under random loading[J].International Journal of Fatigue,2001,23:283~291.
[59] S. Kwofie. An exponential stress functions for predicting fatigue strength and life due tomean stresses[J]. International Journal of Fatigue,2001,23:829~836.
[60]冯振宇,诸德培,林富甲.随机载荷下的疲劳寿命估算[J].机械科学与技术,1996,15(6):879~882.
[61] M. Nagode, M. Fajdiga. A general multi-modal probability density function suitable for therainflow ranges of stationary random processes[J]. International Journal of Fatigue,1998,20(3):211-223.
[62]王明珠．结构振动疲劳寿命分析方法研究[D]．南京:南京航空航天大学,2009．
[63] T. Dirlik. Application of computers in fatigue analysis,[Ph.D. Dissertation]. Coventry:University of Warwick,1985.
[64] N. W. M. Bishop, Z. Hu, R. Wang, D. Quarton. Methods for rapid evaluation of fatiguedamage on the Howden HWP330wind turbine[C]. British Wind Energy Conference, York,1993.
[65]韩鲁明.基于CAE技术的某半挂车车架疲劳寿命预估研究[D].南京:南京理工大学,2007.
[66]阳光武.机车车辆零部件的疲劳寿命预测仿真[D].西安:西南交通大学,2000.
[67]王成国,孟广伟,原亮明,刘敬辉.新型高速客车构架的疲劳寿命数值仿真分析[J].中国铁道科学.2001(3):62-65.
[68] HalfpennyA,林晓斌.基于功率谱密度信号的疲劳寿命估计[J].中国机械工程.1998(11):41-45.
[69]林晓斌.基于有限元的疲劳设计分析系统MSC/FATIGUE[J].中国机械工程.1998(11):12-16.
[70]孟广伟,王成国,刘敬辉,原亮明.用虚拟疲劳样机技术分析转8A型转向架侧架的疲劳寿命[J].中国铁道科学.2002(04):74-77.
[71] Sridhar Srikantan, Shekar YerraPalli, Hamid Keshtkar. Durability design process for truckbody structures [J], International Journal of Vehicle Design.2000,23(1/2):95-108.
[72] Mede PalliS, Rao R.Prediction of road loads for fatigue design,a sensitivity study[J].International Journal of vehicle Design,2000,23(l/2):161-175.
[73] Su, Hong.Automotive CAE Durability Analysis Using Random VibrationApproach[C]//MSC and World wide Automotive Conference, Dearborn, MI, oct.2000.
[74] H.Riener, D.Peiskammer. Modal Durability analysis of a Passenger Cars Front supportingframe due to full vehicle simulation loads[C]//Adams user conference, North America.2001.
[75] Kim K S,Yim H J, Kim C B.Computational durability Prediction of body structure inPrototype vehicle[J]. International Journal of automotive technology, vol,3,2002:129-136.
[76] Sigmund Kyrre As.Fatigue assessment of aluminum automotive structure.PhD thesis,Norwegian University of Science and Technology, Norwegian,2002,8.
[77]1Shiniehi CHIBA, Kimihiko AOYAMA, Kenji YANABU. Fatigue Strength Prediction OfTruck Cab by CAE [J].Technical review,2003(15):53-58.
[78] Mika Baekstrom. Multiaxial fatigue life assessment of welds based on nominal and hotstresses.PhD thesis, Norwegian University of Science and Technology, Finland,2003,8.
[79] R.K.Luo, B.L.Gabbitas, B.V.Briekie. Fatigue life evaluation for a railway vehicle bogie usingan integrated dynamic simulation [J]. Proc Instn Mech Engre vol208,1994,23-132.
[80] R.K.Luo, B.L.Gabbitas, B.V.Briekle. Fatigue damage evaluation for a railway vehicle bogieusing appropriate sampling frequencies [J].Vehicle System Dynamics.1998,(28):405-415.
[81] Stefan Dietz, Helmuth Netter and Sachau. Fatigue life Prediction of a railway bogie underdynamic loads through simulation [J].Vehicle System Dynamics.1998(29):385-402.
[82] A.Payne.A reliability approach to the fatigue.Probability aspects of fatigue [J]. ASME,STP5ll,1972.
