交通荷载作用下桥梁振动与噪声问题研究
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摘要
随着交通运输的发展,交通荷载引起的桥梁结构振动问题日益突出,尤其是复杂异形桥梁的车桥耦合振动、交通荷载作用下斜拉桥及斜拉索的振动问题以及由车桥振动衍生的低频噪声问题等,这些问题为桥梁工程的相关理论研究提出了新的挑战。传统方法和理论模型已无法满足复杂结构、新结构、新问题提出的新要求,因此有必要发展新的理论模型和计算方法。
本文针对复杂异形钢管混凝土拱桥,建立考虑吊杆局部振动影响的空间索-拱-梁组合有限元模型。针对吊杆采用空间铰接杆模型,并引入自由度凝聚概念,以吊杆基本振型代替索单元体系的所有自由度,从而克服传统以索单元直接计算吊杆振动所造成的计算效率低的缺点。以宁波长丰大桥的设计方案为对象,应用新型桥梁模型结合多质点体系车辆模型的车桥耦合振动理论,研究路面粗糙度、行车速度、结构阻尼对车辆轮压荷载、拱肋和主梁的挠度及拉索张力冲击系数的影响。
针对中等跨径斜拉桥的交通振动问题,建立考虑拉索侧向振动的有限元方法,以杭州湾跨海大桥北航道桥为例,分析该类斜拉桥的交通振动特性和动力冲击效应。针对超大跨径斜拉桥的拉索振动问题,建立基于车桥耦合振动理论的柔性拉索在支点激励下非线性振动理论,以跨径1400 m的斜拉桥设计方案为对象,分析不同行车条件下钢和CFRP拉索的非线性振动响应,探讨CFRP拉索在斜拉桥中的应用前景。
针对车桥耦合振动辐射低频噪声问题,本文开展了细致深入的研究。首先采用基于点声源的解析解法对简支钢板梁桥振动辐射低频噪声进行数值模拟,这里建立考虑剪切板影响的格子梁模型并采用有限单元法(FEM)计算得到车桥耦合振动响应。其次,针对桥梁辐射声场推导三维边界积分方程,并采用边界元法(BEM)进行求解并自行开发BEM程序代码,从而与钢板梁桥结构动力分析的FEM构成车桥耦合振动辐射低频噪声的FEM-BEM混合求解体系。最后,采用镜像法考察地面边界对声波的反射作用,综合评估车桥耦合振动辐射低频噪声在桥梁附近空间的分布特性和声压水平。
将所提FEM-BEM混合求解体系用于简支和连续钢板梁桥车桥耦合振动辐射低频噪声的稳态和瞬态响应分析。通过与桥梁振动辐射噪声现场实测数据的对比,验证三维边界积分公式和BEM程序的正确性以及FEM-BEM混合求解方法的计算精度。给出了振动桥梁附近噪声水平的数值结果、声压的空间分布及其随时间的变化规律。详细讨论了路面粗糙度、车速度以及桥面距地高度的变化对声压水平和声场分布特性的影响。
利用所提FEM-BEM混合方法开展桥梁减振降噪研究。以连续钢板梁桥为例,提出桥梁减振降噪设计方案,并采用该方法评估各方案的可行性和降噪效果,最终提出有效的减振降噪措施。
With the rapid development in transportation of China, bridges have encountered increasing new dynamic problems due to heavy traffic load, including vehicle-bridge coupling vibration (VBCV) of bridges with complex configurations, vibration of cable-stayed bridges and stay cables due traffic load, and low-frequency noise induced by vehicle-bridge vibrations, etc. The traditional methodologies are not always applicable for these new problems, for which great endeavor should be made to establish new models and methodologies.
In this thesis, a finite element (FE) model of spatial cable-arch-beam system including the effects of local vibration of cables is developed for concrete-filled steel tube arch bridges having complex profiles. For each hanger cable, the multiple degrees of freedom (MDOF) are reduced to two end nodes by replacing all of inner nodes using the eigen-functions of the whole cable, thus avoiding heavy computational costs in the traditional FE simulations with direct use of cable elements. Based on the theory of VBCV with a vehicle model of MDOF, the newly proposed model is then applied to simulate the Changfeng Bridge in Ningbo. Intensive investigations are performed to the effects of road surface roughness, vehicle velocity, and structural damping on wheel load and impact factors of arch ribs, main girder, and cable tension.
The VBCV of cable-stayed bridges (CSB) are also studied using the proposed FE model considering the effects of local vibration of stay cables. As a case of medium-span CSB, the subpart of Hangzhou Bay Bridge over the north channel is analyzed with emphasis on the impact effects on its dynamic responses. For super long-span CSB, attentions are focused on the vibration of stay cables. The equations of motion in incremental forms are established for the nonlinear vibration of long and flexible stay cables based on the theory of VBCV. A long span CSB with span of 1400 m is investigated as an example. Both nonlinear vibrations of steel and CFRP cables are analyzed comparatively, and the potential applicability of CFRP cables in long-span CSB is evaluated.
A major part of the thesis is devoted to the low-frequency noise induced by the vibration of bridges. Firstly, numerical results based on the analytical solutions for acoustic radiation of point source are presented for a simply supported steel girder bridge. Here, the bridge deck is modeled as a beam-plate system considering merely the shear deformation of the plates fully supported by beams. Secondly, the boundary integral equations are derived for three-dimensional sound field, which is solved using the boundary element method (BEM). Thus, a combined method of FEM-BEM is developed for the problem of VBCV-induced low-frequency noise for steel girder bridges. Finally, the image method is adopted to incorporate the effects of reflection of acoustic waves by the ground on the sound field near the bridge deck.
The proposed hybrid FEM-BEM is employed to analyze to the steady-state and transient acoustic radiation by the VBCV of simply supported or continuous steel girder bridges. By comparing numerical results to the on-site tested data, the correctness of the present formulations and BEM code, as well as the effectiveness and efficiency of the proposed method, is firmly validated. Numerical results are given both for the noise level around the bridge deck and for the distribution of sound pressure in spatial and time domains. Comprehensive analyses are carried out against the effects of road surface roughness, velocity of vehicles, and distance of bridge deck away from the ground on the noise level and distributions of sound field. Finally, the hybrid FEM-BEM is applied to evaluate and verify effective strategies for noise reduction for continuous steel girder bridges.
