结构声学灵敏度计算方法研究
|
摘要
本文开展基于空间傅里叶变换和分布源边界点法的声学灵敏度分析方面的研究。声学灵敏度分析的信息揭示了结构振动引起的声学量(声压、声强和声功率等)与设计变量间的函数关系，为产品低噪声设计提供优化方向和量化依据，它在机械优化设计中具有重要意义。
本文在详细论述声辐射计算及声学灵敏度分析研究进展的基础上，针对目前声学灵敏度分析中存在的问题，提出一系列的解决方法：基于空间傅里叶变换，提出适用于柱面结构的声学灵敏度分析方法，提高了计算效率；针对任意形状声源，提出基于分布源边界点法的声学灵敏度分析方法，并将其应用于结构腔体内声学灵敏度分析中，该方法避免了边界元法固有的缺点，计算效率更高；针对设计变量多于目标函数的情况，提出基于分布源边界点法的声学灵敏度分析的伴随变量法，该方法避免了重复计算，减少了计算量；针对高频声场，提出一种分布能量源边界点法，该方法能够实现任意形状声源空间场点处高频声辐射和声学灵敏度的计算。本文主要研究内容如下：
第一章首先探讨声学灵敏度分析的研究意义，详细论述声辐射计算和声学灵敏度分析的研究进展，讨论现有方法具有的优缺点，在此基础上明确需要解决的问题，确定本论文的研究内容。
第二章研究基于空间傅里叶变换的声学灵敏度分析。针对平面声源，采用空间傅里叶变换推导了平面声源声学灵敏度计算公式，从理论上分析了计算过程中存在的误差及其控制办法，通过一个简支铝板的算例验证了该方法的正确性。针对柱面声源，进一步提出了基于空间傅里叶变换的柱面结构声学灵敏度分析方法，分别推导了无限长和有限长柱面结构声学灵敏度分析的计算公式，并从理论上分析了计算过程中存在的误差及其控制办法，通过有限长和无限长圆柱的数值仿真验证了基于空间傅里叶变换的柱面结构声学灵敏度分析方法的正确性。
第三章提出基于分布源边界点法的声学灵敏度分析方法，建立了基于分布源边界点法的声学灵敏度理论模型，根据设计变量的不同，分别推导了基于分布源边界点法的声学尺寸灵敏度、形状灵敏度、频率灵敏度和阻抗灵敏度计算公式，数值仿真和实验研究的结果验证了基于分布源边界点法的声学灵敏度分析方法的有效性，其中数值仿真中与边界元法在计算时间上的对比证明了基于分布源边界点法的声学灵敏度分析方法的计算效率。最后将分布源边界点法应用于结构腔体内声场分析中，该方法能够实现结构腔体内场点声学灵敏度的计算，数值仿真的结果验证了基于分布源边界点法腔体内声学灵敏度分析方法的有效性。
第四章提出基于分布源边界点法的声学灵敏度分析的伴随变量法，针对实际中存在的设计变量多于目标函数的情况，建立了基于分布源边界点法的声学灵敏度分析的伴随变量法理论模型，推导了其计算公式。该方法能够避免声学灵敏度分析的直接求导法中边界条件的重复计算，减少了计算量。数值仿真的结果证明了基于分布源边界点法的声学灵敏度分析的伴随变量法的正确性。
第五章提出了一种新型的基于分布能量源边界点法的高频声辐射计算及声学灵敏度分析方法，建立了基于分布能量源边界点法高频声辐射计算和声学灵敏度分析的理论模型，推导了其计算公式。该方法能够实现任意形状声源空间场点处高频声辐射及声学灵敏度的计算，避免了其他高频声场分析方法的一些缺点，数值仿真的结果验证了文中基于分布能量源边界点法的高频声辐射计算及声学灵敏度分析方法的正确性。
第六章总结本文的主要研究成果，指出需要进一步研究和解决的问题。
Acoustic sensitivity analysis based on spatial fourier transform and distributed source boundarypoint method (DSBPM) were investigated in this dissertation. Acoustic sensitivity informationprovides a quantitative estimate of the change of design variables, which indicates the change of theacoustical characteristics (sound pressure, sound intensity and sound power etc.) with respect to thechange of the design variable. Based on acoustic sensitivity analysis, engineers can decide thedirection and amount of design change needed to improve the objective function, and it has greatsignificance in mechanical optimization design.
Considering the research significance and development of the acoustic radiation and acousticsensitivity analysis, problems existing in acoustic sensitivity analysis were investigated anddiscussed deeply, and then the corresponding solutions were provided. Based on spatial fouriertransform, calculation formulas of acoustic sensitivity analysis of cylindrical radiators were deduced,the computational efficiency was improved because of the use of spatial fourier transform. By usingthe DSBPM, acoustic sensitivity analysis which is suitable for a radiator with arbitrary shape wasanalyzed, and this method was applied in the structure interior acoustic sensitivity analysis, whichcan avoid the shortcomings of BEM and has higher computational efficiency. Based on the adjointvariable method and the DSBPM, acoustic sensitivity analysis based on the DSBPM with adjointvariable method was proposed, which can significantly reduces computational costs compared to thedirect differentiation method, as the number of performance measures is in general less than thenumber of design variables. A new distributed energy source boundary point method (DESBPM)was proposed here, based on the DESBPM, the high frequency acoustic radiation and sensitivityanalysis of a radiator with arbitrary shape could be achieved. The detailed research contents of thisdissertation are summarized as follows:
In chapter one, the research significance of the acoustic sensitivity analysis was first elaborated,and then the development of the acoustic radiation and acoustic sensitivity analysis was discussed,by reviewing existing approaches of acoustic sensitivity analysis, the research topics of thisdissertation were determined finally.