[83] N.R.Mann, R.E.Schafer, N.D.Singpurwalla. Methods for statistical analysis of reliability andlife data[J]. John Wiley&Sons,1974.
[84] S.D.Downing, D.F.Socie.Simple rainflow counting algorithms [J].International Journal ofFatigue,1982,4(1):31~40.
[85]李德勇,王明珠.随机振动疲劳计算方法比较[J].江苏航空,2010,12(S2):12-17.
[86] S. Sakai, H. Okamura. On the distribution of rain flow range for Gaussian random processeswith bimodal PSD[J]. JSME International Journal, Series A,1995,38(4):440~445.
[87] T.-T. Fu, D.Cebon. Prediction fatigue lives for bi-modal stress spectral densities[J].International Journal of Fatigue,2000,22:11~21.
[88] C. Braccesi, F. Cianetti, G. Lori, D. Pioli. Fatigue behaviour analysis of mechanicalcomponents subject to random bimodal stress process: frequency domain approach[J].International Journal of Fatigue,2005,27:335~345.
[89] T. Lagoda, E. Macha, R. Pawliczek. The influence of the mean stress on fatigue life of10HNAP steel under random loading[J].International Journal of Fatigue,2001,23:283~291.
[90] S. Kwofie. An exponential stress functions for predicting fatigue strength and life due tomean stresses[J]. International Journal of Fatigue,2001,23:829~836.
[91] Bishop N W M. The use of frequency domain parameters to predict structural fatigue,
[Ph.D.Dissertation]. Coventry: University of Warwick,1988.
[92] D.P.Kihl, S.Sarkani, J.E.Beach. Stochastic fatigue damage accumulation under broadb andloadings[J]. International Journal of Fatigue,1995,17(5):321~329.
[93] D. Benasciutti, R. Tovo. Comparison of spectral methods for fatigue analysis of broad-bandGaussian random processes.[J] Probabilistic Engineering Mechanics,2005,1:1~13.
[94] D. Benasciutti, R. Tovo. Spectral method for lifetime prediction under wide-band stationaryrandom processes[J]. International Journal of Fatigue,2005,27:867~877.
[95] M. Nagode, M. Fajdiga. A general multi-modal probability density function suitable for therainflow ranges of stationary random processes[J]. International Journal of Fatigue,1998,20(3):211~223.
[96]刘文光.考虑结构裂纹扩展的振动疲劳寿命计算方法[J].振动工程学报,2012,25(1):79-84.
[97] M. Nagode, M. Fajdiga. An improved algorithm for parameter estimation suitable for mixedWeibull distributions[J]. International Journal Fatigue,2000,22(1):75~80.
[98] R. Tovo. A damage-based evaluation of probability density distribution for rain-flow rangesfrom random processes[J]. International Journal of Fatigue,2000,22:425~429.
[99] R.J. Anthes. Modified rainflow counting keeping the load sequence[J]. International Journalof Fatigue,1997,19(7):529~535.
[100] M. Nagode, M. Fajdiga. On a new method for prediction of the scatter of loading spectra[J].International Journal of Fatigue,1998,20(4):271~277.
[101] S．Suresh．Fatigue of Materials．国防工业出版社,1993.
[102]赵少汴,王忠保．抗疲劳设计方法与数据[M]．机械工业出版社,1997.
[103]高镇同．疲劳应用统计学[M]．国防工业出版社,1986.
[104]王永涛,藏勇,吴迪平等.CSP轧机扭振中“伪拍振”的研究[J].振动、测试与诊断,2009,29(2):42-46.
[105]王亚涛,谭静,陈辉等.结构在不同约束下的位移模态和应变模态分析[C]//第二十一届全国振动与噪声高技术及应用学术会议,合肥,2008.8.
[106]李德葆,陆秋海.实验模态分析及其应用[M].北京:科学出版社,2001.
[107]罗明军,赵永玲,宋立新等.汽车后扭力梁结构的模态分析[J].南昌大学学报（工科版）,2013,35(02):172-176.