本文针对复杂异形钢管混凝土拱桥,建立考虑吊杆局部振动影响的空间索-拱-梁组合有限元模型。针对吊杆采用空间铰接杆模型,并引入自由度凝聚概念,以吊杆基本振型代替索单元体系的所有自由度,从而克服传统以索单元直接计算吊杆振动所造成的计算效率低的缺点。以宁波长丰大桥的设计方案为对象,应用新型桥梁模型结合多质点体系车辆模型的车桥耦合振动理论,研究路面粗糙度、行车速度、结构阻尼对车辆轮压荷载、拱肋和主梁的挠度及拉索张力冲击系数的影响。
针对中等跨径斜拉桥的交通振动问题,建立考虑拉索侧向振动的有限元方法,以杭州湾跨海大桥北航道桥为例,分析该类斜拉桥的交通振动特性和动力冲击效应。针对超大跨径斜拉桥的拉索振动问题,建立基于车桥耦合振动理论的柔性拉索在支点激励下非线性振动理论,以跨径1400 m的斜拉桥设计方案为对象,分析不同行车条件下钢和CFRP拉索的非线性振动响应,探讨CFRP拉索在斜拉桥中的应用前景。
针对车桥耦合振动辐射低频噪声问题,本文开展了细致深入的研究。首先采用基于点声源的解析解法对简支钢板梁桥振动辐射低频噪声进行数值模拟,这里建立考虑剪切板影响的格子梁模型并采用有限单元法(FEM)计算得到车桥耦合振动响应。其次,针对桥梁辐射声场推导三维边界积分方程,并采用边界元法(BEM)进行求解并自行开发BEM程序代码,从而与钢板梁桥结构动力分析的FEM构成车桥耦合振动辐射低频噪声的FEM-BEM混合求解体系。最后,采用镜像法考察地面边界对声波的反射作用,综合评估车桥耦合振动辐射低频噪声在桥梁附近空间的分布特性和声压水平。
将所提FEM-BEM混合求解体系用于简支和连续钢板梁桥车桥耦合振动辐射低频噪声的稳态和瞬态响应分析。通过与桥梁振动辐射噪声现场实测数据的对比,验证三维边界积分公式和BEM程序的正确性以及FEM-BEM混合求解方法的计算精度。给出了振动桥梁附近噪声水平的数值结果、声压的空间分布及其随时间的变化规律。详细讨论了路面粗糙度、车速度以及桥面距地高度的变化对声压水平和声场分布特性的影响。
利用所提FEM-BEM混合方法开展桥梁减振降噪研究。以连续钢板梁桥为例,提出桥梁减振降噪设计方案,并采用该方法评估各方案的可行性和降噪效果,最终提出有效的减振降噪措施。
With the rapid development in transportation of China, bridges have encountered increasing new dynamic problems due to heavy traffic load, including vehicle-bridge coupling vibration (VBCV) of bridges with complex configurations, vibration of cable-stayed bridges and stay cables due traffic load, and low-frequency noise induced by vehicle-bridge vibrations, etc. The traditional methodologies are not always applicable for these new problems, for which great endeavor should be made to establish new models and methodologies.
In this thesis, a finite element (FE) model of spatial cable-arch-beam system including the effects of local vibration of cables is developed for concrete-filled steel tube arch bridges having complex profiles. For each hanger cable, the multiple degrees of freedom (MDOF) are reduced to two end nodes by replacing all of inner nodes using the eigen-functions of the whole cable, thus avoiding heavy computational costs in the traditional FE simulations with direct use of cable elements. Based on the theory of VBCV with a vehicle model of MDOF, the newly proposed model is then applied to simulate the Changfeng Bridge in Ningbo. Intensive investigations are performed to the effects of road surface roughness, vehicle velocity, and structural damping on wheel load and impact factors of arch ribs, main girder, and cable tension.
The VBCV of cable-stayed bridges (CSB) are also studied using the proposed FE model considering the effects of local vibration of stay cables. As a case of medium-span CSB, the subpart of Hangzhou Bay Bridge over the north channel is analyzed with emphasis on the impact effects on its dynamic responses. For super long-span CSB, attentions are focused on the vibration of stay cables. The equations of motion in incremental forms are established for the nonlinear vibration of long and flexible stay cables based on the theory of VBCV. A long span CSB with span of 1400 m is investigated as an example. Both nonlinear vibrations of steel and CFRP cables are analyzed comparatively, and the potential applicability of CFRP cables in long-span CSB is evaluated.
A major part of the thesis is devoted to the low-frequency noise induced by the vibration of bridges. Firstly, numerical results based on the analytical solutions for acoustic radiation of point source are presented for a simply supported steel girder bridge. Here, the bridge deck is modeled as a beam-plate system considering merely the shear deformation of the plates fully supported by beams. Secondly, the boundary integral equations are derived for three-dimensional sound field, which is solved using the boundary element method (BEM). Thus, a combined method of FEM-BEM is developed for the problem of VBCV-induced low-frequency noise for steel girder bridges. Finally, the image method is adopted to incorporate the effects of reflection of acoustic waves by the ground on the sound field near the bridge deck.
The proposed hybrid FEM-BEM is employed to analyze to the steady-state and transient acoustic radiation by the VBCV of simply supported or continuous steel girder bridges. By comparing numerical results to the on-site tested data, the correctness of the present formulations and BEM code, as well as the effectiveness and efficiency of the proposed method, is firmly validated. Numerical results are given both for the noise level around the bridge deck and for the distribution of sound pressure in spatial and time domains. Comprehensive analyses are carried out against the effects of road surface roughness, velocity of vehicles, and distance of bridge deck away from the ground on the noise level and distributions of sound field. Finally, the hybrid FEM-BEM is applied to evaluate and verify effective strategies for noise reduction for continuous steel girder bridges.
引文
[1]中华人民共和国铁道部,《中长期铁路网规划(2008年调整)》.
[2]梁艳,陈艾荣.城市标志性桥梁设计原则[J].桥梁建设,5：48-54,2006.
[3]中国土木工程学会桥梁及结构分会.中国优秀桥梁[M].北京：人民交通出版社,2006.
[4]赵林强,许荣华,郑宪政.杭州市钱江四桥总体设计[J].桥梁建设,1：27～30,2004.
[5]戴志中,郑圣峰.城市桥空间[M].南京：东南大学出版社,2003.
[6]赵洋.系杆拱桥吊杆更换研究[D].浙江大学硕士论文.2006.
[7]张鹤,张治成,谢旭等.月牙形多拱肋钢管混凝土桁架拱-桥动力冲击系数理论研究[J],工程力学.25(7)：118-124,2008.
[8]Chriristoffersen J., Hauge L., Elaard J. H., et al. Design and construction of a CFRP cable-stayed footbridge [C]. Cable-stayed bridges-past, present and future. Proceedings of IABSE Conference. Sweden:IABSE,1999
[9]吕志涛,梅葵花.国内首座CFRP索斜拉桥的研究[J],土木工程学报,2007,40(1)：54-59
[10]李耀中.噪声控制技术[M].化学工业出版社,2004.
[11]M. Heckl. Tyre noise generation [J], Wear,113(1-1):157-170,1986.
[12]PERISSE J.. A study of radial vibrations of a rolling tyre for tyre-road noise characteristation [J], Mechanical Systems and Signal Processing,16(6): 1043-1058,2002.
[13]Larsson K., Kropp W.. A high-frequency three-dimensional tyre model based on two coupled elastic layers [J]. Journal of Sound and Vibration,253(4): 889-908,2002.