In chapter two, acoustic sensitivity analysis based on spatial fourier transform was investigated.Calculation formulas of acoustic sensitivity analysis of a plane radiator were deduced based onspatial fourier transform, its errors as well as the corresponding control methods were analyzed intheory and the correctness was verified with a numerical simulation of a simply supported plate.Based on spatial fourier transform, acoustic sensitivity analysis of cylindrical radiators was proposed, calculation formulas of acoustic sensitivity analysis of finite and infinite length cylinders werededuced, its errors as well as the corresponding control methods were analyzed in theory, and thevalidity was verified with numerical simulations of infinite and finite length cylinders.
In chapter three, acoustic sensitivity analysis based on the DSBPM was proposed, the acousticsensitivity model based on DSBPM was established. According to the type of design variables,acoustic sizing sensitivity analysis, acoustic shape sensitivity analysis, acoustic frequency sensitivityanalysis and acoustic impedance sensitivity analysis were presented based on the DSBPM, thecorrectness and validity was verified by the numerical simulation and an experiment of a box, inwhich the advantage of computational efficiency is shown by the comparison of computational timewith BEM. Finally, the DSBPM was used to analyze the structure interior acoustic field, andstructural interior acoustic sensitivity could be achieved based on DSBPM, its validity was verifiedby the numerical simulation.
In chapter four, acoustic sensitivity analysis based on the DSBPM with adjoint variable methodwas proposed, the acoustic sensitivity model based on this method was established, and thencalculation formulas were deduced. The proposed method can significantly reduces computationalcosts compared to the direct differentiation method, as the number of performance measures is ingeneral less than the number of design variables, the correctness of this method was shown by thenumerical simulation finally.
In chapter five, a new distributed energy source boundary point method (DESBPM) wasproposed here for solving the high frequency acoustic radiation and sensitivity analysis, the acousticsensitivity model based on this method was established, and then calculation formulas was deduced.Based on the DESBPM, the high frequency acoustic radiation and sensitivity analysis of a radiatorwith arbitrary shape could be achieved, in which the shortcomings of other high frequency acousticanalysis methods could be avoid, its correctness was verified by the numerical simulation finally.
In chapter six, researches in this dissertation were summarized, and the topics needing furtherstudy were proposed.
本文在详细论述声辐射计算及声学灵敏度分析研究进展的基础上，针对目前声学灵敏度分析中存在的问题，提出一系列的解决方法：基于空间傅里叶变换，提出适用于柱面结构的声学灵敏度分析方法，提高了计算效率；针对任意形状声源，提出基于分布源边界点法的声学灵敏度分析方法，并将其应用于结构腔体内声学灵敏度分析中，该方法避免了边界元法固有的缺点，计算效率更高；针对设计变量多于目标函数的情况，提出基于分布源边界点法的声学灵敏度分析的伴随变量法，该方法避免了重复计算，减少了计算量；针对高频声场，提出一种分布能量源边界点法，该方法能够实现任意形状声源空间场点处高频声辐射和声学灵敏度的计算。本文主要研究内容如下：
第一章首先探讨声学灵敏度分析的研究意义，详细论述声辐射计算和声学灵敏度分析的研究进展，讨论现有方法具有的优缺点，在此基础上明确需要解决的问题，确定本论文的研究内容。
第二章研究基于空间傅里叶变换的声学灵敏度分析。针对平面声源，采用空间傅里叶变换推导了平面声源声学灵敏度计算公式，从理论上分析了计算过程中存在的误差及其控制办法，通过一个简支铝板的算例验证了该方法的正确性。针对柱面声源，进一步提出了基于空间傅里叶变换的柱面结构声学灵敏度分析方法，分别推导了无限长和有限长柱面结构声学灵敏度分析的计算公式，并从理论上分析了计算过程中存在的误差及其控制办法，通过有限长和无限长圆柱的数值仿真验证了基于空间傅里叶变换的柱面结构声学灵敏度分析方法的正确性。
第三章提出基于分布源边界点法的声学灵敏度分析方法，建立了基于分布源边界点法的声学灵敏度理论模型，根据设计变量的不同，分别推导了基于分布源边界点法的声学尺寸灵敏度、形状灵敏度、频率灵敏度和阻抗灵敏度计算公式，数值仿真和实验研究的结果验证了基于分布源边界点法的声学灵敏度分析方法的有效性，其中数值仿真中与边界元法在计算时间上的对比证明了基于分布源边界点法的声学灵敏度分析方法的计算效率。最后将分布源边界点法应用于结构腔体内声场分析中，该方法能够实现结构腔体内场点声学灵敏度的计算，数值仿真的结果验证了基于分布源边界点法腔体内声学灵敏度分析方法的有效性。
第四章提出基于分布源边界点法的声学灵敏度分析的伴随变量法，针对实际中存在的设计变量多于目标函数的情况，建立了基于分布源边界点法的声学灵敏度分析的伴随变量法理论模型，推导了其计算公式。该方法能够避免声学灵敏度分析的直接求导法中边界条件的重复计算，减少了计算量。数值仿真的结果证明了基于分布源边界点法的声学灵敏度分析的伴随变量法的正确性。
第五章提出了一种新型的基于分布能量源边界点法的高频声辐射计算及声学灵敏度分析方法，建立了基于分布能量源边界点法高频声辐射计算和声学灵敏度分析的理论模型，推导了其计算公式。该方法能够实现任意形状声源空间场点处高频声辐射及声学灵敏度的计算，避免了其他高频声场分析方法的一些缺点，数值仿真的结果验证了文中基于分布能量源边界点法的高频声辐射计算及声学灵敏度分析方法的正确性。
第六章总结本文的主要研究成果，指出需要进一步研究和解决的问题。
Acoustic sensitivity analysis based on spatial fourier transform and distributed source boundarypoint method (DSBPM) were investigated in this dissertation. Acoustic sensitivity informationprovides a quantitative estimate of the change of design variables, which indicates the change of theacoustical characteristics (sound pressure, sound intensity and sound power etc.) with respect to thechange of the design variable. Based on acoustic sensitivity analysis, engineers can decide thedirection and amount of design change needed to improve the objective function, and it has greatsignificance in mechanical optimization design.
