高速车辆外部气动噪声场数值模拟研究
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摘要
随着高速铁路和高速公路的迅捷发展,车辆的行驶速度不断提高,车辆工程技术的进步使得车辆总噪声中的其它噪声(如汽车行驶过程中的动力系统噪声、传动系噪声、进排气噪声等)得到有效控制并逐步降低,而车辆行驶时所诱发的气动噪声是随车速的六次方增长,气动噪声已逐渐上升成为车辆总噪声中越来越重要的组成部分,并明显地影响到车辆行驶时所产生的总噪声值。本文以Lighthill声类比理论为基础,采用边界元法并与计算流体动力学相结合,探讨了高速车辆在不同车速下所诱发的外部气动噪声场的分布规律特征。
本文的主要研究工作和结论主要体现在以下几个方面：
1)运动单极子声源和偶极子声源指向性因子研究
从经典的声源理论出发,利用广义格林函数和运动声源的多普勒效应,从理论上研究了独立的匀速直线运动单极子声源(点声源)和偶极子声源的声辐射特征,并结合广义Lighthill方程推导出反映声源运动特征的一般运动声源(单极子声源、偶极子声源)以及流场中运动固壁所诱发的表面气动偶极子声源的指向性因子。
2)车辆外流场空气动力学特性的三维数值分析
分别建立了轿车和高速列车的几何模型和外流场三维数值分析模型；从提高数值模拟计算精度的角度出发,确定了稳态流下采用Realizable k-ε两方程湍流模型并与增强壁面函数法(Enhanced Wall Treatment)相结合的方案,并在不同车速工况下对高速车辆外部流场空气动力特性的进行三维数值分析；确定车辆外流场大涡模拟(LES)的计算方案,在非稳态流下对高速车辆外部流场进行三维数值计算并得到流场边界的空气压力脉动情况。
3)基于宽带声源模型的车辆外部气动噪声源分布初步预测
以宽带声源模型理论为基础,在明线环境下分别采用基于Proudman公式的宽带声源模型和基于Curle积分方程的宽带声源模型对稳态流状态下高速车辆表面气动噪声源分布进行初步预测,并对两种宽带声源模型进行了理论和模拟结果对比分析；采用具有较高精度的基于Curle积分方程的宽带声源模型,对隧道环境下高速车辆表面和隧道侧壁所诱发的气动噪声源强弱及分布特点进行初步数值分析；对原规范中公路隧道几何断面进行了初步改良设计,以降低隧道环境下车辆所诱发的气动噪声源强度,并验证了改良设计的有效性。
4)高速车辆车身表面气动噪声偶极子声源分布数值分析
采用计算流体动力学(CFD)中的流场大涡模拟(LES)方法并结合Lighthill声类比理论,对高速车辆车身表面气动噪声偶极子声源的强弱及其分布进行数值模拟分析和研究,获得了不同车速工况下的轿车和列车车身表面气动偶极子声源分布特征。
5)高速车辆外部气动噪声场数值模拟研究
以车身表面分布的偶极子声源作为声源边界条件,利用直接边界元法将相关声学基本方程的积分形式转化为外部无限空间区域边界上(即车辆表面边界)的积分,对声学Helmholz方程求解,实现了高速车辆外部气动噪声场的数值模拟分析,并对车辆表面分布的偶极子声源的指向特性进行了探讨。
With the development of high-speed rail and highway,the speed of the vehicle continuously improve. Thanks to the development of vehicle engineering technology, the vehicle's gross noises (such as the power system noise, power train noise, intake and exhuast noise, etc.) have been effectively controlled and reduced. However, the vehicle aerodynamic noise is six square of the speed, so the aerodynamic noise has been gradually become an important part of the gross vehicle noise. In this paper, based on the Lighthill's acoustic analogy theory, the bondary element method (BEM) combined with the computational fluid dynamics (CFD) was utilized to analysys the distribution characteristics of high-speed vehicle's external aerodynamic noise field. The main research work and conclusion were divided into following areas:
1) Study of the moving monopole and dipole acoustic source's directivity factor
Based on the acoustic equation in the ideal fluid medium, the generalized Green's function combined with the Doppler Effect of moving acoustic source were utilized in this paper to study the characters of monopole (point source) and dipole acoustic source under uniform moving state. The directivity factor of the moving monopole, dipole and aerodynamic dipole acoustic source have been study, and compared with the corresponding type of acoustic source under stationary state.
2) Study of the numerical analysis programs on vehicle's external steady flow-field
Considering the improvement of calculation accuracy, the Realizable k-s two-equation turbulence model combined with the enhanced wall function method was applied to simulating the high-speed vehicle's external flow field. And the aerodynamic characteristics of external flow field of the car and the high-speed train were carefully discussed in this paper.
3) Prediction of vehicle's acoustic source based on broadband sound source model
Based on the broadband acoustic model theory, two broadband acoustic models (the Proudman formula broadband acoustic model and the Curie internal equation broadband acoustic model) were utilized to simulating the distribution of aerodynamic acoustic source on the high-speed vehicle surface in the opening-environment respectively. And the comparative analysis of the simulation results of these two kinds of broadband acoustic source models was completed in this paper. Then the distribution of aerodynamic acoustic sources on the vehicle and the tunnel surface were simulated by utilizing the broadband acoustic source model based on Curie integral equation with higher accuracy. In order to reduce the strength of aerodynamic noise source on vehicle surface and tunnel wall, an improved design for the highway tunnel's cross-section in the original standard was also discussed here. Then the effectiveness of the tunnel cross-section geometry improved design was verified.
4) Numerical analysis of the aerodynamic dipole source distribution on vehicle's surface
The vehicle's aerodynamic noise comes mainly from the aerodynamic dipole source on vehicle surface, and its intensity and distribution determine the characteristics of the vehicle's external acoustic field. In this paper, the large-eddy simulation was firstly executed to get the pressure fluctuations near vehicle surface, then the boundary element method (BEM) combined with the computational fluid dynamics (CFD) was utilized to simulate the distribution of aerodynamic dipole acoustic source near vehicle surface.
5) Simulation of the high-speed-vehicles external aerodynamic noise field
In this paper, the aerodynamic dipole sources on vehicle body surface were converted to the acoustic source boundary conditions, then the boundary element method (BEM) was applied to simulating the high-speed vehicle's external aerodynamic noise field by converting the volume integral of the relevant basic acoustics equations into the boundary integral of the infinite external space (i.e., solving the acoustic Helmholz equation on the vehicle's surface boundary). The distribution characteristics of vehicles' external aerodynamic noise field under different speed conditions were studied, and the directivity of aerodynamic dipole source on vehicle's surface was also discussed here.