[108]陈林,张立民,段合朋等.基于环境激励的车辆系统工作模态试验分析[J].噪声与振动控制,2008,(6):81-84.
[109] LI H.L, CHU W.Y, GAO K.W, et al.Stress corrosion cracking of high-strength steels [J].Steel Research,2001,72(9):366-370.
[110]吴旭东,左曙光,杨先武,等.基于摩擦自振的轮胎-扭力梁悬架系统仿真分析[J].振动与冲击,2011,30(9):76-78;2011,30(9):135.
[111]姚戈,田继丰.汽车扭力梁开裂原因分析[C]//2010年海峡两岸材料破坏/断裂学术会议.台湾,北京科技大学出版社,2010:84-90.
[112]陈立平,张云清编著.机械系统动力学分析及ADAMS应用教程[M].北京:清华大学出版社,2005.11.
[113]赵熙俊,王洪亮,陈慧岩．AMT可靠性台架试验方法研究[J].汽车工程,2009,31(9):882-886.
[114]宋子康、蔡文安.材料力学[M].上海:同济大学出版社,2005.7.
[115]缪炳荣.基于多体动力学和有限元法的机车车体结构疲劳仿真研究[D].西安:西南交通大学,2006.
[116] Conle F A, Mousseau C W.Using vehicle dynamics simulations and finite elementResults to generate fatigue Life contours for chassis components[J].International JournalOf Fatigue,1991,13(3):195-20.
[117]刘江华.振动疲劳特性的频率效应与寿命预估研究[D].西安:西北工业大学,2008.
[118] Morrissey R J, McDowell D L, Nicholas T. Frequency and stress ratio effects in high cyclefatigue of T-i6A-l4V[J]. International Journal of Fatigue,1999,21:679-685.
[119]奥本海姆,威尔.信号与系统（第2版·精编版）[M].西安:西安交通大学出版社,2010.11.
[120]赵熙俊,王洪亮,陈慧岩．AMT可靠性台架试验方法研究[J].汽车工程,2009,31(9):882-886.
[121] Martin Cesnik, Janko Slavic, Miha Boltezar. Uninterrupted and accelerated vibrationalfatigue testing with Simultaneous monitoring of the natural frequency anddamping[J].Journal of Sound and Vibration,2012,331(11):5370–5382.
[122] Guirong Yan, Alessandro De Stefano, Emiliano Matta, Ruoqiang Feng. A novel approach todetecting breathing fatigue cracks based on dynamic characteristics[J].Journal of Soundand Vibration,2013,332(10):407–422.
[123] Yan-Shin Shih,Guan-Yuan Wu. Effect of vibration on fatigue crack growth of an edge crackfor a rectangular plate[J]. International Journal of Fatigue,2002,24(2):557–566.
[124] Seung-Ho Han,Dae-Gyun An,Seong-Jong Kwak,Ki-Weon Kang.Vibration fatigue analysisfor multi-point spot-welded joints based on frequency response changes due to fatiguedamage accumulation[J].International Journal of Fatigue,2013,48(2):170–177.
[125] A.Rama Rao, B.K. Dutta. Vibration analysis for detecting failure of compressorblade[J].Engineering Failure Analysis,2012,25(3):211-218.
[126] E. Poursaeidi, A. Babaei, M.R. Mohammadi Arhani. Effects of natural frequencies on thefailure of R1compressor blades[J].Engineering Failure Analysis,2012,25(1):304-315.
[127] Tommy J. George, Jeremy Seidt, M.-H. Herman Shen, Theodore Nicholas. Development ofa novel vibration-based fatigue testing methodology[J]. International Journal of Fatigue,2004,26(6):477-486.
[128] Murat Aykan, Mehmet Celik. Vibration fatigue analysis and multi-axial effect in testing ofAerospace structures [J]. Mechanical Systems and Signal Processing,2009,23(4):897-907.
[129] GAO Yun,ZONG Zhi,SUN Lei.Numerical prediction of fatigue damage in steel catenaryriser due to ortex-induced vibration[J].Journal of Hydrodynamics,2011,23(2):154-163
[2] Ridnou, James Andrew.Methodology for evaluating vehicle fatigue life and durability. PhDthesis, The University of Tennessee, Knoxville,2003,12.