Considering the research significance and development of the acoustic radiation and acousticsensitivity analysis, problems existing in acoustic sensitivity analysis were investigated anddiscussed deeply, and then the corresponding solutions were provided. Based on spatial fouriertransform, calculation formulas of acoustic sensitivity analysis of cylindrical radiators were deduced,the computational efficiency was improved because of the use of spatial fourier transform. By usingthe DSBPM, acoustic sensitivity analysis which is suitable for a radiator with arbitrary shape wasanalyzed, and this method was applied in the structure interior acoustic sensitivity analysis, whichcan avoid the shortcomings of BEM and has higher computational efficiency. Based on the adjointvariable method and the DSBPM, acoustic sensitivity analysis based on the DSBPM with adjointvariable method was proposed, which can significantly reduces computational costs compared to thedirect differentiation method, as the number of performance measures is in general less than thenumber of design variables. A new distributed energy source boundary point method (DESBPM)was proposed here, based on the DESBPM, the high frequency acoustic radiation and sensitivityanalysis of a radiator with arbitrary shape could be achieved. The detailed research contents of thisdissertation are summarized as follows:
In chapter one, the research significance of the acoustic sensitivity analysis was first elaborated,and then the development of the acoustic radiation and acoustic sensitivity analysis was discussed,by reviewing existing approaches of acoustic sensitivity analysis, the research topics of thisdissertation were determined finally.
In chapter two, acoustic sensitivity analysis based on spatial fourier transform was investigated.Calculation formulas of acoustic sensitivity analysis of a plane radiator were deduced based onspatial fourier transform, its errors as well as the corresponding control methods were analyzed intheory and the correctness was verified with a numerical simulation of a simply supported plate.Based on spatial fourier transform, acoustic sensitivity analysis of cylindrical radiators was proposed, calculation formulas of acoustic sensitivity analysis of finite and infinite length cylinders werededuced, its errors as well as the corresponding control methods were analyzed in theory, and thevalidity was verified with numerical simulations of infinite and finite length cylinders.
In chapter three, acoustic sensitivity analysis based on the DSBPM was proposed, the acousticsensitivity model based on DSBPM was established. According to the type of design variables,acoustic sizing sensitivity analysis, acoustic shape sensitivity analysis, acoustic frequency sensitivityanalysis and acoustic impedance sensitivity analysis were presented based on the DSBPM, thecorrectness and validity was verified by the numerical simulation and an experiment of a box, inwhich the advantage of computational efficiency is shown by the comparison of computational timewith BEM. Finally, the DSBPM was used to analyze the structure interior acoustic field, andstructural interior acoustic sensitivity could be achieved based on DSBPM, its validity was verifiedby the numerical simulation.
In chapter four, acoustic sensitivity analysis based on the DSBPM with adjoint variable methodwas proposed, the acoustic sensitivity model based on this method was established, and thencalculation formulas were deduced. The proposed method can significantly reduces computationalcosts compared to the direct differentiation method, as the number of performance measures is ingeneral less than the number of design variables, the correctness of this method was shown by thenumerical simulation finally.
In chapter five, a new distributed energy source boundary point method (DESBPM) wasproposed here for solving the high frequency acoustic radiation and sensitivity analysis, the acousticsensitivity model based on this method was established, and then calculation formulas was deduced.Based on the DESBPM, the high frequency acoustic radiation and sensitivity analysis of a radiatorwith arbitrary shape could be achieved, in which the shortcomings of other high frequency acousticanalysis methods could be avoid, its correctness was verified by the numerical simulation finally.
In chapter six, researches in this dissertation were summarized, and the topics needing furtherstudy were proposed.
引文
[1]百度百科-噪声http://baike.baidu.com/view/77735.htm.
[2]杨莉.客车车身结构动力学、声学CAE关键技术研究[D].2005.
[3]张军.声学_结构灵敏度及结构_声学优化设计研究[D].2006.
[4]程昊.基于边界元法的声学灵敏度分析若干关键问题研究[D].2010.
[5]刘宝山.结构振动声辐射灵敏度分析及优化设计研究[D].2010.
[6]郑昌军.三维声学灵敏度分析的宽频快速多级边界元法研究[D].2011.
[7]李善德.大规模声学问题的快速多极边界元方法研究[D].2011
[8]何作镛，赵玉芳.声学理论基础.北京：国防工业出版社，1981.
[9] Lee C., Benkeser P.J. A computationally efficient method for the calculation of the transientfield of acoustic radiators[J]. Journal of the Acoustical Society of America.1994,96(1):545-551.
[10] Mitzner K M. Numerical solutions for transient scattering from a hard surface of arbitraryshape—retarded potential technical[J]. Journal of the Acoustical Society of America.1967,42:1305-1313.
[11] Hu Q, Wu S F. Sound radiation from a finite cylinder[C], Proceedings of the ASME NoiseControl and Acoustics Division,1996,22:39-45.
[12] Hu Q, Wu S F. An explicit integral formulation for transient acoustic radiation[J]. The Journalof the Acoustical Society of America.1998,104(6):3251-3258.
[13]余爱萍.瞬态声振耦合问题的边界元分析和实验研究[D].1988.
[14]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,1989,23(3):82-89.
[15] Wu T W, Ciskowski R D, Seybert A F. Vectorization and parallelization of the acousticboundary element code BEMAP on the IBM ES/3090VF[J]. Engineering Analysis withBoundary Element,1992,10(1):17-26.