[14]Fujikawa T., Koike H., Oshino Y., Tachibana H.. Definition of road roughness parameters for tire vibration noise control [J]. Applied Acoustics,66(5): 501-512,2005.
[15]Machida N., Effect and evaluation of infra and low frequency sound [J], Journal of INCE/Japan,23(5):302-305,1999.
[16]Inoue Y., Actual state and control of low frequency noise [J], Journal of INCE/Japan,23(5):311-318,1999.
[17]广西质量监督导报,低频噪声威胁市民健康,2006年4月.
[18]张雁歌,声振动病的研究进展[J],航空军医,33(1)：38-40,2005.
[19]Yamada S., Actual condition of low frequency noise problems and recommendation level of foreign countries [J], Journal of INCE/Japan,23(5): 297-300,1999.
[20]http://www.xjepb.gov.cn/Article_Print.asp?ArticleID=2291(转载《环球时报》2004年10月12日).
[21]http://news.hit.edu.cn/articles/2007/01-26/01083409.htm.
[22]http://www.chengdu.gov.cn/special/zx/detail.jsp?ClassID=0201072608&ID=651 44.
[23]Murai I., The low frequency noise problem about the road project [J], Journal of INCE/Japan,23(5):319-323,1999.
[24]Tokunaga N., Hino Y., Nushimura T., Study on the traffic vibration around elevated road and factor of associated complaints [J], Bridge and Foundation Engineering,98(3):51-56,1998.
[25]Murai I., Handling of low frequency noise in case of environmental assessment by road project [J], Journal of INCE/Japan,24(4):242-247,2000.
[26]日本环境厅大气保全局,低频噪音的测定方法[S],2000.
[27]日本环境省环境管理局大气生活环境室,低频噪音防止对策事例集[M],
[28]Willis R. Appendix of the report of commissioners appointed to inquire application of iron to railway structures [R]. His Majesty's stationary office, London,1849.
[29]Stockes G.G. Discussion of a differential equation relating to the breaking of railway bridges [J]. Trans. Cambridge Phil. Soc.8(5):707-735,1849.
[30]Krylov A.N.. Mathematical collection of papers of the academy of sciences [M]. 61 Petersburg,1905.
[31]Timoshenko S. P.. On the forced vibration of bridge [J]. Philosoph Magazine, Ser 6.1922.
[32]Inglis C. E.. A mathematical treatise on vibrations in railway bridges [M]. The University Press, Cambridge London,1934.
[33]Biggs J.M., Suer H.S., Louw J.M.. Vibration of simple-span highway bridges [J]. Journal of the structural division, ASCE,83(ST2), Proceedings paper 1186: 291-318,1957.
[34]Wen R.K.L.. Dynamic response of breams traversed by two-axle loads [J]. Journal of engineering mechanics division, ASCE,86(EM5):91-111,1960.
[35]Fryba L.. Vibration of solids and structures under moving loads [J]. Noordoff International Publishing, Groningen,1972.
[36]Guo W.H., Xu Y.L.. Fully computerized approach to study cable-stayed bridge-vehicle interaction [J]. Journal of sound and vibration,248(4):745-761, 2001.
[37]Yang Y.B., Chang C.H., Yau J.D.. An element for analysing vehicle-bridge systems considering vehicle's pitching effect [J]. International Journal for Numerical Methods in Engineering,46(7):1031-1047,1999
[38]Obrien E., Li Y.Y., Gonzalez A.. Bridge roughness index as an indicator of bridge dynamic amplification [J]. Computers and structures,84:759-769,2006.
[39]Law S.S., Zhu X.Q.. Bridge dynamic responses due to road surface roughness and braking of vehicle [J]. Journal of sound and vibration,282:805-830,2005.
[40]Zhang X., Sennah K., Kennedy J.B.. Evaluation of impact factors for composite concrete-steel cellular straight bridges [J]. Engineering Structures,25:313-321, 2003.
[41]Yang F.H., Ghislain A.F.. Dynamic response of cable-stayed bridges under moving loads [J]. Journal of engineering mechanics,124(7):741-747,1998.
[42]韩万水.风-汽车-桥梁系统空间耦合振动研究[D].同济大学,2006.
[43]Law S.S., Bu J.Q., Zhu X.Q., et. al. Moving load identification on a simply supported orthotropic plate [J]. International Journal of Mechanical Sciences, 49(11):1262-1275,2007.
[44]Senthilvason J., Thambiratnam D.P., Brameld G.H.. Dynamic response of a curved bridge under moving truck load [J]. Engineering structures,24:1283-1293, 2002.
[45]Huang D. Z.. Dynamic and impact behavior of half-through arch bridges [J]. Journal of Bridge Engineering, ASCE,10(2):133-141,2005.
[46]Liu C.H., Huang D.Z., Wang T.L.. Analytical dynamic impact study based on correlated road roughness [J]. Computers and Structures,80:1639-1650,2002.
[47]Au F.T.K., Cheng Y.S., Cheung Y.K.. Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles [J]. Computers & Structures,79:853-872, 2001.
[48]Kim C.W., Kawatani M., Kwon Y.R.. Impact coefficient of reinforced concrete slab on a steel girder bridge [J]. Engineering Structures,29(4):576-590,2007.
[49]Cai C.S., Chen S.R.. Framework of vehicle-bridge-wind dynamic analysis [J]. Journal of Wind Engineering and Industrial Aerodynamics,92:579-607,2004.
[50]Guo W.H.. Dynamic analysis of coupled road vehicle and long span cable-stayed bridge systems under cross winds [D]. These for PhD in Hong Kong Polytechnic university,2003.
[51]Xie X., Chen H.Z., and Yamashita M.. Study on Low-Frequency Noise Radiated from Simply Supported Steel Bridges [C]. International Seminar on Environmental Vibration, Hangzhou,2003.
[52]Brady S.P., O'Brien E.J., Znidaric A. Effect of vehicle velocity on the dynamic amplification of a vehicle crossing a simply supported bridge [J]. Journal of Bridge Engineering,11(2):241-249,2006.
[53]Kwasniewski L., Wekezer J., Roufa G., et al.. Experimental evaluation of dynamic effects for a selected highway bridge [J]. Journal of Performance of Constructed Facilities,20(3):253-260,2006.
[54]Kwasniewski L., Li H.Y., Wekezer J., Malachowski J.. Finite element analysis of vehicle-bridge interaction [J]. Finite element in analysis and design 42:950-959, 2006.
[55]Ayre R.S., Ford G., Jacobsen L.S.. Transverse vibration of a two-span beam under action of a moving constant force [J]. Applied Mechanics Division,17(1): 1-12,1950.
[56]Sridharan N., Mallik A.K.. Numerical analysis of vibration of beams subjected to moving loads [J]. Journal of sound and vibrations.65:147-150,1979.
[57]Tan C.P., Shore S.. Dynamic response of a horizontally curved bridge [J]. Journal of the Structural Division, ASCE,94(3):761-781,1968a.