本文的主要研究工作和结论主要体现在以下几个方面：
1)运动单极子声源和偶极子声源指向性因子研究
从经典的声源理论出发,利用广义格林函数和运动声源的多普勒效应,从理论上研究了独立的匀速直线运动单极子声源(点声源)和偶极子声源的声辐射特征,并结合广义Lighthill方程推导出反映声源运动特征的一般运动声源(单极子声源、偶极子声源)以及流场中运动固壁所诱发的表面气动偶极子声源的指向性因子。
2)车辆外流场空气动力学特性的三维数值分析
分别建立了轿车和高速列车的几何模型和外流场三维数值分析模型；从提高数值模拟计算精度的角度出发,确定了稳态流下采用Realizable k-ε两方程湍流模型并与增强壁面函数法(Enhanced Wall Treatment)相结合的方案,并在不同车速工况下对高速车辆外部流场空气动力特性的进行三维数值分析；确定车辆外流场大涡模拟(LES)的计算方案,在非稳态流下对高速车辆外部流场进行三维数值计算并得到流场边界的空气压力脉动情况。
3)基于宽带声源模型的车辆外部气动噪声源分布初步预测
以宽带声源模型理论为基础,在明线环境下分别采用基于Proudman公式的宽带声源模型和基于Curle积分方程的宽带声源模型对稳态流状态下高速车辆表面气动噪声源分布进行初步预测,并对两种宽带声源模型进行了理论和模拟结果对比分析；采用具有较高精度的基于Curle积分方程的宽带声源模型,对隧道环境下高速车辆表面和隧道侧壁所诱发的气动噪声源强弱及分布特点进行初步数值分析；对原规范中公路隧道几何断面进行了初步改良设计,以降低隧道环境下车辆所诱发的气动噪声源强度,并验证了改良设计的有效性。
4)高速车辆车身表面气动噪声偶极子声源分布数值分析
采用计算流体动力学(CFD)中的流场大涡模拟(LES)方法并结合Lighthill声类比理论,对高速车辆车身表面气动噪声偶极子声源的强弱及其分布进行数值模拟分析和研究,获得了不同车速工况下的轿车和列车车身表面气动偶极子声源分布特征。
5)高速车辆外部气动噪声场数值模拟研究
以车身表面分布的偶极子声源作为声源边界条件,利用直接边界元法将相关声学基本方程的积分形式转化为外部无限空间区域边界上(即车辆表面边界)的积分,对声学Helmholz方程求解,实现了高速车辆外部气动噪声场的数值模拟分析,并对车辆表面分布的偶极子声源的指向特性进行了探讨。
With the development of high-speed rail and highway,the speed of the vehicle continuously improve. Thanks to the development of vehicle engineering technology, the vehicle's gross noises (such as the power system noise, power train noise, intake and exhuast noise, etc.) have been effectively controlled and reduced. However, the vehicle aerodynamic noise is six square of the speed, so the aerodynamic noise has been gradually become an important part of the gross vehicle noise. In this paper, based on the Lighthill's acoustic analogy theory, the bondary element method (BEM) combined with the computational fluid dynamics (CFD) was utilized to analysys the distribution characteristics of high-speed vehicle's external aerodynamic noise field. The main research work and conclusion were divided into following areas:
1) Study of the moving monopole and dipole acoustic source's directivity factor
Based on the acoustic equation in the ideal fluid medium, the generalized Green's function combined with the Doppler Effect of moving acoustic source were utilized in this paper to study the characters of monopole (point source) and dipole acoustic source under uniform moving state. The directivity factor of the moving monopole, dipole and aerodynamic dipole acoustic source have been study, and compared with the corresponding type of acoustic source under stationary state.
2) Study of the numerical analysis programs on vehicle's external steady flow-field
Considering the improvement of calculation accuracy, the Realizable k-s two-equation turbulence model combined with the enhanced wall function method was applied to simulating the high-speed vehicle's external flow field. And the aerodynamic characteristics of external flow field of the car and the high-speed train were carefully discussed in this paper.
3) Prediction of vehicle's acoustic source based on broadband sound source model
Based on the broadband acoustic model theory, two broadband acoustic models (the Proudman formula broadband acoustic model and the Curie internal equation broadband acoustic model) were utilized to simulating the distribution of aerodynamic acoustic source on the high-speed vehicle surface in the opening-environment respectively. And the comparative analysis of the simulation results of these two kinds of broadband acoustic source models was completed in this paper. Then the distribution of aerodynamic acoustic sources on the vehicle and the tunnel surface were simulated by utilizing the broadband acoustic source model based on Curie integral equation with higher accuracy. In order to reduce the strength of aerodynamic noise source on vehicle surface and tunnel wall, an improved design for the highway tunnel's cross-section in the original standard was also discussed here. Then the effectiveness of the tunnel cross-section geometry improved design was verified.
4) Numerical analysis of the aerodynamic dipole source distribution on vehicle's surface
The vehicle's aerodynamic noise comes mainly from the aerodynamic dipole source on vehicle surface, and its intensity and distribution determine the characteristics of the vehicle's external acoustic field. In this paper, the large-eddy simulation was firstly executed to get the pressure fluctuations near vehicle surface, then the boundary element method (BEM) combined with the computational fluid dynamics (CFD) was utilized to simulate the distribution of aerodynamic dipole acoustic source near vehicle surface.
5) Simulation of the high-speed-vehicles external aerodynamic noise field
In this paper, the aerodynamic dipole sources on vehicle body surface were converted to the acoustic source boundary conditions, then the boundary element method (BEM) was applied to simulating the high-speed vehicle's external aerodynamic noise field by converting the volume integral of the relevant basic acoustics equations into the boundary integral of the infinite external space (i.e., solving the acoustic Helmholz equation on the vehicle's surface boundary). The distribution characteristics of vehicles' external aerodynamic noise field under different speed conditions were studied, and the directivity of aerodynamic dipole source on vehicle's surface was also discussed here.
引文
[1]纪玉荣.高速公路交通噪声对环境的影响和危害[J].中国科技纵横.2010,Vol.17：128
[2]韩增盛,马松花.城市轨道交通车辆噪声产生的原因与降低措施[J].铁道运营技术.2008,Vol.14(2)：1-2
[3]司春棣,陈恩利,杨绍普等.基于声阵列技术的汽车噪声源识别试验研究[J].振动与冲击.2009,Vol.28(6)：171-174
[4]郑拯宇,李人宪,高速流线型车辆稳态下速度风噪声源数值分析[J].重庆工学院学报(自然科学).2009,Vol.26(6)：1-4
[5]GB 1495-2002,汽车加速行驶车外噪声限值及测量方法.北京：中国标准出版社,2002.