[16] Harris P J, Amini S. On the Burton and Miller boundary integral formulation of the exterioracoustic problem[J]. Transactions of the ASME.1992,114:540-545.
[17]赵键,汪鸿振,朱物华.边界元方法计算已知振速封闭面的声辐射[J].声学学报,1989,14(4):250-257.
[18]王有成,刘钊,吴约.边界元技术中的全特解场方法[C].第四届全国工程中的边界元方法学术会议论文集,南京:河海大学出版社,1994.
[19]高耀南,韩玉雄,沈文钧.关于时域边界元方法的若干研究[J].应用力学学报,1993,l0(4):60-64.
[20] Bitsie F. The Structural-Acoustic Energy Finite Element Method and Energy BoundaryElement Method[D].1996.
[21] Zienkiewicz O C, Taylor R L. The finite element method [M]. London: McGraw-hill,1977.
[22] Reddy J N. An introduction to the finite element method[M]. New York: McGraw-Hill,2006.
[23] Dhatt G, Touzot G. Finite Element Method[M]. John Wiley&Sons,2012.
[24] Smith R R, Hunt J T, Barach D. Finite element analysis of acoustically radiating structureswith application to sonar transducers[J]. The Journal of the Acoustical Society of America,1973,54:1277-1288.
[25] Tetambe R P, Rajakumar C. A simplified finite element method for studying acousticcharacteristics inside a car cavity[J]. Journal of Sound and Vibration,1979,63(1):61-72.
[26] Nefske D J, Wolf J A, HowellL J. Structural-acoustic finite element analysis of the automobilepassenger compartment: a review of current practice[J]. Journal of Sound and Vibration,1982,80(3):247-266.
[27] Kagawa Y, Yamabuchi T, Sugihara K., et al. Loudspeaker characteristic calculation by thefinite element method—Comparison with measured results[J]. Journal of Sound and Vibration,1983,91(4):604-607.
[28] Tetambe R P, Rajakumar C. Estimation of error in finite element acoustic analysis[J].Computers&Structures,1996,61(1):13-19.
[29] Thompson L L. A review of finite-element methods for time-harmonic acoustics[J]. Journal ofthe Acoustical Society of America,2006,119(3):1315-1330.
[30] Harari I. A survey of finite element methods for time-harmonic acoustics[J]. ComputerMethods in Applied Mechanics and Engineering,2006,195(13-16):1594-1607.
[31]朱才朝,秦大同,李润方.车身结构振动与车内噪声声场混合分析与控制[J].机械工程学报,2002,38(8):54-58.
[32]杨莉,孙庆鸿.自由阻尼处理结构的有限元建模及声辐射分析[J].振动工程学报,2004,17(3):306-310.
[33]陈军明,陈应波,黄玉盈.水中双向正交加肋圆柱壳体声辐射的有限元法[J].武汉理工大学学报,2004,26(4):74-76.
[34] Kirkup S. The boundary element method in acoustics[M]. Hebden Bridge: Integrated SoundSoftware,1998.
[35] Wu T W. Boundary element acoustics: fundamentals and computer codes[M]. Southampton,UK; Boston: WIT Press,2000.
[36] Schanz M, Steinbach O. Boundary Element Analysis[M]. New York: Springer-Verlag BerlinHeidelberg,2007.
[37] Beer G, Smith I M, Duenser C. The boundary element method with programming: forengineers and scientists[M]. Wien; New York: Springer,2008.
[38]王元淳.边界元法基础[M].上海:上海交通大学出版社,1988.
[39]杜庆华.边界积分方程方法-边界元法[M].北京:高等教育出版社,1989.
[40]申光宪.边界元法[M].北京:机械工业出版社,1998.
[41] Chen L H, Schweikert D G. Sound Radiation from an Arbitrary Body[J]. The Journal of theAcoustical Society of America,1963,35(10):1626-1632.
[42] Chertock G. Sound Radiation from Vibrating Surfaces[J]. The Journal of the AcousticalSociety of America,1964,36(7):1305-1313.
[43] Schenck H A. Improved integral formulation for acoustic radiation problems[J]. The Journal ofthe Acoustical Society of America,1968,44(1):41-58.
[44] Seybert A F, Rengarajan T K. The use of CHIEF to obtain unique solutions for acousticradiation using boundary integral equations[J]. The Journal of the Acoustical Society ofAmerica,1987,81(5):1299-1306.
[45] Wu T W, Seybert A F. A weighted residual formulation for the CHIEF method in acoustics [J].The Journal of the Acoustical Society of America,1991,90(3):1608-1614.
[46] Lee L, Wu T W. An enhanced CHIEF method for steady-state elastodynamics[J]. EngineeringAnalysis with Boundary Element,1993,12(2):75-83.
[47] Juhl P. A numerical study of the coefficient matrix of the boundary element method nearcharacteristic frequencies[J]. Journal of Sound and Vibration,1994,175(1):39-50.
[48] Li W L, Wu T W, Seybert A F. A half-space boundary element method for acoustic problemswith a reflecting plane of arbitrary impedance[J]. Journal of Sound and Vibration,1994,171(2):173-184.
[49] Park J M, Eversman W. A Boundary Element Method For Propagation Over AbsorbingBoundaries[J]. Journal of Sound and Vibration,1994,175(2):197-218.
[50] Burton A J, Miller G F. The Application of Integral Equation Methods to the NumericalSolution of Some Exterior Boundary-Value Problems [J]. Proceedings of the Royal Society ofLondon Series A-Mathematical and Physical Sciences,1971,323(1553):201-210.
[51] Chien C C, Rajiyah H, Atluri S N. An effective method for solving the hyper-singular integralequations in3-D acoustics[J]. Journal of the Acoustical Society of America,1990,88(2):918-937.
[52] Yan Z Y, Hung K C, Zheng H. Solving the hypersingular boundary integral equation inthree-dimensional acoustics using a regularization relationship[J]. Journal of the AcousticalSociety of America,2003,113(5):2674-2683.