[3]姚起杭,姚军.结构振动疲劳问题的特点与分析方法[J].机械科学与技术,2000,19(s):56-58.
[4]姚起杭,姚军.工程结构的振动疲劳研究[J].飞机工程,2005,3:5-8.
[5]姚起杭,姚军.工程结构的振动疲劳问题[J].应用力学学报,2006,23(1):12-15.
[6]刘艳华.轿车扭力梁后悬架的开发研究[J].沈阳大学学报,2006,18(4):5-9.
[7]肖寿庭,杜修德.飞机结构振动疲劳问题[C].第六届全国疲劳学术会议论文集(下),厦门,1993.
[8]军用飞机强度和刚度规范(振动)[S].北京:航空工业部630研究所,1985.
[9]美国军用规范飞机强度和刚度MIL-A-8860B(AS)系列[S].北京:航空航天工业部飞行试验研究中心飞机强度规范研究室,1988.
[10] Osgood C C. Fatigue design [M]. Oxford: Pergamon press,1982.
[11] Crandall S H. Random vibration [M]. New York: Technology Press of MIT and John WileyandSons,1958.
[12] Crandall S H, Mark W D. Random Vibration in Mechanical Systems [M].Academic Press,1963.
[13]姚起杭.谈谈加速振动试验问题[J].航空标准与质量,1975.06:7-18.
[14] M. Nagode, M. Fajdiga. An improved algorithm for parameter estimation suitable for mixedWeibull distributions [J]. International Journal Fatigue,2000,22(1):75~80.
[15]姚起杭,姚军.结构振动疲劳问题的特点与分析方法[J].机械科学与技术,2000,19(S):56-58.
[16]何泽夏.振动与疲劳[J].火箭推进,1994,3:14-20.
[17] C.格林.振动手册[M].北京:《强度与环境》编辑部,1982.
[18]刘光文.结构共振疲劳试验及裂纹构件的振动疲劳耦合分析[D].南京:南京航空航天大学,2010.
[19] M.Haiba, D.c. Barton,P.c.Brooks. Review of life assessment techniques applied todynamically loaded automotive components[J].Computers and structures.2002(80):481-494.
[20] S. D. Downing, D.F. Socie. Simple rainflow counting algorithms [J]. International Journal ofFatigue,1982,4(1):31-40.
[21] R.J. Anthes. Modified rainflow counting keeping the load sequence[J]. International Journalof Fatigue,1997,19(7):529-535.
[22] M. P. Repetto. Cycle counting methods for bi-modal stationary Gaussian processes[J]Probabilistic Engineering Mechanics,2005,20:229-238.
[23] M. Grigoriu. A spectral representation based modal for Monte Carlo simulation[J].Probabilistic Engineering Mechanics,2000,15:365-370.
[24]侯传亮,张永林.工程平稳随机过程的数值模拟研究[J].武汉工业学院学报,2003,22(3):27-29.
[25]刘献栋,邓志党,高峰.基于逆变换的路面不平度仿真研究[J].中国公路学报,2005,18(1):122~126.
[26]陈春俊,李华超.频域采样三角级数法模拟轨道不平顺信号[J].铁道学报,2006,28(3):38-42.
[27]刘寅华,李芾,黄运华.轨道不平顺数值模拟方法[J].交通运输工程学报,2006,6(1):29-33.
[28]安刚,龚鑫茂.随机振动环境下结构的疲劳失效分析[J].机械科学与技术,2000,19(s):40-42.
[29]徐菲,肖寿庭.结构声疲劳寿命估算的功率谱密度法[J].机械强度,1996,18(4):38-42.
[30] P. H. Wirsching. Fatigue under wide band random stress[J]. Journal of the Structural Division,1980,1593-1606.
[31] G. Chaudhury. Spectral fatigue of broad-band stress spectrum with one or more peaks[J].OTC5333,1986,387-396.
[32] L. D. Lutes, S. Sarkani. Stochastic analysis of structural and mechanical vibrations [J]. NewJersey: Prentice-Hall,1997.