[58]Tan C.P., Shore S.. Dynamic response of a horizontally curved bridge [J]. Journal of the Structural Division, ASCE,94(3):761-781,1968b.
[59]Wu J.S., Dai C.W.. Dynamic responses of multispan nonuniform beam due to moving loads [J]. Journal of structure engineering, ASCE,113(3):458-474,1987.
[60]Jeffcott H.H.. On the vibrations of beams under the action of moving loads [J]. Philosoph Magazine, Ser 7,8(48):66-97,1928.
[61]Ting E.C., Genin J., Ginsberg J.H.. A general algorithm for the moving mass problem [J]. Journal of Sound and Vibration,33(1):49-58,1974.
[62]Chatterjee P.K., Datta T.K., Surana C.S.. Vibration of continuous bridges under moving vehicles [J]. Journal of Sound and Vibration 169(5):619-632,1994.
[63]Green M.F., Cebon D.. Dynamic interaction between heavy vehicles and highway bridges [J]. Computers and Structures 62(2):253-264,1997.
[64]Lu S., Deng X.J.. Prediction vertical dynamic loads caused by vehicle-pavement interaction [J]. Journal of Transportation Engineering.124(5):470-477,1998.
[65]Chompooming K., Yener M.. The influence of roadway surface irregularities and vehicle deceleration on bridge dynamics using the method of lines [J]. Journal of Sound and Vibration,183(4):567-589,1995.
[66]Fafard M., Bennur M., Savard M.. A general multi-axle vehicle model to study the bridge-vehicle interaction [J]. Engineering Computation.14(5):491-508, 1997.
[67]Kou J.W., Dewolf J.T.. Vibration behavior of continuous span highway bridge influencing variables [J]. Journal of Structural Engineering 123(3):333-344, 1997.
[68]过学迅,徐占,李孟良等.路面不平度测量技术研究综述[J].中外公路,5：47-51,2009.
[69]ISO 8608. Mechanical vibration-Road surface profiles-Reporting of measured data [S]. ISO,1995
[70]Honda H., Kajikawa Y., Kobori T. Spectra of road surface roughness on bridges [J]. J Struct Div ASCE 108(ST9):1956-1966,1982.
[71]谢旭,朱越峰,申永刚.大跨度钢索和CFRP索斜拉桥交通振动研究[J].工程力学,24(增刊Ⅰ)：53-61,2007.
[72]Musharraf Z., Micheal R. T., Anuradha K.. Dynamic response of cable-stayed bridges to moving vehicles using the structural impedance method [J]. Applied Mathematical Modelling,20:877-889,1996.
[73]Animesh Das, Anjan Dutta, Sudip Talukdar. Efficient dynamic analysis of cable-stayed bridges under vehicular movement using space and time adaptivity [J]. Finite Elements in Analysis and Design,40(4):407-424,2004.
[74]Calcada R., Cunha A., and Delgado R., Analysis of Traffic-Induced Vibrations in a Cable-Stayed Bridge. Part I:Numerical Modeling and Stochastic Simulation [J]. Journal of Bridge Engineering,10(4):370-385,2005.
[75]Calcada R., Cunha A., and Delgado R.. Analysis of Traffic-Induced Vibrations
in a Cable-Stayed Bridge. Part II:Numerical Modeling and Stochastic Simulation [J]. Journal of Bridge Engineering,10(4):386-397,2005.
[76]Wu, Q.X. Takahashi, K. Okabayashi, T. et al. Response characteristics of local vibrations in stay cables on an existing cable-stayed bridges [J]. Journal of sound and vibration,261:403-420,2003.
[77]Wu, Q.X., Takahashi, K. Chen, B.C.. Using cable finite elements to analyze parametric vibrations of stay cables in cable-stayed bridges [J]. Structural engineering and mechanics,23(6):691-711,2006.
[78]杨素哲,陈艾荣.超长斜拉索的参数振动[J].同济大学学报(自然科学版),33(10)：1303-1307,2005.
[79]陈水生,孙炳楠.斜拉桥索-桥耦合非线性参数振动数值研究[J].土木工程学报,36(4)：70-75,2003.
[80]Uhrig, R.. On kinetic response of cables of cable-stayed bridges due to combined parametric and forced excitation [J]. Journal of sound and vibration,165(1): 185-192,1993.
[81]Lilien, J.L. Pinto, D.C.A.. Vibration amplitudes caused by parametric excitation of cable stayed structures [J]. Journal of sound and vibration,174(1):69-90, 1994.
[82]张治成,谢旭,张鹤.大跨度斜拉桥钢和碳纤维拉索设计安全系数[J].浙江大学学报(工学版),41(9)：1443-1449,2007.
[83]谢旭,朱越峰.CFRP拉索设计对大跨度斜拉桥力学特性的影响[J].工程力学,24(11)：113-120,2007.
[84]谢旭,张鹤,朱越峰.CFRP拉索在横向风荷载作用下的振动特性[J].浙大学报工学版,42(1)：145-151,2008.
[85]日本钢桥研究会成立桥梁防音设计研究会,钢桥防音设计手册[M].1991.
[86]日本土木研究所资料第33078号(ISSN 0386-5878)[M].1992.
[87]日本土木研究所资料第3436号(ISSN 0386-5878)[M].1996.
[88]日本高速公路公团(JH)试验研究所技术资料第929号,噪音振动处理事例集
[M].1996.
[89]Oshima T., et. al.. Analysis of low frequency sound level radiating from bridge by means of beam theory [J]. Journal of structural mechanics and earthquake engineering, JSCE,356(1-3):527-536,1985.
[90]Goromaru H., Shiraishi K., Hara H., et al.. Analysis of low frequency sound radiating from simple girder highway bridge by a moving vehicle [J]. Journal of construction management and engineering,427(VI-14):133-142,1991.
[91]Fukasawa Y., Sugiyama T., Nakahara K. et al., Fundamental characteristics of low frequency sound radiated from highway bridges under the passage of heavy vehicles [J]. Journal of Structural Engineering, JSCE,37(A):945-956,1991.
[92]Sugiyama T., Kobayashi T., Shimizu K.. Characteristics of low-frequency sound radiated from both steel concrete girder highway bridges and reduction measure against low-frequency sound radiated from steel ones [J]. Journal of Structural Engineering, JSCE,45(A):671-681,1999.
[93]杜功焕,朱哲民,龚秀芬.声学基础(M),南京大学出版社,2001.
[94]何作镛,赵玉芳.声学理论基础[M].北京：国防工业出版社,1981.
[95]马大猷,沈壕.声学手册[M].北京：科学出版社,1983.
[96]梁昆淼.数学物理方法[M].北京：高等教育出版社,1996
[97]Michael J. A.. Stochastic analysis of structural/acoustic systems [D]. These for PhD in University of Michigan,2001.
[98]朱才朝,秦大同,李润方.车身结构振动与车内噪声声场耦合分析与控制[J].机械工程学报,38(8)：54-58,2002.