[6]GB 12525-9011,铁路边界噪声值及其测量办法.北京：中国标准出版社,2008.
[7]S.Haruna, M.Hashiguchi, I.Kamimoto. Numerical Study of Aerodynamics Noise Radiated from a Three-Dimensional Wing[J]. SAE paper 920341,1992
[8]S.Haruna, I.Kamimoto, S.Okamoto. Estimation Method for Automobile Aerodynamic Noise[J]. SAE paper 920205,1992
[9]W.F. King, D. Beckert. Aerodynamic Noise Generated by High-Speed Tans[J]. Noise Control Engineering,1979
[10]汪怡平,谷正气等.汽车气动噪声数值计算分析[J].汽车工程.2009,Vol.31(4)：385-388
[11]R. Buchheim, J. Marketzke, R. Piatek. The Control of Aerodynamic Parameters Influencing Vehicle Dynamics[J]. SAE Technical Paper Series 850279,1985
[12]R. Buchheim, W. Dobrxynski, H. Mankau,etc. Vehicle Interior Noise Related to External Aerodynamics[[J]. International Journal of Vehicle Desig, Special Publication SP3,1983:197-209
[13]王东屏,兆文忠,杉山弘等.CFD数值仿真在高速列车设计中的应用[J].铁道学报.2009,Vol.29(5)：64-68
[14]W.H. Hucho. The Aerodynamic Drag of Cars[J]. In:Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles, Plenum,New York,1978:1-44
[15]A. George. Automobile Aerodynamic Noise [J]. SAE Technical Paper 900315, 1990.
[16]伍荣林,王振羽.风洞设计原理[M].北京：北京航空学院出版社,1985
[17]马静,贾青,杨志刚.基于数值计算的高速列车气动阻力风洞试验缩比模型选取方法.计算机辅助工程.2007,Vol(3)
[18]S.R. Ahmed. A Survey of Automobile Aero-Acoustic Activities in Germany [J]. SAE paper 950623,1995.
[19]B. Barsikow. Experiences with Various Configurations of Microphone Arrays Used to Locate Sound Sources on Railway Trains Operated by the DBAG [J]. Journal of Sound and Vibration,1996, Vol.193(1):283-293.
[20]T. Kitagawa, K. Nagakura. Localization of Aerodynamic Noise Sources of Shinkansen Trains [J]. Journal of Sound and Vibration,2006,293(3):547-556.
[21]张曙光.350km.h-1高速列车噪声机理.声源识别及控制[J].中国铁道科学,2009,Vol.30(1)：86-90.
[22]毛晓群,罗禹贡,杨殿阁等.使用阵列技术识别高速行驶轿车的辐射声源[J].汽车技术.2003,No.09：6-9
[23]许峰,连小珉,杨殿阁.用于汽车运动噪声源识别的随机阵列生成法[J].汽车工程.2006,Vo1.28(3)：281-285
[24]阎超,都彦喆.CFD技术及其在大飞机研制中的应用[J].航空制造技术.2008,No.14：42-44
[25]J.T. Batina, A Gridless Euler/Navier-Stokes Solution Algorith for Complex Aircraft Applications[J], AIAA 93-0333,1993.
[26]居鸿宾,沈孟育.计算气动声学的问题、方法与进展[J].力学与实践.1995,No.05：1-9
[27]R.W. Stoker, M. J. Smith. An Evaluation of Finite Volume Direct Simulation and Perturbation Methods in CAA Applications[J]. AIAA-93-0151.1993.
[28]C.K.W. Tam. Computational Aeroacoustics:Issues and Methods [J]. J. AIAA, 1995. Vol.33(10):1788-1796
[29]J.C. Hardin, M.Y. Hussaini. Computational Aeroacoustics for Low Mach Number Flows [J]. Computational Aeroacoustics. Springer:New York,1993: 50-68.
[30]王泽晖,罗柏华,刘宇陆.关于气动声学数值计算的方法与进展[J].力学季刊.2003,Vol.24(2)：219-225
[31]铁道部统计中心.中华人民共和国铁道部2010年铁道统计公报[J].中国铁路.2011,No.06
[32]交通运输部综合规划司.2010年公路水路交通运输行业发展统计公报[J].交通财会.2011.No.04
[33]王建军.高速公路管理设施系统设计理论与方法[M].北京：人民交通出版社,2008
[34]A. Riedler. The Scientific Determination of the Merits of Automobiles:Reports I-X of the Laboratory for Motor-Cars at the Royal Technical University. Berlin Charlottenburg Verl,1911.
[35]傅立敏.汽车设计与空气动力学[M].北京：机械工业出版社,2010
[36]W. Kamm, C. Schmid. Automobile Testing [M]. Berlin:Springer,1938.
[37]A. J. Scibor-Rylski, D. M. Sykes. Road Vehicle Aerodynamics [M]. London: Pentech Press,1984
[38]W. H. Hucho. Aerodynamics of Road Vehicle [M]. United Kingdom: Butterworth-Heinemann Co. Ltd,1987
[39]M. J. Lighthill. On Sound Generated Aerodynamically. Ⅰ. General Theory [J]. Processdings of the Royal Society of London.1952, Vol.211(1107):564-587
[40]M. J. Lighthill. On Sound Generated Aerodynamically. Ⅱ. Turbulence as a Source of Sound [J]. Processdings of the Royal Society of London.1954, Vol.222(1148):1-32
[41]孙晓峰,周盛.气动声学[M].北京：国防工业出版社,1994.
[42]L.D. Landau, E.M. Lifshitz. Fluid Mechanics [M]. Pergamon Press, Oxford, 2nd edition,1987.
[43]N. Curle. The Influence of Solid Boundaries upon Aerodynamic Sound. Proceedings of the Royal Society of London [J]. Series A, Mathematical and Physical Sciences,1955, Vol.231(1187):505-514.
[44]J. E. Ffowcs-Williams, D. L. Hawkings. Sound Generation by Turbulence and Surfaces in Arbitrary Motion. Philosophical Transactions for the Royal Society of London [J]. Series A, Mathematical and Physical Sciences.1969, Vol.264(1151):321-342
[45]F. Farassat, J. H. Casper. Towards an airfarme noise prediction methodology: Survey of Current Approaches[R]. The 44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada, United States.2006, AIAA-2006-0210
[46]J. Casper, F. Farassat. A New Time Domain Formulation for Broadband Noise Predictions[J]. International Journal of Aeroacoustics.2002, Vol.1(3):207-240.