[53] Kress R. Minimizing the condition number of boundary integral operators in acoustic andelectromagnetic scattering[J]. The Quarterly Journal of Mechanics and Applied Mathematics,1985,38(2):323-341.
[54] Amini S. On the chose of the coupling parameter in boundary integral formulations of theexterior acoustic problem[J]. Applicable analysis,1990,35(1-4):75-92.
[55] Cunefare K A, Koopmann G, Brod K. A boundary element method for acoustic radiation validfor all wavenumbers[J]. The Journal of the Acoustical Society of America,1989,85(1):39-48.
[56] Meyer W L, Bell W A, Zinn B T, et al. Boundary integral solutions of three dimensionalacoustic radiation problems[J]. Journal of Sound and Vibration,1978,59(2):245-262.
[57] Reut Z. On the boundary integral methods for the exterior acoustic problem[J]. Journal ofSound and Vibration,1985,103(2):297-298.
[58] Tobocman W. Extension of the Helmholtz integral equation method to shorter wavelengths[J].The Journal of the Acoustic Society of America.1986,80(6):1828-1837.
[59] Amini S. Harcis P J. A comparison between various boundary integral formulations of theexterior acoustic problem[J]. Computer Methods in Applied Mechanics Engineering,1990,84(1):59-75.
[60] Marburg S, Amini S. Cat's eye radiation with boundary elements: Comparative study ontreatment of irregular frequencies[J]. Journal of Computational Acoustics,2005,13(1):21-45.
[61] Cheng C Y R, Seybert A F, Wu T W. Multidomain boundary element solution for silencer andmuffler performance prediction[J]. Journal of Sound and Vibration,1991,151(1):119-129.
[62] Wu T W, Wan G C. Muffler performance studies using a direct mixed-body boundary elementmethod and a three-point method for evaluating transmission loss[J]. Journal of Vibration andAcoustics,1996,118(3):479-484.
[63] Wu T W, Cheng C Y R, Zhang P. A direct mixed-body boundary element method for packedsilencers[J]. The Journal of the Acoustical Society of America,2002,111(6):2566-2572.
[64] Pan K L, Chu C I, Wu T W. A direct mixed-body boundary element method for mufflers withinternal thin components covered by lining and a perforated panel[J]. Journal of ComputationalAcoustics,2007,15(1):145-157.
[65] Liu Y. Fast multipole boundary element method: theory and applications in engineering[M].Cambridge; New York: Cambridge University Press,2009.
[66] Chen Z S, Waubke H, Kreuzer W. A formulation of the fast multipole boundary elementmethod for acoustic radiation and scattering from three-dimensional structures[J]. Journal ofComputational Acoustics,2008,16(2):303-320.
[67] Fischer M, Gaul L. Application of the fast multipole bem for structural-acoustic simulations[J].Journal of Computational Acoustics,2005,13(1):87-98.
[68]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,2000,40(4):391-394.
[69]闰再友,姜揖,严明.利用边界元法计算无界声场中结构体声辐射[J].上海交通大学学报,2000,34(4):520-523.
[70]王秀峰,陈心昭.进一步改进边界元方法以克服振动声辐射计算中解的非唯一性[J].应用声学,2001,21(3):2-5.
[71]王炳和,相敬林.舰船水下声场边界元法建模与计算机模拟[J].计算机工程与应用,2004,40(7):217-210.
[72]李宏伟,文立华,陈克安.非光滑结构表面声学边界元法中奇异积分计算方法[J].西北工业大学学报,2006,24(4):498-500.
[73] Coyette J P, Fyfe K R. Improved formulation for acoustic eigenmode extraction from boundaryelement models[J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design,1990,112(3):392-397.
[74]赵志高.结构声辐射的机理与数值方法研究[D].2005.
[75] Lyon R H. Statistical energy analysis of dynamical systems: theory and applications[M].Cambridge, MA: MIT press,1975.
[76] Langley R S. A derivation of the coupling loss factors used in statistical energy analysis [J].Journal of Sound and Vibration,1990,141(2):207-219.
[77] Ren W, Keith A. Prediction of sound fields in rooms using statistical energy analysis[J].Applied Acoustics,1991,34(3):207-220.
[78] Chen H. Statistical Energy Analysis Modeling of a Passenger Vehicle[C]. Proc. Inter-Noise95,Newport Beach, CA.1239-1242,1995.
[79] Renji K. On the number of modes required for statistical energy analysis-based calculations [J].Journal of Sound and Vibration,2004,269(3-5):1128-1132.
[80] Wang C, Lai J C S. Discussions on “On the number of modes required for statistical energyanalysis-based calculations”[J]. Journal of Sound and Vibration,2005,281(1-2):475-480.
[81] Mace B R. Statistical energy analysis: coupling loss factors, indirect coupling and systemmodes[J]. Journal of Sound and Vibration,2005,279(1-2):141-170.
[82] Zhou R. Crocker M J. Sound transmission loss of foam-filled honeycomb sandwich panelsusing statistical energy analysis and theoretical and measured dynamic properties[J]. Journal ofSound and Vibration,2010,329(6):673-686.
[83] Cotoni V. Shorter P. Numerical and experimental validation of a hybrid finiteelement-statistical energy analysis method[J]. The Journal of the Acoustical Society ofAmerica,2007,122(1):259-270.
[84]王绍茹,高淑英.统计能量法预测题录声屏障的降噪效果[J].西南交通大学学报,2001,36(6):645-647.
[85]张建润,孙庆鸿,陈南.轿车声学建模的统计能量法[J].中国机械工程,2004,15(20):1865-1868.
[86]伍先俊,朱石坚.统计能量法及其在船舶声振预测中的应用综述[J].武汉理工大学学报(交通科学与工程版),2004,28(2):212-215.