[99]丁桂保,郑史维.高速铁路桥梁的低频噪声研究[J].西南交通大学学报,33(2)：127-131,1998.
[100]惠巍,刘更,吴立言.轿车声固耦合低频噪声的有限元分析[J].汽车工程,28(12)：1073-1077,2006.
[101]Chen L.H., Schweikert D.G.. Sound radiation from an arbitrary body [J]. Journal of Acoustic Society of America,35:1626-1632,1963.
[102]Baron M.L., Mccormick J.M.. Sound radiation from submerged cylindrical shells of finite length [J]. Transactions of ASME, Ser, B87:393-405,1963.
[103]Chertock G.. Sound radiation from vibrating surface [J]. Journal of Acoustic Society of America,36(7):1305-1313,1964
[104]Smith R.R., Hunt J.T., Barach D.. Finite element analysis of acoustically radiating structure with application to sonar transducers [J]. Journal of Acoustic Society of America,55:1277-1288,1974.
[105]Ursell F.. On the exterior problems of acoustics [J]. Proceedings of Cambridge Philosophy Society,74:117-125,1973.
[106]Jones D.S.. Integral equation for the exterior acoustic problem [J]. Journal of Mechanics and Applied Mathematics,27(1):129-142,1974.
[107]Coply L.G.. Integral equation method for radiation from vibrating bodies [J]. Journal of Acoustic Society of America,4:807-816,1967.
[108]Coply L.G.. Fundamental results concerning integral representations in acoustic radiation [J]. Journal of Acoustic Society of America,44:28-32,1968.
[109]Seybert A.F., Soenarko B., Rizzo F.J., et. al.. Application of the BIE method to sound radiation problems using an isoparametric element [J]. ASME Transactions, Journal of Vbration, Acoustics, Stress and Reliability Design.106:414-420, 1984.
[110]Seybert A.F., Soenarko B., Rizzo F.J., et. al.. An advanced computational method for radiation and scattering of acoustic waves in three dimensions [J]. Journal of Acoustic Society of America,77(2):362-368,1985
[111]祝家麟.边界元方法中的奇异性[J].重庆建筑工程学院学报,13(2)：90-102,1991.
[112]许晶月,杜善义,孟庆元.边界元区域积分奇异性的半解析处理法[J].哈尔滨工程大学学报,25(2)：97-103,1993.
[113]臧跃龙.关于边界元法中奇异积分的处理[J].固体力学学报,15(2)：161-165,1994.
[114]黎胜,赵德有.用边界元法计算结构振动辐射声场[J].大连理工大学学报,40(4)：391-394,2000.
[115]汪鸿振,郭梵.用边界元法计算声辐射时高次奇异积分的处理方法[J].声学技术,15(3)：97-100,1996.
[116]刘钊,陈心昭.结构声辐射分析的全特解场边界元方法[J].振动工程学报,9(4)：341-347,1996.
[117]刘钊,王有成,陈心昭.全特解场边界元法及其在计算振动体声辐射中的应用[J].合肥工业大学学报(自然科学版),17(4)：14-21,1994.
[118]Raveendra S. T.. An efficient indirect boundary element technique for multi-frequency acoustic analysis [J]. Int.J.Numer.Meth.Engng.44:59-78,1999.
[119]Li S.. An efficient technique for multi-frequency acoustic analysis by boundary element method [J]. Journal of Sound and Vibration,283(3-5):971-980,2005.
[120]杨德庆,郑靖明.基于SYSNOISE软件的船舶振动声学数值计算[J].中国造船,43(4)：32-38,2002.
[121]康永,朱静,高翔.摊铺机地板声辐射对驾驶员耳旁噪声的影响计算[J].噪声与振动控制,25(3)：48-50,2005.
[122]刘鹏,刘更,吴立言等.有限元／边界元方法在卡车驾驶室声学分析中的应用[J].噪声与振动控制,25(3)：25-28,2005.
[123]韩洪伟,王敏庆,胡卫强等.基于SYSNOISE的建筑模板耦合振动及声辐射特性研究[J].噪声与振动控制,26(5)：37-40,2006.
[124]袁亮,倪樵,刘攀等.用有限元／边界元方法计算U型管振动声辐射[J].华中科技大学学报(城市科学版),23(1)：39-42,2006.
[125]Misljenovic D. M.. Boundary element method and wave equation [J]. Applied Mathematics Modelling,6:205-208,1982.
[126]Makespeace D.. Some aspects of the boundary element method [J]. Applied mathematics Modelling,6:229-236,1982.
[127]Mansur W.J., Brebbia C.A.. Formulation of the boundary element method for transient problems governed by the scalar wave equation [J]. Applied Mathematics Modelling,6:307-311,1982.
[128]Dohner J.L., Shoureski R., Bernhard R.J.. Transient analysis of three dimensional wave propagation using the boundary element method [J]. International Journal for Numerical Methods in Engineering,24:621-634,1987.
[129]余爱萍,张重超,骆振黄.瞬态声场特性的时域边界元分析和实验研究[J].上海交通大学学报,23(3)：82-89,1989.
[130]刘林芽,雷晓燕,练松良.铁路线路噪声特点分析[J].噪声与振动控制,3：77-80,2006.
[131]朱彦,陈光冶,林常明.城市高架轨道桥辐射噪声的计算与分析[J].噪声与振动控制,3：37-41,2005.
[132]Nagai M., Nii J., Kawabata O.. Three dimensional dynamic analysis of cable-stayed bridges including cable local vibration [C]. Proceeding of the 4th East Asia-Pacific Conference on Structural Engineering & Construction,20(22): 1845-1850, Seoul, Korea,1993.
[133]Oshita S., Egawa S.. A proposal of analytical solution for bridge with steel deck connected to chord members [J]. Journal of structural mechanics and earthquake engineering, JSCE,27(516),197-206,1995.
[134]中华人民共和国建设部.城市桥梁设计荷载标准(CJJ 77-98)[S].中国建筑工业出版社,北京,1998.
[135]雷晓燕,圣小珍.铁路交通噪声与振动[M].科学出版社,2004.
[2]梁艳,陈艾荣.城市标志性桥梁设计原则[J].桥梁建设,5：48-54,2006.
[3]中国土木工程学会桥梁及结构分会.中国优秀桥梁[M].北京：人民交通出版社,2006.
[4]赵林强,许荣华,郑宪政.杭州市钱江四桥总体设计[J].桥梁建设,1：27～30,2004.
[5]戴志中,郑圣峰.城市桥空间[M].南京：东南大学出版社,2003.
[6]赵洋.系杆拱桥吊杆更换研究[D].浙江大学硕士论文.2006.
[7]张鹤,张治成,谢旭等.月牙形多拱肋钢管混凝土桁架拱-桥动力冲击系数理论研究[J],工程力学.25(7)：118-124,2008.