[47]F. Farassat. Theory of Noise Generation from Moving Bodyies with an Application to Helicopter Rotors [J]. NASATR R-451,1975
[48]M. Goldstein. Unified Approach to Aerodynamic Sound Generation in the Presence of Sound Boundaries [J]. Journal of the Acoustical Society of America.1974, Vol.56(2):497-509
[49]P. E. Doak. Acoustic Radiation from a Turbulent Fluid Containing Foreign Bodies [J]. Proc. Roy. Lodon Soc.1960, Vol.254(1276):129-145
[50]A. Powell. Aerodynamic Noise and the Plane Boundary [J]. The Journal of the Acoustical Society of America.1960, Vol.32(8):982-990
[51]J.E. Ffowcs-Williams, L.H. Hall. Aerodynamic Sound Generation by Turbulent Flow in the Vicinity of Scatering Half Plane [J]. Journal of Fluid Mechanics. 1970, Vol.40(4):657-670
[52]A. Powell. Theory of Vortex Sound [J]. The Journal of Acoustical Society America,1964, Vol.36(1):177-195.
[53]M.V. Lowson. The Sound Field for Singularities in Motion [J]. Proceedings of the Royal Society in London, Series A.1965, Vol.286(1407):559-572
[54]J.C. Hardin, D.S. Pope. A new technique for aerodynamic noise calculation [J]. DGLR/AIAA Aeroacoustics Conference,14th, Aachen, Germany, AIAA.1992, Vol.1 (A93-1912605-71):448-456.
[55]J.A. Ekaterinaris. New Formulation of Hardin-Pope Equations for Aeroacoustics [J]. AIAA Journal.1999, Vol.37(9):1033-1039
[56]A. Uzun, A.S. Lyrintzis, G.A. Blaisdell. Coupling of integral acoustics methods with LES for jet noise prediction [J]. The 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA2004-0517, Reno, NV, U.S.A.2004
[57]C.Peric, S. Watkins, E. Lindqvist. Wind turbulence effects on aerodynamic noise with relevance to road vehicle interior noise[J]. Journal of Wind Engineering and Industrial Aerodynamics.1997, Vol.69-71:423-435
[58]J. Block, S. Dalley, Andrew. Aero-acoustic tests and analysis to predict internal and external railway vehicle aerodynamically-generated noise [J]. Proceedings of the Tenth International Congress on Sound and Vibration.2003. p 1697-1704
[59]H.Posson, F. Perot, Far-field evaluation of the noise radiated by a side mirror using les and acoustic analogy [J]. Collection of Technical Papers-12th AIAA/CEAS Aeroacoustics Conference, v 6, p 4093-4095,2006
[60]T. Nouzawa, Y. Li, N. Kasaki, etc. Structure of aerodynamic noise sources generated in production automobile. Nihon Kikai Gakkai Ronbunshu[J], B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B,2009, Vol.75(758):1989-1995
[61]李世岩,宫镇,蔡超.车辆内部声场的贡献度分析[J].农业机械学报.1994,Vol.25(4)：76-80
[62]姚志远,彭如海,宫镇.车辆内部气流噪声计算方法[J].力学与实践.1998,Vol.20(2)：23-26
[63]罗柏华,刘宇陆.湍流边界层流场与噪声实验研究[J].实验力学.2001,Vol.16(4)：378-386
[64]刘红光,陆森林.高速车辆气流噪声计算方法[J].交通运输工程学报.2002,Vol.6(2)：41-44
[65]夏恒,宫镇,陆森林等.关于高速车辆内部气流噪声计算方法的研究[J].汽车工程.2003,Vol.25(1)：78-81
[66]陆森林,宫镇,曾发林.高速车辆表面脉动压力特性的研究[J].轻型汽车技术.2003,Vol.161(1)：18-21
[67]胡维撷.地铁和隧道通风亭设计中气流噪声值的确定[J].地下工程与隧道.200,No.4：46-47
[68]杨博,傅立敏.稳态数值模拟在轿车外气动噪声源预测中的应用[J].吉林大学学报(工学版),2007,Vol.37(5)：1005-1008.
[69]肖友刚.康志成.高速列车车头曲面气动噪声的数值预测[J].中南大学学报(自然科学版),2008,Vol.39(6)：1267-1272
[70]肖友刚,田红旗,张洪.高速列车司机室内气动噪声预测[J].交通运输工程学报.2008,Vol.8(3)10：14
[71]汪怡平,谷正气,杨雪等.微型客车后视镜气动噪声仿真分析与控制[J].航空动力学报.2009,Vol.24(7)：1577-1583
[72]杨帆,郑百林,贺鹏飞.高速列车集电部气动噪声数值模拟[J].计算机辅助工程.2010,Vol.19(1)：44-47.
[73]孙振旭,王一伟,安亦然.高速列车气动噪声的计算研究.水动力学研究与进展：A辑.2010,Vol.25(5)：660-668
[74]郑拯宇,李人宪.高速列车表面气动噪声偶极子声源分布数值分析.西南交通大学学报(自然科学版).2011,Vol.46(6)：996-1002
[75]马大猷.现代声学理论基础[M].北京：科学出版社,2004
[76]P.M.莫尔斯著,南京大学《振动与声》翻译组译.振动与声[M].北京：科学出版社,1974
[77]汪怡平,谷正气,李伟平等.汽车气动噪声数值计算分析.汽车工程.2009,Vol.31(4)：385-388
[78]李人宪.有限体积法基础[M].北京：国防工业出版社.2005
[79]张涵信,沈孟育.计算流体力学[M].北京：国防工业出版社.2003
[80]李福田,倪浩清.工程湍流模式的研究开发及其应用.水利学报.2001,No.05：22-31
[81]H.K. Versteeg, W. Malalasekra. An Introduction to Computational Fluid Dynamics [M]. England:Prentice Hall Press,1996
[82]是勋刚.湍流[M].天津：天津大学出版社,1994
[83]陈义良.湍流计算模型[M].合肥：中国科学技术大学出版社.1991.
[84]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京：清华大学出版社.2005
[85]周培源.关于准相似性条件和湍流理论[J].力学学报.1986,No.01
[86]陈十一,周培源.准相似性条件在湍流模式理论中的应用[J].水动力学研究与进展A辑.1987,Vol.2(2)：1-14
[87]万曦.湍流大涡数值模拟的现状与展望[J].航空科学技术.2011,No.02：55-56
[88]W. C. Reynolds. Fundamentals of turbulence for turbulence modeling and simulation[J]. Lecture Notes for Von Karman Institute, Agard Report No.755, 1987.