[87]马纪军,张军,兆文忠.统计能量法及其在提速客车噪声预测中的应用[J].大连铁道学院学报,2005,26(1):53-56.
[88]伍先俊,翁雪涛,朱石坚.基于有限元法对比的统计能量法研究[J].振动与冲击,2005,24(1):58-62.
[89]丁少春,朱石坚,楼京俊.运用统计能量法研究壳体的振动与声辐射特性[J].船舶工程,2007,29(6):30-32.
[90]和卫平,陈美霞,高菊,等.基于统计能量法的环肋圆柱壳中、高频振动与声辐射性能数值分析[J].中国舰船研究,2008,3(6):7-12.
[91]陈书明,王登峰,曹晓琳等.车内噪声FE-SEA混合建模及分析方法[J].振动工程学报,2010,23(2):140-144.
[92] Vlahopoulos N, Zhao X. An Approach for Evaluating Power Transfer Coefficients forSpot-Welded Joints in an Energy Finite Element Formulation[J]. Journal of Sound andVibration,1999,220(1):135-154.
[93] Bernhard R J, Huff J E. Structural-Acoustic design at high frequency using the energy finiteelement method [J]. Journal of vibration of acoustics,1999,121(3):295-301.
[94] Borlase G A, Vlahopoulos N. An energy finite element optimization process for reducinghigh-frequency vibration in large-scale structures[J]. Finite elements in analysis and design,2000,36(1):51-67.
[95] Zhang W, Wang A, Vlahopoulos N. Validation of the EFEA Method through Correlation withConventional FEA and SEA Results[J].2001SAE Noise and Vbration Conference, SAE PaperNo.2001-01-1618,2001.
[96] Wang S. Theory and Applications of a Simplified Energy Finite Element Method and ItsSimilarity to SEA[J]. Noise Control Engineering Journal,2002,50(2):63-72.
[97] Zhang W, Wang A, Vlahopoulos N. A vibration analysis of stiffened plates under heavy fluidloading by an energy finite element analysis formulation[J]. Finite elements in analysis anddesign,2005,41(11):1056-1078.
[98] Zhang W, Vlahopoulos N, Wu K. An energy finite element formulation for high-frequencyvibration analysis of externally fluid-loaded cylindrical shells with periodic circumferentialstiffeners subjected to axi-symmetric excitation[J]. Journal of sound and vibration,2005,282(3):679-700.
[99] Yan X. Energy finite element analysis developments for high frequency vibration analysis ofcomposite structures[D].2008.
[100] Vlahopoulos N, Wu K, Medyanik S. Energy Finite Element Analysis for Structural-AcousticDesign of Naval Vehicles[J]. Journal of Ship Production and Design,2012,28(1):42-48.
[101]孙丽萍.能量有限元法研究及其应用[D].2004.
[102]吴轶钢.零阶能量有限元方法及其在船舶结构声辐射中的应用研究[D].2008.
[103]孙丽萍,聂武.能量有限元法在船舶结构中的应用[J].哈尔滨工业大学学报,2008,40(9):1491-1494.
[104]游进,李鸿光,孟光.耦合板结构随机能量有限元分析[J].振动与冲击,2009,28(11):43-46.
[105] Xie M X, Chen H L, Wu J H, et al. Application of energy finite element method tohigh-frequency structural-acoustic coupling of an aircraft cabin with truncated conical shape[J]. Computer Modeling in Engineering&Sciences (CMES),2010,61(1):1-22.
[106] Xie M, Li Y, Chen H. Prediction of High-frequency Vibro-acoustic Coupling in AnechoicChamber Using Energy Finite Element Method and Energy Boundary Element Method[J].Computer Modeling in Engineering&Sciences (CMES),2012,85(1):65-78.
[107] Wang A, Vlahopoulos N, Wu K. An energy boundary element formulation for sound radiationat high frequency[C]. The International Congress and Exposition on Noise ControlEngineering, ASME paper No.2002-405,2002.
[108] Wang A, Vlahopoulos N, Zhu J, et al. An Energy Boundary Element Formulation forPredicting the Acoustic Field around a Vehicle at High Frequencies due to Airborne NoiseSources[J]. Proceedings of ASME IMECE, ASME Paper No. IMECE2003-55334,2003.
[109] Wang A, Vlahopoulos N, Wu K. Development of an energy boundary element formulation forcomputing high-frequency sound radiation from incoherent intensity boundary conditions [J].Journal of Sound and Vibration,2004,278(1):413-436.
[110] Zhang G, Vlahopoulos N. An Energy Based Boundary Element Method for Computing theAcoustic Field around a Vehicle[J]. Ann Arbor,1001:48109-2145.
[111] Zhang G, Vlahopoulos N. Combining an energy boundary element analysis with an energyfinite element analysis for computing airborne noise inside a flexible structure due to anexterior acoustic source[J]. The Journal of the Acoustical Society of America,2006,119(5):3418.
[112] Ma Z D, Hagiwara I. Sensitivity analysis methods for coupled acoustic-structural systems partI. Modal sensitivities[J]. AIAA Journal,1991,29(11):1787-1795.
[113] Ma Z D, Hagiwara I. Sensitivity analysis methods for coupled acoustic-structural systems partII. Direct frequency response and its sensitivities[J]. AIAA Journal,1991,29(11):1796-1801.
[114] Hagiwara I, Kozukue W, Ma Z D. The development of eigenmode sensitivity analysis methodsfor coupled acoustic-structural systems and their application to reduction of vehicle interiornoise[J]. Finite elements in analysis and design,1993,14(2):235-248.
[115] Ma Z D, Hagiwara I. Development of Eigenmode and Frequency Response SensitivityAnalysis Methods for Coupled Acoustic-Structrual Systems[J]. JSME International Journal,SeriesⅢ,1995,35(2):229-235.