[8]Chriristoffersen J., Hauge L., Elaard J. H., et al. Design and construction of a CFRP cable-stayed footbridge [C]. Cable-stayed bridges-past, present and future. Proceedings of IABSE Conference. Sweden:IABSE,1999
[9]吕志涛,梅葵花.国内首座CFRP索斜拉桥的研究[J],土木工程学报,2007,40(1)：54-59
[10]李耀中.噪声控制技术[M].化学工业出版社,2004.
[11]M. Heckl. Tyre noise generation [J], Wear,113(1-1):157-170,1986.
[12]PERISSE J.. A study of radial vibrations of a rolling tyre for tyre-road noise characteristation [J], Mechanical Systems and Signal Processing,16(6): 1043-1058,2002.
[13]Larsson K., Kropp W.. A high-frequency three-dimensional tyre model based on two coupled elastic layers [J]. Journal of Sound and Vibration,253(4): 889-908,2002.
[14]Fujikawa T., Koike H., Oshino Y., Tachibana H.. Definition of road roughness parameters for tire vibration noise control [J]. Applied Acoustics,66(5): 501-512,2005.
[15]Machida N., Effect and evaluation of infra and low frequency sound [J], Journal of INCE/Japan,23(5):302-305,1999.
[16]Inoue Y., Actual state and control of low frequency noise [J], Journal of INCE/Japan,23(5):311-318,1999.
[17]广西质量监督导报,低频噪声威胁市民健康,2006年4月.
[18]张雁歌,声振动病的研究进展[J],航空军医,33(1)：38-40,2005.
[19]Yamada S., Actual condition of low frequency noise problems and recommendation level of foreign countries [J], Journal of INCE/Japan,23(5): 297-300,1999.
[20]http://www.xjepb.gov.cn/Article_Print.asp?ArticleID=2291(转载《环球时报》2004年10月12日).
[21]http://news.hit.edu.cn/articles/2007/01-26/01083409.htm.
[22]http://www.chengdu.gov.cn/special/zx/detail.jsp?ClassID=0201072608&ID=651 44.
[23]Murai I., The low frequency noise problem about the road project [J], Journal of INCE/Japan,23(5):319-323,1999.
[24]Tokunaga N., Hino Y., Nushimura T., Study on the traffic vibration around elevated road and factor of associated complaints [J], Bridge and Foundation Engineering,98(3):51-56,1998.
[25]Murai I., Handling of low frequency noise in case of environmental assessment by road project [J], Journal of INCE/Japan,24(4):242-247,2000.
[26]日本环境厅大气保全局,低频噪音的测定方法[S],2000.
[27]日本环境省环境管理局大气生活环境室,低频噪音防止对策事例集[M],
[28]Willis R. Appendix of the report of commissioners appointed to inquire application of iron to railway structures [R]. His Majesty's stationary office, London,1849.
[29]Stockes G.G. Discussion of a differential equation relating to the breaking of railway bridges [J]. Trans. Cambridge Phil. Soc.8(5):707-735,1849.
[30]Krylov A.N.. Mathematical collection of papers of the academy of sciences [M]. 61 Petersburg,1905.
[31]Timoshenko S. P.. On the forced vibration of bridge [J]. Philosoph Magazine, Ser 6.1922.
[32]Inglis C. E.. A mathematical treatise on vibrations in railway bridges [M]. The University Press, Cambridge London,1934.
[33]Biggs J.M., Suer H.S., Louw J.M.. Vibration of simple-span highway bridges [J]. Journal of the structural division, ASCE,83(ST2), Proceedings paper 1186: 291-318,1957.
[34]Wen R.K.L.. Dynamic response of breams traversed by two-axle loads [J]. Journal of engineering mechanics division, ASCE,86(EM5):91-111,1960.
[35]Fryba L.. Vibration of solids and structures under moving loads [J]. Noordoff International Publishing, Groningen,1972.
[36]Guo W.H., Xu Y.L.. Fully computerized approach to study cable-stayed bridge-vehicle interaction [J]. Journal of sound and vibration,248(4):745-761, 2001.
[37]Yang Y.B., Chang C.H., Yau J.D.. An element for analysing vehicle-bridge systems considering vehicle's pitching effect [J]. International Journal for Numerical Methods in Engineering,46(7):1031-1047,1999
[38]Obrien E., Li Y.Y., Gonzalez A.. Bridge roughness index as an indicator of bridge dynamic amplification [J]. Computers and structures,84:759-769,2006.
[39]Law S.S., Zhu X.Q.. Bridge dynamic responses due to road surface roughness and braking of vehicle [J]. Journal of sound and vibration,282:805-830,2005.
[40]Zhang X., Sennah K., Kennedy J.B.. Evaluation of impact factors for composite concrete-steel cellular straight bridges [J]. Engineering Structures,25:313-321, 2003.
[41]Yang F.H., Ghislain A.F.. Dynamic response of cable-stayed bridges under moving loads [J]. Journal of engineering mechanics,124(7):741-747,1998.
[42]韩万水.风-汽车-桥梁系统空间耦合振动研究[D].同济大学,2006.
[43]Law S.S., Bu J.Q., Zhu X.Q., et. al. Moving load identification on a simply supported orthotropic plate [J]. International Journal of Mechanical Sciences, 49(11):1262-1275,2007.
[44]Senthilvason J., Thambiratnam D.P., Brameld G.H.. Dynamic response of a curved bridge under moving truck load [J]. Engineering structures,24:1283-1293, 2002.
[45]Huang D. Z.. Dynamic and impact behavior of half-through arch bridges [J]. Journal of Bridge Engineering, ASCE,10(2):133-141,2005.
[46]Liu C.H., Huang D.Z., Wang T.L.. Analytical dynamic impact study based on correlated road roughness [J]. Computers and Structures,80:1639-1650,2002.
[47]Au F.T.K., Cheng Y.S., Cheung Y.K.. Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles [J]. Computers & Structures,79:853-872, 2001.
[48]Kim C.W., Kawatani M., Kwon Y.R.. Impact coefficient of reinforced concrete slab on a steel girder bridge [J]. Engineering Structures,29(4):576-590,2007.
[49]Cai C.S., Chen S.R.. Framework of vehicle-bridge-wind dynamic analysis [J]. Journal of Wind Engineering and Industrial Aerodynamics,92:579-607,2004.
[50]Guo W.H.. Dynamic analysis of coupled road vehicle and long span cable-stayed bridge systems under cross winds [D]. These for PhD in Hong Kong Polytechnic university,2003.
[51]Xie X., Chen H.Z., and Yamashita M.. Study on Low-Frequency Noise Radiated from Simply Supported Steel Bridges [C]. International Seminar on Environmental Vibration, Hangzhou,2003.
[52]Brady S.P., O'Brien E.J., Znidaric A. Effect of vehicle velocity on the dynamic amplification of a vehicle crossing a simply supported bridge [J]. Journal of Bridge Engineering,11(2):241-249,2006.