[89]B. E. Launder and D. B. Spalding. Lectures in Mathematical Models of Turbulence[M]. Academic Press, London, England,1972.
[90]C.A. Wagner, T. huttl, P. Sagaut. Large-Eddy Simulation for Acoustics [M]. Cambridge, England,2006
[91]王福军.计算流体动力学分析-CFD软件原理与应用[M].北京：清华大学出版社.2006.
[92]张兆顺,崔桂利等.湍流大涡数值模拟的理论和应用[M].北京：清华大学出版社.2008.
[93]E. Gamier, P. Sagaut, N. Adams. Large Eddy Simulation for Compressible Flows[M]. Springer.2009
[94]王汉青.王志勇.寇广孝.大涡模拟理论进展及其在工程中的应用[J].流体机械.2004,Vo1.32(7)：23-27
[95]A.Leonard. Energy Cascade in Large-Eddy Simulations of Turbulent Fuid Fows. Advances in Geophysics A.1974, Vol.18:237-248.
[96]J. Smagorinsky. General Circulation Experiments with the Primitive Equations [J]. The basic experiment, Monthly Weather Review.1963.Vol.91(3):99-165.
[97]D.K. Lilly. A Proposed Modification of the Germano Subgrid-scale Closure Method [J]. Physics of Fluids A.1992,Vol.4(3):633-635.
[98]李兴毅,陈健,赵佩章等.伽利略变换的物理意义[J].河南师范大学学报(自然科学版).2002,Vo1.30(1)：39-42
[99]张义民.机械振动[M].北京：华大学出版社.2007
[100]P. M.A. Dirac量子力学原理[M].北京：科学出版社.2008
[101]G. Green. An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. Nottingham[R]. Printed for the Author by T. Wheelhouse, Nottingham.1828.
[102]L.施瓦兹(Laurent Schwartz)广义函数论[M].北京：高等教育出版社.2010
[103]傅立敏.汽车空气动力学[M].北京：机械工业出版社.1998
[104]谷正气.汽车空气动力学[M].北京：人民交通出版社.2005
[105]I. Proudman. The Generation of Noise by Isotropic Turbulence. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences[J].1952, Vol.214(1116):119-132
[106]S. Sarkar. M. Y. Hussaini. Computation of the Sound Generated by Isotropic Turbulence[R]. NASA Contract Report 93-74, NASA Langley Research Center, Hampton, VA 24681,1993
[107]G. M. Lilley. The Radiated Noise From Isotropic Turbulence Revisited[R]. NASA Contract Report 93-75, NASA Langley Research Center,Hampton,VA, 1993.
[108]Fluent.Inc, FLUENT 6.3 Documentation [CP/DK].[2006-10-12].
[109]祝家麟,袁政强.边界元分析[M].北京：科学出版社.2009
[110]姚振汉,王海涛.边界元法[M].北京：高等教育出版社.2010
[111]杜功焕,朱哲民,龚秀芬.声学基础[M].南京：南京大学出版社.2001
[112]杨训仁,陈宇著.大气声学[M].北京：科学出版社.2007
[113]程建春.数学物理方程及其近似方法[M].北京：科学出版社.2004
[114]黄其柏,赵志高Helmholtz边界积分方程的多频计算[J].声学学报(中文版).2005,Vol.30(3)：255-263
[115]李瑞遐Helmholtz方程外边值问题的自然边界元法[J].高校应用数学学报：A辑.1997,Vol.12(3)：369-374
[116]李增刚,詹福良Virtual.Lab Acoustics声学仿真计算高级应用实例[M].北京：国防工业出版社.2010
[117]R.P. Banaugh, W. Goldsmith. Diffraction of Steady Acoustic Waves by Surface of Arbitrary Ahape [J]. Journal of the Acoustical Society of America. 1963, Vol.35(10):1590-1601
[118]D. Habault. Diffraction of a Spherical Wave by Different Models of Ground: Approximate Formulas. Journal of Sound and Vibration.1980, Vol.68(3): 413-425
[119]Y. Kawai, T. Terai. The Application of Integral Equation Methods to the Calculation of Sound Attenuation by Barriers. Applied Acoustics. 1990, Vol.31 (1):101-117.
[120]朱克勤,许春晓.粘性流体力学[M].高等教育出版社,2009
[121]潘小卫,谷正气,何忆斌.F1赛车气动特性的CFD仿真和试验研究[J].汽车工程.2009,Vol.31(3)：274-277
[122]M. Mafi. Investigation of Turbulence Created by Formula OneTM Cars with the Aid of Numerical Fluid Dynamics and Optimization of Overtaking Potential. ANSYS Conference & 25th CADFEM Users'Meeting. Congress Center Dresden, Germany,2007:1-10
[123]S. Perzon, L. Davidson. On Transient Modeling of the Flow around Vehicles Using the Reynolds Equations [J]. ACFD 2000 Beijing, China.2000:720-727
[124]梁建永,梁军.轿车外流场CFD分析中常用k-ε湍流模型的对比[J].汽车工程.2008,Vol.30(1)：846-852
[125]B. Kader. Temperature and Concentration Profiles in Fully Turbulent Boundary Layers [J]. Int. J. Heat Mass Transfer.1981, Vol.24(9):1541-1544
[126]尹霄丽,范德维格特.数字信号处理基础.北京：电子工业出版社.2009
[127]C.E. Shannon. Communication in the Presence of Noise. Proceedings of the Institute of Radio Engineers.1949, Vol.37(1):10-21
[128]李增刚SYSNOISE Rev5.6详解[M].北京：国防工业出版社.2005
[129]A. Atalla. Review of numerical solutions for low frequency structural-acoustics problem. Applied Acoustics[J].1994, No.43:271-294
[130]LMS Corporation. SYSNOISE Revision 5.6 Documentation [CP/CD]. [S.1]: LMS Corporation,2003.
[131]S. L. Moyne, J. L. Tebec. Ribs effects in acoustic radiation of a gearbox-their modeling in a boundary element method. Applied Acoustics.2002, No.63:223-233
[132]梁兴雨,舒歌群.基于SYSNOISE的柴油机外声场模拟研究[J].内燃机工程.2008,Vol.29(2)：37-41
[133]梁延德,凌宏,张媛.超声系统辐射声场的研究[J].机械设计与制造.2010,No.11：194-196
[2]韩增盛,马松花.城市轨道交通车辆噪声产生的原因与降低措施[J].铁道运营技术.2008,Vol.14(2)：1-2
[3]司春棣,陈恩利,杨绍普等.基于声阵列技术的汽车噪声源识别试验研究[J].振动与冲击.2009,Vol.28(6)：171-174
[4]郑拯宇,李人宪,高速流线型车辆稳态下速度风噪声源数值分析[J].重庆工学院学报(自然科学).2009,Vol.26(6)：1-4
[5]GB 1495-2002,汽车加速行驶车外噪声限值及测量方法.北京：中国标准出版社,2002.