[33] Andrew Halfpenny.基于功率谱密度信号的疲劳寿命分析[J].中国机械工程,1998,9(11):16-19.
[34]伍义生.随机载荷下疲劳损伤计算[J].机械科学与技术.1996,11:879-882.
[35]李超.基于功率谱密度的疲劳寿命估算[J].机械设计与研究,2005,21(2):6-8.
[36]王琳,倪樵,张强,刘攀.随机激励下高压管道的疲劳寿命分析[J].华中科技大学学报(自然科学版),2003,31(12):100-102.
[37]吴启鹤,叶笃毅.一种估算结构件随机疲劳寿命的新方法[J].工程力学,1995,12(2):87-94.
[38]骆红云,陈志刚,张卫波,梁淑卿.窄带随机应力下机械构件寿命预测法[J].吉林工学院学报,2000,21(4):32-34.
[39] S. D. Downing, D.F. Socie. Simple rainflow counting algorithms[J]. International Journal ofJournal of Fatigue,2002,24:1137-1147.
[40] Bishop N W M. The use of frequency domain parameters to predict structural fatigue,[Ph.D.Dissertation]. Coventry: University of Warwick,1988.
[41] D. P. Kihl, S. Sarkani, J. E. Beach. Stochastic fatigue damage accumulation under broadbandloadings[J]. International Journal of Fatigue,1995,17(5):321-329.
[42] D. Benasciutti, R. Tovo. Comparison of spectral methods for fatigue analysis of broad-bandGaussian random processes[J]. Probabilistic Engineering Mechanics,2005,1:1-13.
[43] D. Benasciutti, R. Tovo. Spectral method for lifetime prediction under wide-band stationaryrandom processes[J]. International Journal of Fatigue,2005,27:867-877.
[44] M. Frendhal, I. Rychlik. Rainflow analysis: Markov method[J]. InternationalJournal of Fatigue,1993,15:265~273.
[45] M. Nagode, M. Fajdiga. On a new method for prediction of the scatter of loading spectra[J].International Journal of Fatigue,1998,20(4):271-277.
[46] M. Nagode, M. Fajdiga. An improved algorithm for parameter estimation suitable for mixedWeibull distributions[J]. International Journal Fatigue,2000,22(1):75-80.
[47] R. Tovo. A damage-based evaluation of probability density distribution for rain-flow rangesfrom random processes[J]. International Journal of Fatigue,2000,22:425-429.
[48]吕澎民.宽带随机载荷谱下结构疲劳寿命估算[J].长安大学学报.2004,24(1):76-78.
[49]阳光武,肖守讷,金鼑昌.基于分段S-N曲线的频域疲劳损伤估计[J].机械强度,2005,27(4):544-548.
[50] Pengmin Lu, Banghua Zhao, Junmao Yan. Efficient algorithm for fatigue life calculationsunder broad band loading based on peak approximation[J]. Journal Engineering Mechanics,1998,5:233~236.
[51] C. L. Chow, D. L. Li. An analytical solution for fast fatigue assessment under wide-bandrandom loading[J]. International Journal of Fatigue,1991,13(5):395~404.
[52] J. C. P. Kam. Recent development in the fast corrosion fatigue analysis of offshore structuresunder random wave loading [J]. International Journal of Fatigue,1990,12(6):458~468.
[53]吕澎民,赵邦华,严隽耄.宽带随机谱下一种实用的等效应力计算模型[J].甘肃工业大学学报.1996,22(5):76~82.
[54]屠海明,邓洪渊.桅杆结构风振疲劳分析[J].四川建筑科学研究,2001,27(2):6~8.
[55] S. Sakai, H. Okamura. On the distribution of rainflow range for Gaussian random processeswith bimodal PSD[J]. JSME International Journal, Series A,1995,38(4):440~445.
[56] T.-T. Fu, D. Cebon. Prediction fatigue lives for bi-modal stress spectral densities[J].International Journal of Fatigue,2000,22:11~21.
[57] C. Braccesi, F. Cianetti, G. Lori, D. Pioli. Fatigue behaviour analysis of mechanicalcomponents subject to random bimodal stress process: frequency domain approach[J].International Journal of Fatigue,2005,27:335~345.