[116] Gates A A, Accorsi M L. Automatic shape optimization of three-dimensional shell structureswith large shape changes[J]. Computers&structures,1993,49(1):167-178.
[117] Hambric S.A. Sensitivity Calculations for Broad-Band Acoustic Radiated Noise DesignOptimization Problems[J]. Journal of Vibration and Acoustics,1996,118(3):529-532.
[118] Choi K K, Shim I, Wang S. Design sensitivity analysis of structure-induced noise and vibration[J]. Journal of Vibration and Acoustics,1997,119(3):173-179.
[119] Wang S. Design Sensitivity Analysis of Noise, Vibration, and Harshness of Vehicle BodyStructure[J]. Journal of Structural Mechanics,1999,27(3):317-335.
[120] Scarpa F. Parametric sensitivity analysis of coupled acoustic-structural systems [J]. Journal ofVibration and Acoustics,2000,122(2):109-115.
[121]王登峰,殷涌光,程悦荪,等.拖拉机驾驶室内部噪声响应的灵敏度分析[J].农业机械学报,1993,24(1):25-30.
[122] Wang H W, Gu Y X, Gao J. Sensitivity Analysis and Design Optimization for Sound PressureLevel Integral of Structure-Acoustics System[C]. Proceeding of the Fourth World Congress ofStructural and Multidisciplinary Optimization, June4-8,2001, Dalian, China:120-121.
[123]高剑.声场与结构耦合系统的模态分析与灵敏度计算[D].2002.
[124]王海文.声场结构耦合系统的有限元分析及灵敏度计算[D].2004.
[125]张军,兆文忠,谢素明,等.结构耦合系统声压响应优化设计研究[J].振动工程学报，2005,18(4):519-523.
[126]张军,兆文忠,张维英.声场-结构耦合系统声压约束下板重量优化设计研究[J].应用力学学报,2006,23(4):568-571.
[127]陈钢,赵国忠,顾元宪.声场-结构耦合系统灵敏度分析及优化设计研究[J].振动与冲击,2007,26(4):86-89.
[128]赵冠军,刘更,吴立言.汽车驾驶室声固祸合系统的灵敏度分析[J].机械设计,2008,25(1):53-55.
[129]赵志高,黄其柏,何锃,等.有限元与声辐射模态的薄板声辐射灵敏度分析[J].声学技术,2008,27(3):464-468.
[130] Kane J H, Mao S, Everstine G C. A boundary element formulation for acoustic shapesensitivity analysis[J]. The Journal of the Acoustical Society of America,1991,90(1):561-573.
[131] Grabacki J. Boundary integral equations in sensitivity analysis[J]. Applied mathematicalmodeling,1991,15(4):170-181.
[132] Smith D C, Bernhard R J. Computation of Acoustic Shape Design Sensitivity Using aBoundary Element Method[J]. Journal of Vibration and Acoustics-transactions of The ASME,1992,114(1):127-132.
[133] Vlahopoulos N. Boundary element formulations for acoustic sensitivities with respect tostructural design variable and acoustic impedance[C]. Recent Developments in Air-andStructure-Borne Sound and Vibration,1992,1:1019-1026.
[134] Cunefare K A, Koopmann G H. Acoustic design sensitivity for structural radiators[J]. ASMETransactions Journal of Vibration Acoustics,1992,114(2):178-186.
[135] Matsumoto T, Tanaka M, Miyagawa M, et al. Optimum design of cooling lines in injectionmoulds by using boundary element design sensitivity analysis[J]. Finite elements in analysisand design,1993,14(2):177-185.
[136] Matsumoto T, Tanaka M, Yamada Y. Design sensitivity analysis of steady-state acousticproblems using boundary integral equation formulation[J]. JSME international journal. Ser. C,Dynamics, control, robotics, design and manufacturing,1995,38(1):9-16.
[137] Burczyński T, Kane J H, Balakrishna C. Shape design sensitivity analysis via materialderivative‐adjoint variable technique for3‐D and2‐D curved boundary elements[J].International journal for numerical methods in engineering,1995,38(17):2839-2866.
[138] Koo B U. Shape design sensitivity of acoustic problem using a boundary element method[J].Computers&Structures,1997,65(5):713-719.
[139] Koo B U. Acoustic shape sensitivity analysis using boundary integral equation[J]. The Journalof the Acoustical Society of America,1998,104(5):2851-2860.
[140] Crane S P, Cunefare K A, Engelstad S P, et al. Comparison of design optimization formulationsfor minimization of noise transmission in a cylinder[J]. Journal of aircraft,1997,34(2):236-243.
[141] Christensen S T. Design sensitivity analysis in structural acoustics[C].7thAIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St.Louis, MO: AIAA,1998.
[142] Hahn S R, Ferri A A. Sensitivity analysis of coupled structural-acoustic problems usingperturbation techniques[J]. The Journal of the Acoustical Society of America,1997,101(2):918-918.
[143] Allen M J, Sbzagio R, Vlahopoulos N. Structural/acoustic Sensitivity Analysis of a StructrueSubject to Stochastic Excitation [J]. AIAA Journal,2001,39(7):1270-1279.
[144] Wang S, Lee J. Acoustic design sensitivity analysis and optimization for reduced exterior noise[J]. AIAA journal,2001,39(4):574-580.
[145] Ricardo S. A three-dimensional formulation for deriving the acoustic shape sensitivity usingthe boundary element method[D]. Ann Arbor: University of Michigan,2001.
[146] Marburg S. Efficient optimization of a noise transfer function by modification of a shellstructure geometry–Part I: Theory[J]. Structural and Multidisciplinary Optimization,2002,24(1):51-59.