[6]GB 12525-9011,铁路边界噪声值及其测量办法.北京：中国标准出版社,2008.
[7]S.Haruna, M.Hashiguchi, I.Kamimoto. Numerical Study of Aerodynamics Noise Radiated from a Three-Dimensional Wing[J]. SAE paper 920341,1992
[8]S.Haruna, I.Kamimoto, S.Okamoto. Estimation Method for Automobile Aerodynamic Noise[J]. SAE paper 920205,1992
[9]W.F. King, D. Beckert. Aerodynamic Noise Generated by High-Speed Tans[J]. Noise Control Engineering,1979
[10]汪怡平,谷正气等.汽车气动噪声数值计算分析[J].汽车工程.2009,Vol.31(4)：385-388
[11]R. Buchheim, J. Marketzke, R. Piatek. The Control of Aerodynamic Parameters Influencing Vehicle Dynamics[J]. SAE Technical Paper Series 850279,1985
[12]R. Buchheim, W. Dobrxynski, H. Mankau,etc. Vehicle Interior Noise Related to External Aerodynamics[[J]. International Journal of Vehicle Desig, Special Publication SP3,1983:197-209
[13]王东屏,兆文忠,杉山弘等.CFD数值仿真在高速列车设计中的应用[J].铁道学报.2009,Vol.29(5)：64-68
[14]W.H. Hucho. The Aerodynamic Drag of Cars[J]. In:Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles, Plenum,New York,1978:1-44
[15]A. George. Automobile Aerodynamic Noise [J]. SAE Technical Paper 900315, 1990.
[16]伍荣林,王振羽.风洞设计原理[M].北京：北京航空学院出版社,1985
[17]马静,贾青,杨志刚.基于数值计算的高速列车气动阻力风洞试验缩比模型选取方法.计算机辅助工程.2007,Vol(3)
[18]S.R. Ahmed. A Survey of Automobile Aero-Acoustic Activities in Germany [J]. SAE paper 950623,1995.
[19]B. Barsikow. Experiences with Various Configurations of Microphone Arrays Used to Locate Sound Sources on Railway Trains Operated by the DBAG [J]. Journal of Sound and Vibration,1996, Vol.193(1):283-293.
[20]T. Kitagawa, K. Nagakura. Localization of Aerodynamic Noise Sources of Shinkansen Trains [J]. Journal of Sound and Vibration,2006,293(3):547-556.
[21]张曙光.350km.h-1高速列车噪声机理.声源识别及控制[J].中国铁道科学,2009,Vol.30(1)：86-90.
[22]毛晓群,罗禹贡,杨殿阁等.使用阵列技术识别高速行驶轿车的辐射声源[J].汽车技术.2003,No.09：6-9
[23]许峰,连小珉,杨殿阁.用于汽车运动噪声源识别的随机阵列生成法[J].汽车工程.2006,Vo1.28(3)：281-285
[24]阎超,都彦喆.CFD技术及其在大飞机研制中的应用[J].航空制造技术.2008,No.14：42-44
[25]J.T. Batina, A Gridless Euler/Navier-Stokes Solution Algorith for Complex Aircraft Applications[J], AIAA 93-0333,1993.
[26]居鸿宾,沈孟育.计算气动声学的问题、方法与进展[J].力学与实践.1995,No.05：1-9
[27]R.W. Stoker, M. J. Smith. An Evaluation of Finite Volume Direct Simulation and Perturbation Methods in CAA Applications[J]. AIAA-93-0151.1993.
[28]C.K.W. Tam. Computational Aeroacoustics:Issues and Methods [J]. J. AIAA, 1995. Vol.33(10):1788-1796
[29]J.C. Hardin, M.Y. Hussaini. Computational Aeroacoustics for Low Mach Number Flows [J]. Computational Aeroacoustics. Springer:New York,1993: 50-68.
[30]王泽晖,罗柏华,刘宇陆.关于气动声学数值计算的方法与进展[J].力学季刊.2003,Vol.24(2)：219-225
[31]铁道部统计中心.中华人民共和国铁道部2010年铁道统计公报[J].中国铁路.2011,No.06
[32]交通运输部综合规划司.2010年公路水路交通运输行业发展统计公报[J].交通财会.2011.No.04
[33]王建军.高速公路管理设施系统设计理论与方法[M].北京：人民交通出版社,2008
[34]A. Riedler. The Scientific Determination of the Merits of Automobiles:Reports I-X of the Laboratory for Motor-Cars at the Royal Technical University. Berlin Charlottenburg Verl,1911.
[35]傅立敏.汽车设计与空气动力学[M].北京：机械工业出版社,2010
[36]W. Kamm, C. Schmid. Automobile Testing [M]. Berlin:Springer,1938.
[37]A. J. Scibor-Rylski, D. M. Sykes. Road Vehicle Aerodynamics [M]. London: Pentech Press,1984
[38]W. H. Hucho. Aerodynamics of Road Vehicle [M]. United Kingdom: Butterworth-Heinemann Co. Ltd,1987
[39]M. J. Lighthill. On Sound Generated Aerodynamically. Ⅰ. General Theory [J]. Processdings of the Royal Society of London.1952, Vol.211(1107):564-587
[40]M. J. Lighthill. On Sound Generated Aerodynamically. Ⅱ. Turbulence as a Source of Sound [J]. Processdings of the Royal Society of London.1954, Vol.222(1148):1-32
[41]孙晓峰,周盛.气动声学[M].北京：国防工业出版社,1994.
[42]L.D. Landau, E.M. Lifshitz. Fluid Mechanics [M]. Pergamon Press, Oxford, 2nd edition,1987.
[43]N. Curle. The Influence of Solid Boundaries upon Aerodynamic Sound. Proceedings of the Royal Society of London [J]. Series A, Mathematical and Physical Sciences,1955, Vol.231(1187):505-514.
[44]J. E. Ffowcs-Williams, D. L. Hawkings. Sound Generation by Turbulence and Surfaces in Arbitrary Motion. Philosophical Transactions for the Royal Society of London [J]. Series A, Mathematical and Physical Sciences.1969, Vol.264(1151):321-342
[45]F. Farassat, J. H. Casper. Towards an airfarme noise prediction methodology: Survey of Current Approaches[R]. The 44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada, United States.2006, AIAA-2006-0210
[46]J. Casper, F. Farassat. A New Time Domain Formulation for Broadband Noise Predictions[J]. International Journal of Aeroacoustics.2002, Vol.1(3):207-240.