[58] T. Lagoda, E. Macha, R. Pawliczek. The influence of the mean stress on fatigue life of10HNAP steel under random loading[J].International Journal of Fatigue,2001,23:283~291.
[59] S. Kwofie. An exponential stress functions for predicting fatigue strength and life due tomean stresses[J]. International Journal of Fatigue,2001,23:829~836.
[60]冯振宇,诸德培,林富甲.随机载荷下的疲劳寿命估算[J].机械科学与技术,1996,15(6):879~882.
[61] M. Nagode, M. Fajdiga. A general multi-modal probability density function suitable for therainflow ranges of stationary random processes[J]. International Journal of Fatigue,1998,20(3):211-223.
[62]王明珠．结构振动疲劳寿命分析方法研究[D]．南京:南京航空航天大学,2009．
[63] T. Dirlik. Application of computers in fatigue analysis,[Ph.D. Dissertation]. Coventry:University of Warwick,1985.
[64] N. W. M. Bishop, Z. Hu, R. Wang, D. Quarton. Methods for rapid evaluation of fatiguedamage on the Howden HWP330wind turbine[C]. British Wind Energy Conference, York,1993.
[65]韩鲁明.基于CAE技术的某半挂车车架疲劳寿命预估研究[D].南京:南京理工大学,2007.
[66]阳光武.机车车辆零部件的疲劳寿命预测仿真[D].西安:西南交通大学,2000.
[67]王成国,孟广伟,原亮明,刘敬辉.新型高速客车构架的疲劳寿命数值仿真分析[J].中国铁道科学.2001(3):62-65.
[68] HalfpennyA,林晓斌.基于功率谱密度信号的疲劳寿命估计[J].中国机械工程.1998(11):41-45.
[69]林晓斌.基于有限元的疲劳设计分析系统MSC/FATIGUE[J].中国机械工程.1998(11):12-16.
[70]孟广伟,王成国,刘敬辉,原亮明.用虚拟疲劳样机技术分析转8A型转向架侧架的疲劳寿命[J].中国铁道科学.2002(04):74-77.
[71] Sridhar Srikantan, Shekar YerraPalli, Hamid Keshtkar. Durability design process for truckbody structures [J], International Journal of Vehicle Design.2000,23(1/2):95-108.
[72] Mede PalliS, Rao R.Prediction of road loads for fatigue design,a sensitivity study[J].International Journal of vehicle Design,2000,23(l/2):161-175.
[73] Su, Hong.Automotive CAE Durability Analysis Using Random VibrationApproach[C]//MSC and World wide Automotive Conference, Dearborn, MI, oct.2000.
[74] H.Riener, D.Peiskammer. Modal Durability analysis of a Passenger Cars Front supportingframe due to full vehicle simulation loads[C]//Adams user conference, North America.2001.
[75] Kim K S,Yim H J, Kim C B.Computational durability Prediction of body structure inPrototype vehicle[J]. International Journal of automotive technology, vol,3,2002:129-136.
[76] Sigmund Kyrre As.Fatigue assessment of aluminum automotive structure.PhD thesis,Norwegian University of Science and Technology, Norwegian,2002,8.
[77]1Shiniehi CHIBA, Kimihiko AOYAMA, Kenji YANABU. Fatigue Strength Prediction OfTruck Cab by CAE [J].Technical review,2003(15):53-58.
[78] Mika Baekstrom. Multiaxial fatigue life assessment of welds based on nominal and hotstresses.PhD thesis, Norwegian University of Science and Technology, Finland,2003,8.
[79] R.K.Luo, B.L.Gabbitas, B.V.Briekie. Fatigue life evaluation for a railway vehicle bogie usingan integrated dynamic simulation [J]. Proc Instn Mech Engre vol208,1994,23-132.
[80] R.K.Luo, B.L.Gabbitas, B.V.Briekle. Fatigue damage evaluation for a railway vehicle bogieusing appropriate sampling frequencies [J].Vehicle System Dynamics.1998,(28):405-415.
[81] Stefan Dietz, Helmuth Netter and Sachau. Fatigue life Prediction of a railway bogie underdynamic loads through simulation [J].Vehicle System Dynamics.1998(29):385-402.