[53]Kwasniewski L., Wekezer J., Roufa G., et al.. Experimental evaluation of dynamic effects for a selected highway bridge [J]. Journal of Performance of Constructed Facilities,20(3):253-260,2006.
[54]Kwasniewski L., Li H.Y., Wekezer J., Malachowski J.. Finite element analysis of vehicle-bridge interaction [J]. Finite element in analysis and design 42:950-959, 2006.
[55]Ayre R.S., Ford G., Jacobsen L.S.. Transverse vibration of a two-span beam under action of a moving constant force [J]. Applied Mechanics Division,17(1): 1-12,1950.
[56]Sridharan N., Mallik A.K.. Numerical analysis of vibration of beams subjected to moving loads [J]. Journal of sound and vibrations.65:147-150,1979.
[57]Tan C.P., Shore S.. Dynamic response of a horizontally curved bridge [J]. Journal of the Structural Division, ASCE,94(3):761-781,1968a.
[58]Tan C.P., Shore S.. Dynamic response of a horizontally curved bridge [J]. Journal of the Structural Division, ASCE,94(3):761-781,1968b.
[59]Wu J.S., Dai C.W.. Dynamic responses of multispan nonuniform beam due to moving loads [J]. Journal of structure engineering, ASCE,113(3):458-474,1987.
[60]Jeffcott H.H.. On the vibrations of beams under the action of moving loads [J]. Philosoph Magazine, Ser 7,8(48):66-97,1928.
[61]Ting E.C., Genin J., Ginsberg J.H.. A general algorithm for the moving mass problem [J]. Journal of Sound and Vibration,33(1):49-58,1974.
[62]Chatterjee P.K., Datta T.K., Surana C.S.. Vibration of continuous bridges under moving vehicles [J]. Journal of Sound and Vibration 169(5):619-632,1994.
[63]Green M.F., Cebon D.. Dynamic interaction between heavy vehicles and highway bridges [J]. Computers and Structures 62(2):253-264,1997.
[64]Lu S., Deng X.J.. Prediction vertical dynamic loads caused by vehicle-pavement interaction [J]. Journal of Transportation Engineering.124(5):470-477,1998.
[65]Chompooming K., Yener M.. The influence of roadway surface irregularities and vehicle deceleration on bridge dynamics using the method of lines [J]. Journal of Sound and Vibration,183(4):567-589,1995.
[66]Fafard M., Bennur M., Savard M.. A general multi-axle vehicle model to study the bridge-vehicle interaction [J]. Engineering Computation.14(5):491-508, 1997.
[67]Kou J.W., Dewolf J.T.. Vibration behavior of continuous span highway bridge influencing variables [J]. Journal of Structural Engineering 123(3):333-344, 1997.
[68]过学迅,徐占,李孟良等.路面不平度测量技术研究综述[J].中外公路,5：47-51,2009.
[69]ISO 8608. Mechanical vibration-Road surface profiles-Reporting of measured data [S]. ISO,1995
[70]Honda H., Kajikawa Y., Kobori T. Spectra of road surface roughness on bridges [J]. J Struct Div ASCE 108(ST9):1956-1966,1982.
[71]谢旭,朱越峰,申永刚.大跨度钢索和CFRP索斜拉桥交通振动研究[J].工程力学,24(增刊Ⅰ)：53-61,2007.
[72]Musharraf Z., Micheal R. T., Anuradha K.. Dynamic response of cable-stayed bridges to moving vehicles using the structural impedance method [J]. Applied Mathematical Modelling,20:877-889,1996.
[73]Animesh Das, Anjan Dutta, Sudip Talukdar. Efficient dynamic analysis of cable-stayed bridges under vehicular movement using space and time adaptivity [J]. Finite Elements in Analysis and Design,40(4):407-424,2004.
[74]Calcada R., Cunha A., and Delgado R., Analysis of Traffic-Induced Vibrations in a Cable-Stayed Bridge. Part I:Numerical Modeling and Stochastic Simulation [J]. Journal of Bridge Engineering,10(4):370-385,2005.
[75]Calcada R., Cunha A., and Delgado R.. Analysis of Traffic-Induced Vibrations
in a Cable-Stayed Bridge. Part II:Numerical Modeling and Stochastic Simulation [J]. Journal of Bridge Engineering,10(4):386-397,2005.
[76]Wu, Q.X. Takahashi, K. Okabayashi, T. et al. Response characteristics of local vibrations in stay cables on an existing cable-stayed bridges [J]. Journal of sound and vibration,261:403-420,2003.
[77]Wu, Q.X., Takahashi, K. Chen, B.C.. Using cable finite elements to analyze parametric vibrations of stay cables in cable-stayed bridges [J]. Structural engineering and mechanics,23(6):691-711,2006.
[78]杨素哲,陈艾荣.超长斜拉索的参数振动[J].同济大学学报(自然科学版),33(10)：1303-1307,2005.
[79]陈水生,孙炳楠.斜拉桥索-桥耦合非线性参数振动数值研究[J].土木工程学报,36(4)：70-75,2003.
[80]Uhrig, R.. On kinetic response of cables of cable-stayed bridges due to combined parametric and forced excitation [J]. Journal of sound and vibration,165(1): 185-192,1993.
[81]Lilien, J.L. Pinto, D.C.A.. Vibration amplitudes caused by parametric excitation of cable stayed structures [J]. Journal of sound and vibration,174(1):69-90, 1994.
[82]张治成,谢旭,张鹤.大跨度斜拉桥钢和碳纤维拉索设计安全系数[J].浙江大学学报(工学版),41(9)：1443-1449,2007.
[83]谢旭,朱越峰.CFRP拉索设计对大跨度斜拉桥力学特性的影响[J].工程力学,24(11)：113-120,2007.
[84]谢旭,张鹤,朱越峰.CFRP拉索在横向风荷载作用下的振动特性[J].浙大学报工学版,42(1)：145-151,2008.
[85]日本钢桥研究会成立桥梁防音设计研究会,钢桥防音设计手册[M].1991.
[86]日本土木研究所资料第33078号(ISSN 0386-5878)[M].1992.
[87]日本土木研究所资料第3436号(ISSN 0386-5878)[M].1996.
[88]日本高速公路公团(JH)试验研究所技术资料第929号,噪音振动处理事例集
[M].1996.
[89]Oshima T., et. al.. Analysis of low frequency sound level radiating from bridge by means of beam theory [J]. Journal of structural mechanics and earthquake engineering, JSCE,356(1-3):527-536,1985.
[90]Goromaru H., Shiraishi K., Hara H., et al.. Analysis of low frequency sound radiating from simple girder highway bridge by a moving vehicle [J]. Journal of construction management and engineering,427(VI-14):133-142,1991.
[91]Fukasawa Y., Sugiyama T., Nakahara K. et al., Fundamental characteristics of low frequency sound radiated from highway bridges under the passage of heavy vehicles [J]. Journal of Structural Engineering, JSCE,37(A):945-956,1991.