[47]F. Farassat. Theory of Noise Generation from Moving Bodyies with an Application to Helicopter Rotors [J]. NASATR R-451,1975
[48]M. Goldstein. Unified Approach to Aerodynamic Sound Generation in the Presence of Sound Boundaries [J]. Journal of the Acoustical Society of America.1974, Vol.56(2):497-509
[49]P. E. Doak. Acoustic Radiation from a Turbulent Fluid Containing Foreign Bodies [J]. Proc. Roy. Lodon Soc.1960, Vol.254(1276):129-145
[50]A. Powell. Aerodynamic Noise and the Plane Boundary [J]. The Journal of the Acoustical Society of America.1960, Vol.32(8):982-990
[51]J.E. Ffowcs-Williams, L.H. Hall. Aerodynamic Sound Generation by Turbulent Flow in the Vicinity of Scatering Half Plane [J]. Journal of Fluid Mechanics. 1970, Vol.40(4):657-670
[52]A. Powell. Theory of Vortex Sound [J]. The Journal of Acoustical Society America,1964, Vol.36(1):177-195.
[53]M.V. Lowson. The Sound Field for Singularities in Motion [J]. Proceedings of the Royal Society in London, Series A.1965, Vol.286(1407):559-572
[54]J.C. Hardin, D.S. Pope. A new technique for aerodynamic noise calculation [J]. DGLR/AIAA Aeroacoustics Conference,14th, Aachen, Germany, AIAA.1992, Vol.1 (A93-1912605-71):448-456.
[55]J.A. Ekaterinaris. New Formulation of Hardin-Pope Equations for Aeroacoustics [J]. AIAA Journal.1999, Vol.37(9):1033-1039
[56]A. Uzun, A.S. Lyrintzis, G.A. Blaisdell. Coupling of integral acoustics methods with LES for jet noise prediction [J]. The 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA2004-0517, Reno, NV, U.S.A.2004
[57]C.Peric, S. Watkins, E. Lindqvist. Wind turbulence effects on aerodynamic noise with relevance to road vehicle interior noise[J]. Journal of Wind Engineering and Industrial Aerodynamics.1997, Vol.69-71:423-435
[58]J. Block, S. Dalley, Andrew. Aero-acoustic tests and analysis to predict internal and external railway vehicle aerodynamically-generated noise [J]. Proceedings of the Tenth International Congress on Sound and Vibration.2003. p 1697-1704
[59]H.Posson, F. Perot, Far-field evaluation of the noise radiated by a side mirror using les and acoustic analogy [J]. Collection of Technical Papers-12th AIAA/CEAS Aeroacoustics Conference, v 6, p 4093-4095,2006
[60]T. Nouzawa, Y. Li, N. Kasaki, etc. Structure of aerodynamic noise sources generated in production automobile. Nihon Kikai Gakkai Ronbunshu[J], B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B,2009, Vol.75(758):1989-1995
[61]李世岩,宫镇,蔡超.车辆内部声场的贡献度分析[J].农业机械学报.1994,Vol.25(4)：76-80
[62]姚志远,彭如海,宫镇.车辆内部气流噪声计算方法[J].力学与实践.1998,Vol.20(2)：23-26
[63]罗柏华,刘宇陆.湍流边界层流场与噪声实验研究[J].实验力学.2001,Vol.16(4)：378-386
[64]刘红光,陆森林.高速车辆气流噪声计算方法[J].交通运输工程学报.2002,Vol.6(2)：41-44
[65]夏恒,宫镇,陆森林等.关于高速车辆内部气流噪声计算方法的研究[J].汽车工程.2003,Vol.25(1)：78-81
[66]陆森林,宫镇,曾发林.高速车辆表面脉动压力特性的研究[J].轻型汽车技术.2003,Vol.161(1)：18-21
[67]胡维撷.地铁和隧道通风亭设计中气流噪声值的确定[J].地下工程与隧道.200,No.4：46-47
[68]杨博,傅立敏.稳态数值模拟在轿车外气动噪声源预测中的应用[J].吉林大学学报(工学版),2007,Vol.37(5)：1005-1008.
[69]肖友刚.康志成.高速列车车头曲面气动噪声的数值预测[J].中南大学学报(自然科学版),2008,Vol.39(6)：1267-1272
[70]肖友刚,田红旗,张洪.高速列车司机室内气动噪声预测[J].交通运输工程学报.2008,Vol.8(3)10：14
[71]汪怡平,谷正气,杨雪等.微型客车后视镜气动噪声仿真分析与控制[J].航空动力学报.2009,Vol.24(7)：1577-1583
[72]杨帆,郑百林,贺鹏飞.高速列车集电部气动噪声数值模拟[J].计算机辅助工程.2010,Vol.19(1)：44-47.
[73]孙振旭,王一伟,安亦然.高速列车气动噪声的计算研究.水动力学研究与进展：A辑.2010,Vol.25(5)：660-668
[74]郑拯宇,李人宪.高速列车表面气动噪声偶极子声源分布数值分析.西南交通大学学报(自然科学版).2011,Vol.46(6)：996-1002
[75]马大猷.现代声学理论基础[M].北京：科学出版社,2004
[76]P.M.莫尔斯著,南京大学《振动与声》翻译组译.振动与声[M].北京：科学出版社,1974
[77]汪怡平,谷正气,李伟平等.汽车气动噪声数值计算分析.汽车工程.2009,Vol.31(4)：385-388
[78]李人宪.有限体积法基础[M].北京：国防工业出版社.2005
[79]张涵信,沈孟育.计算流体力学[M].北京：国防工业出版社.2003
[80]李福田,倪浩清.工程湍流模式的研究开发及其应用.水利学报.2001,No.05：22-31
[81]H.K. Versteeg, W. Malalasekra. An Introduction to Computational Fluid Dynamics [M]. England:Prentice Hall Press,1996
[82]是勋刚.湍流[M].天津：天津大学出版社,1994
[83]陈义良.湍流计算模型[M].合肥：中国科学技术大学出版社.1991.
[84]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京：清华大学出版社.2005
[85]周培源.关于准相似性条件和湍流理论[J].力学学报.1986,No.01
[86]陈十一,周培源.准相似性条件在湍流模式理论中的应用[J].水动力学研究与进展A辑.1987,Vol.2(2)：1-14
[87]万曦.湍流大涡数值模拟的现状与展望[J].航空科学技术.2011,No.02：55-56
[88]W. C. Reynolds. Fundamentals of turbulence for turbulence modeling and simulation[J]. Lecture Notes for Von Karman Institute, Agard Report No.755, 1987.