[82] A.Payne.A reliability approach to the fatigue.Probability aspects of fatigue [J]. ASME,STP5ll,1972.
[83] N.R.Mann, R.E.Schafer, N.D.Singpurwalla. Methods for statistical analysis of reliability andlife data[J]. John Wiley&Sons,1974.
[84] S.D.Downing, D.F.Socie.Simple rainflow counting algorithms [J].International Journal ofFatigue,1982,4(1):31~40.
[85]李德勇,王明珠.随机振动疲劳计算方法比较[J].江苏航空,2010,12(S2):12-17.
[86] S. Sakai, H. Okamura. On the distribution of rain flow range for Gaussian random processeswith bimodal PSD[J]. JSME International Journal, Series A,1995,38(4):440~445.
[87] T.-T. Fu, D.Cebon. Prediction fatigue lives for bi-modal stress spectral densities[J].International Journal of Fatigue,2000,22:11~21.
[88] C. Braccesi, F. Cianetti, G. Lori, D. Pioli. Fatigue behaviour analysis of mechanicalcomponents subject to random bimodal stress process: frequency domain approach[J].International Journal of Fatigue,2005,27:335~345.
[89] T. Lagoda, E. Macha, R. Pawliczek. The influence of the mean stress on fatigue life of10HNAP steel under random loading[J].International Journal of Fatigue,2001,23:283~291.
[90] S. Kwofie. An exponential stress functions for predicting fatigue strength and life due tomean stresses[J]. International Journal of Fatigue,2001,23:829~836.
[91] Bishop N W M. The use of frequency domain parameters to predict structural fatigue,
[Ph.D.Dissertation]. Coventry: University of Warwick,1988.
[92] D.P.Kihl, S.Sarkani, J.E.Beach. Stochastic fatigue damage accumulation under broadb andloadings[J]. International Journal of Fatigue,1995,17(5):321~329.
[93] D. Benasciutti, R. Tovo. Comparison of spectral methods for fatigue analysis of broad-bandGaussian random processes.[J] Probabilistic Engineering Mechanics,2005,1:1~13.
[94] D. Benasciutti, R. Tovo. Spectral method for lifetime prediction under wide-band stationaryrandom processes[J]. International Journal of Fatigue,2005,27:867~877.
[95] M. Nagode, M. Fajdiga. A general multi-modal probability density function suitable for therainflow ranges of stationary random processes[J]. International Journal of Fatigue,1998,20(3):211~223.
[96]刘文光.考虑结构裂纹扩展的振动疲劳寿命计算方法[J].振动工程学报,2012,25(1):79-84.
[97] M. Nagode, M. Fajdiga. An improved algorithm for parameter estimation suitable for mixedWeibull distributions[J]. International Journal Fatigue,2000,22(1):75~80.
[98] R. Tovo. A damage-based evaluation of probability density distribution for rain-flow rangesfrom random processes[J]. International Journal of Fatigue,2000,22:425~429.
[99] R.J. Anthes. Modified rainflow counting keeping the load sequence[J]. International Journalof Fatigue,1997,19(7):529~535.
[100] M. Nagode, M. Fajdiga. On a new method for prediction of the scatter of loading spectra[J].International Journal of Fatigue,1998,20(4):271~277.
[101] S．Suresh．Fatigue of Materials．国防工业出版社,1993.
[102]赵少汴,王忠保．抗疲劳设计方法与数据[M]．机械工业出版社,1997.
[103]高镇同．疲劳应用统计学[M]．国防工业出版社,1986.
[104]王永涛,藏勇,吴迪平等.CSP轧机扭振中“伪拍振”的研究[J].振动、测试与诊断,2009,29(2):42-46.
[105]王亚涛,谭静,陈辉等.结构在不同约束下的位移模态和应变模态分析[C]//第二十一届全国振动与噪声高技术及应用学术会议,合肥,2008.8.
[106]李德葆,陆秋海.实验模态分析及其应用[M].北京:科学出版社,2001.
[107]罗明军,赵永玲,宋立新等.汽车后扭力梁结构的模态分析[J].南昌大学学报（工科版）,2013,35(02):172-176.