[92]Sugiyama T., Kobayashi T., Shimizu K.. Characteristics of low-frequency sound radiated from both steel concrete girder highway bridges and reduction measure against low-frequency sound radiated from steel ones [J]. Journal of Structural Engineering, JSCE,45(A):671-681,1999.
[93]杜功焕,朱哲民,龚秀芬.声学基础(M),南京大学出版社,2001.
[94]何作镛,赵玉芳.声学理论基础[M].北京：国防工业出版社,1981.
[95]马大猷,沈壕.声学手册[M].北京：科学出版社,1983.
[96]梁昆淼.数学物理方法[M].北京：高等教育出版社,1996
[97]Michael J. A.. Stochastic analysis of structural/acoustic systems [D]. These for PhD in University of Michigan,2001.
[98]朱才朝,秦大同,李润方.车身结构振动与车内噪声声场耦合分析与控制[J].机械工程学报,38(8)：54-58,2002.
[99]丁桂保,郑史维.高速铁路桥梁的低频噪声研究[J].西南交通大学学报,33(2)：127-131,1998.
[100]惠巍,刘更,吴立言.轿车声固耦合低频噪声的有限元分析[J].汽车工程,28(12)：1073-1077,2006.
[101]Chen L.H., Schweikert D.G.. Sound radiation from an arbitrary body [J]. Journal of Acoustic Society of America,35:1626-1632,1963.
[102]Baron M.L., Mccormick J.M.. Sound radiation from submerged cylindrical shells of finite length [J]. Transactions of ASME, Ser, B87:393-405,1963.
[103]Chertock G.. Sound radiation from vibrating surface [J]. Journal of Acoustic Society of America,36(7):1305-1313,1964
[104]Smith R.R., Hunt J.T., Barach D.. Finite element analysis of acoustically radiating structure with application to sonar transducers [J]. Journal of Acoustic Society of America,55:1277-1288,1974.
[105]Ursell F.. On the exterior problems of acoustics [J]. Proceedings of Cambridge Philosophy Society,74:117-125,1973.
[106]Jones D.S.. Integral equation for the exterior acoustic problem [J]. Journal of Mechanics and Applied Mathematics,27(1):129-142,1974.
[107]Coply L.G.. Integral equation method for radiation from vibrating bodies [J]. Journal of Acoustic Society of America,4:807-816,1967.
[108]Coply L.G.. Fundamental results concerning integral representations in acoustic radiation [J]. Journal of Acoustic Society of America,44:28-32,1968.
[109]Seybert A.F., Soenarko B., Rizzo F.J., et. al.. Application of the BIE method to sound radiation problems using an isoparametric element [J]. ASME Transactions, Journal of Vbration, Acoustics, Stress and Reliability Design.106:414-420, 1984.
[110]Seybert A.F., Soenarko B., Rizzo F.J., et. al.. An advanced computational method for radiation and scattering of acoustic waves in three dimensions [J]. Journal of Acoustic Society of America,77(2):362-368,1985
[111]祝家麟.边界元方法中的奇异性[J].重庆建筑工程学院学报,13(2)：90-102,1991.
[112]许晶月,杜善义,孟庆元.边界元区域积分奇异性的半解析处理法[J].哈尔滨工程大学学报,25(2)：97-103,1993.
[113]臧跃龙.关于边界元法中奇异积分的处理[J].固体力学学报,15(2)：161-165,1994.
[114]黎胜,赵德有.用边界元法计算结构振动辐射声场[J].大连理工大学学报,40(4)：391-394,2000.
[115]汪鸿振,郭梵.用边界元法计算声辐射时高次奇异积分的处理方法[J].声学技术,15(3)：97-100,1996.
[116]刘钊,陈心昭.结构声辐射分析的全特解场边界元方法[J].振动工程学报,9(4)：341-347,1996.
[117]刘钊,王有成,陈心昭.全特解场边界元法及其在计算振动体声辐射中的应用[J].合肥工业大学学报(自然科学版),17(4)：14-21,1994.
[118]Raveendra S. T.. An efficient indirect boundary element technique for multi-frequency acoustic analysis [J]. Int.J.Numer.Meth.Engng.44:59-78,1999.
[119]Li S.. An efficient technique for multi-frequency acoustic analysis by boundary element method [J]. Journal of Sound and Vibration,283(3-5):971-980,2005.
[120]杨德庆,郑靖明.基于SYSNOISE软件的船舶振动声学数值计算[J].中国造船,43(4)：32-38,2002.
[121]康永,朱静,高翔.摊铺机地板声辐射对驾驶员耳旁噪声的影响计算[J].噪声与振动控制,25(3)：48-50,2005.
[122]刘鹏,刘更,吴立言等.有限元／边界元方法在卡车驾驶室声学分析中的应用[J].噪声与振动控制,25(3)：25-28,2005.
[123]韩洪伟,王敏庆,胡卫强等.基于SYSNOISE的建筑模板耦合振动及声辐射特性研究[J].噪声与振动控制,26(5)：37-40,2006.
[124]袁亮,倪樵,刘攀等.用有限元／边界元方法计算U型管振动声辐射[J].华中科技大学学报(城市科学版),23(1)：39-42,2006.
[125]Misljenovic D. M.. Boundary element method and wave equation [J]. Applied Mathematics Modelling,6:205-208,1982.
[126]Makespeace D.. Some aspects of the boundary element method [J]. Applied mathematics Modelling,6:229-236,1982.
[127]Mansur W.J., Brebbia C.A.. Formulation of the boundary element method for transient problems governed by the scalar wave equation [J]. Applied Mathematics Modelling,6:307-311,1982.
[128]Dohner J.L., Shoureski R., Bernhard R.J.. Transient analysis of three dimensional wave propagation using the boundary element method [J]. International Journal for Numerical Methods in Engineering,24:621-634,1987.
[129]余爱萍,张重超,骆振黄.瞬态声场特性的时域边界元分析和实验研究[J].上海交通大学学报,23(3)：82-89,1989.
[130]刘林芽,雷晓燕,练松良.铁路线路噪声特点分析[J].噪声与振动控制,3：77-80,2006.
[131]朱彦,陈光冶,林常明.城市高架轨道桥辐射噪声的计算与分析[J].噪声与振动控制,3：37-41,2005.
[132]Nagai M., Nii J., Kawabata O.. Three dimensional dynamic analysis of cable-stayed bridges including cable local vibration [C]. Proceeding of the 4th East Asia-Pacific Conference on Structural Engineering & Construction,20(22): 1845-1850, Seoul, Korea,1993.
[133]Oshita S., Egawa S.. A proposal of analytical solution for bridge with steel deck connected to chord members [J]. Journal of structural mechanics and earthquake engineering, JSCE,27(516),197-206,1995.
[134]中华人民共和国建设部.城市桥梁设计荷载标准(CJJ 77-98)[S].中国建筑工业出版社,北京,1998.
[135]雷晓燕,圣小珍.铁路交通噪声与振动[M].科学出版社,2004.