[89]B. E. Launder and D. B. Spalding. Lectures in Mathematical Models of Turbulence[M]. Academic Press, London, England,1972.
[90]C.A. Wagner, T. huttl, P. Sagaut. Large-Eddy Simulation for Acoustics [M]. Cambridge, England,2006
[91]王福军.计算流体动力学分析-CFD软件原理与应用[M].北京：清华大学出版社.2006.
[92]张兆顺,崔桂利等.湍流大涡数值模拟的理论和应用[M].北京：清华大学出版社.2008.
[93]E. Gamier, P. Sagaut, N. Adams. Large Eddy Simulation for Compressible Flows[M]. Springer.2009
[94]王汉青.王志勇.寇广孝.大涡模拟理论进展及其在工程中的应用[J].流体机械.2004,Vo1.32(7)：23-27
[95]A.Leonard. Energy Cascade in Large-Eddy Simulations of Turbulent Fuid Fows. Advances in Geophysics A.1974, Vol.18:237-248.
[96]J. Smagorinsky. General Circulation Experiments with the Primitive Equations [J]. The basic experiment, Monthly Weather Review.1963.Vol.91(3):99-165.
[97]D.K. Lilly. A Proposed Modification of the Germano Subgrid-scale Closure Method [J]. Physics of Fluids A.1992,Vol.4(3):633-635.
[98]李兴毅,陈健,赵佩章等.伽利略变换的物理意义[J].河南师范大学学报(自然科学版).2002,Vo1.30(1)：39-42
[99]张义民.机械振动[M].北京：华大学出版社.2007
[100]P. M.A. Dirac量子力学原理[M].北京：科学出版社.2008
[101]G. Green. An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. Nottingham[R]. Printed for the Author by T. Wheelhouse, Nottingham.1828.
[102]L.施瓦兹(Laurent Schwartz)广义函数论[M].北京：高等教育出版社.2010
[103]傅立敏.汽车空气动力学[M].北京：机械工业出版社.1998
[104]谷正气.汽车空气动力学[M].北京：人民交通出版社.2005
[105]I. Proudman. The Generation of Noise by Isotropic Turbulence. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences[J].1952, Vol.214(1116):119-132
[106]S. Sarkar. M. Y. Hussaini. Computation of the Sound Generated by Isotropic Turbulence[R]. NASA Contract Report 93-74, NASA Langley Research Center, Hampton, VA 24681,1993
[107]G. M. Lilley. The Radiated Noise From Isotropic Turbulence Revisited[R]. NASA Contract Report 93-75, NASA Langley Research Center,Hampton,VA, 1993.
[108]Fluent.Inc, FLUENT 6.3 Documentation [CP/DK].[2006-10-12].
[109]祝家麟,袁政强.边界元分析[M].北京：科学出版社.2009
[110]姚振汉,王海涛.边界元法[M].北京：高等教育出版社.2010
[111]杜功焕,朱哲民,龚秀芬.声学基础[M].南京：南京大学出版社.2001
[112]杨训仁,陈宇著.大气声学[M].北京：科学出版社.2007
[113]程建春.数学物理方程及其近似方法[M].北京：科学出版社.2004
[114]黄其柏,赵志高Helmholtz边界积分方程的多频计算[J].声学学报(中文版).2005,Vol.30(3)：255-263
[115]李瑞遐Helmholtz方程外边值问题的自然边界元法[J].高校应用数学学报：A辑.1997,Vol.12(3)：369-374
[116]李增刚,詹福良Virtual.Lab Acoustics声学仿真计算高级应用实例[M].北京：国防工业出版社.2010
[117]R.P. Banaugh, W. Goldsmith. Diffraction of Steady Acoustic Waves by Surface of Arbitrary Ahape [J]. Journal of the Acoustical Society of America. 1963, Vol.35(10):1590-1601
[118]D. Habault. Diffraction of a Spherical Wave by Different Models of Ground: Approximate Formulas. Journal of Sound and Vibration.1980, Vol.68(3): 413-425
[119]Y. Kawai, T. Terai. The Application of Integral Equation Methods to the Calculation of Sound Attenuation by Barriers. Applied Acoustics. 1990, Vol.31 (1):101-117.
[120]朱克勤,许春晓.粘性流体力学[M].高等教育出版社,2009
[121]潘小卫,谷正气,何忆斌.F1赛车气动特性的CFD仿真和试验研究[J].汽车工程.2009,Vol.31(3)：274-277
[122]M. Mafi. Investigation of Turbulence Created by Formula OneTM Cars with the Aid of Numerical Fluid Dynamics and Optimization of Overtaking Potential. ANSYS Conference & 25th CADFEM Users'Meeting. Congress Center Dresden, Germany,2007:1-10
[123]S. Perzon, L. Davidson. On Transient Modeling of the Flow around Vehicles Using the Reynolds Equations [J]. ACFD 2000 Beijing, China.2000:720-727
[124]梁建永,梁军.轿车外流场CFD分析中常用k-ε湍流模型的对比[J].汽车工程.2008,Vol.30(1)：846-852
[125]B. Kader. Temperature and Concentration Profiles in Fully Turbulent Boundary Layers [J]. Int. J. Heat Mass Transfer.1981, Vol.24(9):1541-1544
[126]尹霄丽,范德维格特.数字信号处理基础.北京：电子工业出版社.2009
[127]C.E. Shannon. Communication in the Presence of Noise. Proceedings of the Institute of Radio Engineers.1949, Vol.37(1):10-21
[128]李增刚SYSNOISE Rev5.6详解[M].北京：国防工业出版社.2005
[129]A. Atalla. Review of numerical solutions for low frequency structural-acoustics problem. Applied Acoustics[J].1994, No.43:271-294
[130]LMS Corporation. SYSNOISE Revision 5.6 Documentation [CP/CD]. [S.1]: LMS Corporation,2003.
[131]S. L. Moyne, J. L. Tebec. Ribs effects in acoustic radiation of a gearbox-their modeling in a boundary element method. Applied Acoustics.2002, No.63:223-233
[132]梁兴雨,舒歌群.基于SYSNOISE的柴油机外声场模拟研究[J].内燃机工程.2008,Vol.29(2)：37-41
[133]梁延德,凌宏,张媛.超声系统辐射声场的研究[J].机械设计与制造.2010,No.11：194-196