[108]陈林,张立民,段合朋等.基于环境激励的车辆系统工作模态试验分析[J].噪声与振动控制,2008,(6):81-84.
[109] LI H.L, CHU W.Y, GAO K.W, et al.Stress corrosion cracking of high-strength steels [J].Steel Research,2001,72(9):366-370.
[110]吴旭东,左曙光,杨先武,等.基于摩擦自振的轮胎-扭力梁悬架系统仿真分析[J].振动与冲击,2011,30(9):76-78;2011,30(9):135.
[111]姚戈,田继丰.汽车扭力梁开裂原因分析[C]//2010年海峡两岸材料破坏/断裂学术会议.台湾,北京科技大学出版社,2010:84-90.
[112]陈立平,张云清编著.机械系统动力学分析及ADAMS应用教程[M].北京:清华大学出版社,2005.11.
[113]赵熙俊,王洪亮,陈慧岩．AMT可靠性台架试验方法研究[J].汽车工程,2009,31(9):882-886.
[114]宋子康、蔡文安.材料力学[M].上海:同济大学出版社,2005.7.
[115]缪炳荣.基于多体动力学和有限元法的机车车体结构疲劳仿真研究[D].西安:西南交通大学,2006.
[116] Conle F A, Mousseau C W.Using vehicle dynamics simulations and finite elementResults to generate fatigue Life contours for chassis components[J].International JournalOf Fatigue,1991,13(3):195-20.
[117]刘江华.振动疲劳特性的频率效应与寿命预估研究[D].西安:西北工业大学,2008.
[118] Morrissey R J, McDowell D L, Nicholas T. Frequency and stress ratio effects in high cyclefatigue of T-i6A-l4V[J]. International Journal of Fatigue,1999,21:679-685.
[119]奥本海姆,威尔.信号与系统（第2版·精编版）[M].西安:西安交通大学出版社,2010.11.
[120]赵熙俊,王洪亮,陈慧岩．AMT可靠性台架试验方法研究[J].汽车工程,2009,31(9):882-886.
[121] Martin Cesnik, Janko Slavic, Miha Boltezar. Uninterrupted and accelerated vibrationalfatigue testing with Simultaneous monitoring of the natural frequency anddamping[J].Journal of Sound and Vibration,2012,331(11):5370–5382.
[122] Guirong Yan, Alessandro De Stefano, Emiliano Matta, Ruoqiang Feng. A novel approach todetecting breathing fatigue cracks based on dynamic characteristics[J].Journal of Soundand Vibration,2013,332(10):407–422.
[123] Yan-Shin Shih,Guan-Yuan Wu. Effect of vibration on fatigue crack growth of an edge crackfor a rectangular plate[J]. International Journal of Fatigue,2002,24(2):557–566.
[124] Seung-Ho Han,Dae-Gyun An,Seong-Jong Kwak,Ki-Weon Kang.Vibration fatigue analysisfor multi-point spot-welded joints based on frequency response changes due to fatiguedamage accumulation[J].International Journal of Fatigue,2013,48(2):170–177.
[125] A.Rama Rao, B.K. Dutta. Vibration analysis for detecting failure of compressorblade[J].Engineering Failure Analysis,2012,25(3):211-218.
[126] E. Poursaeidi, A. Babaei, M.R. Mohammadi Arhani. Effects of natural frequencies on thefailure of R1compressor blades[J].Engineering Failure Analysis,2012,25(1):304-315.
[127] Tommy J. George, Jeremy Seidt, M.-H. Herman Shen, Theodore Nicholas. Development ofa novel vibration-based fatigue testing methodology[J]. International Journal of Fatigue,2004,26(6):477-486.
[128] Murat Aykan, Mehmet Celik. Vibration fatigue analysis and multi-axial effect in testing ofAerospace structures [J]. Mechanical Systems and Signal Processing,2009,23(4):897-907.
[129] GAO Yun,ZONG Zhi,SUN Lei.Numerical prediction of fatigue damage in steel catenaryriser due to ortex-induced vibration[J].Journal of Hydrodynamics,2011,23(2):154-163