[147] Zhang Z D, Vlahopoulos N, Raveendra S T. Formulation of a numerical process for acousticimpedance sensitivity analysis based on the indirect boundary element method[J]. Engineeringanalysis with boundary elements,2003,27(7):671-681.
[148] Lee J, Wang S. Shape design sensitivity analysis for the radiated noise from the thin-body[J].Journal of sound and vibration,2003,261(5):895-910.
[149] Kim N H, Dong J, Choi K K, et al. Design sensitivity analysis for sequentialstructural–acoustic problems[J]. Journal of Sound and Vibration,2003,263(3):569-591.
[150] Kim N H, Dong J. Shape sensitivity analysis of sequential structural–acoustic problems usingFEM and BEM[J]. Journal of sound and vibration,2006,290(1):192-208.
[151] Sar gül A S, Secgin A. A study on the applications of the acoustic design sensitivity analysis ofvibrating bodies[J]. Applied Acoustics,2004,65(11):1037-1056.
[152] Dong J, Choi K K, Kim N H. Design optimization for structural-acoustic problems usingFEA-BEA with adjoint variable method[J]. Journal of Mechanical Design,2004,126(3):527-533.
[153] Choi J H, Won J H, Yoon J M. Boundary Method for Shape Design Sensitivity Analysis in theOptimization of Three-Dimensional Elastostatics[C].6thWorld Congresses of Structural andMultidisciplinary Optimization, Rio de Janeiro, Brazil,2005.
[154] Fritze D, Marburg S, Hardtke H J. FEM–BEM-coupling and structural–acoustic sensitivityanalysis for shell geometries[J]. Computers&structures,2005,83(2):143-154.
[155] Rus G, Gallego R. Boundary integral equation for inclusion and cavity shape sensitivity inharmonic electrodynamics[J]. Engineering analysis with boundary elements,2005,29(1):77-91.
[156] Arai Y, Tanaka M, Matsumoto T. A new design sensitivity analysis of acoustic problems basedon BEM avoiding fictitious Eigen frequency issue[J]. Transactions of the Japan Society ofMechanical Engineers Series C,2007,73(729):1392-1399.
[157] Yu Y, Kwak B M. Design sensitivity analysis of acoustical damping and its application todesign of musical bells[J]. Structural and Multidisciplinary Optimization,2011,44(3):421-430.
[158] Brancati A, Aliabadi M H, Mallardo V. A BEM sensitivity formulation for three‐dimensionalactive noise control[J]. International Journal for Numerical Methods in Engineering,2012,90(9):1183-1206.
[159]白杨,汪鸿振.声学-结构设计灵敏度分析[J].振动与冲击,2003,22(03):43-46.
[160]赵志高.结构声辐射的机理与数值方法研究[D].2005.
[161]张军，兆文忠.结构声辐射有限元/边界元法声学一结构灵敏度研究[J].振动工程学报.2005,18(3):366-370.
[162]程昊,高煜,张永斌,等.振动体声学灵敏度分析的边界元法[J].机械工程学报,2008,44(7):45-51.
[163]刘宝山,赵国忠,王剑.基于设计灵敏度分析的圆柱壳声辐射优化[J].大连理工大学学报,2011,51(5):313–319.
[164] Bitsie F, Bernhard R J. Sensitivity Calculations for Structural-Acoustic EFEM Predictions[J].Noise Control Engineering,1998,46(3):91-96.
[165] Bernhard R J, Huff J E. Structural-Acoustic Design at High Frequency Using the Energy FiniteElement Method[J]. Journal of Vibration and Acoustics,1999,121(3):295-301.
[166] Borlase G A, Vlahopoulos N. An Energy Finite Element Optimization Process for ReducingHigh-Frequency Vibration in Large-Scale Structures[J]. Finite Elements in Analysis andDesign,2000,36(1):51-67.
[167] Kim N H, Dong J, Choi K K. Energy flow analysis and design sensitivity of structuralproblems at high frequencies[J]. Journal of sound and vibration,2004,269(1):213-250.
[168] Dong J, Choi K K, Wang A, et al. Parametric design sensitivity analysis of high‐frequencystructural–acoustic problems using energy finite element method[J]. International journal fornumerical methods in engineering,2005,62(1):83-121.
[169] Dong J. Design sensitivity analysis and optimization of high frequency structural-acousticproblems using energy finite element method and energy boundary element method[D].2004.
[170] Dong J, Choi K K, Vlahopoulos N, et al. Sensitivity analysis and optimization using energyfinite element and boundary element methods[J]. AIAA journal,2007,45(6):1187-1198.
[171] Zhang S Y and Chen X Z. The Boundary point method for the calculation of exterior acousticradiation problem[J]. Journal of Sound and Vibration,1999,228(4):761-772.
[172]张胜勇,陈心昭,王有成.分布源边界点法及其在振动体声辐射计算中的应用[J].声学学报,1999,24(2):149-154.
[173]毕传兴.基于分布源边界点法的近场声全息理论与实验研究[D].2004.
[174] Bi C X, Chen J, Chen X Z. Reconstruction and prediction of multi-source acoustic field withthe distributed source boundary point method based nearfield acoustic holography[J]. Sciencein China Series E: Technological Sciences,2004,47(2):216-228.
[175] Bi C X, Chen J, Chen X Z. Distributed Source Boundary Point Method-Based NearfieldAcoustic Holography for Reconstructing the Acoustic Radiation from Arbitrarily ShapedObjects[J]. Journal of Computational Acoustics,2006,14(04):379-395.
[176] Bi C X, Chen X Z, Zhou R, et al. Reconstruction and separation in a semi-free field by usingthe distributed source boundary point method-based nearfield acoustic holography[J]. Journalof vibration and acoustics,2007,129(3):323-329.
[177] Salagame R R, Belegundu A D, Koopman G H. Analytical sensitivity of acoustic powerradiated from plates[J]. Journal of vibration and acoustics,1995,117(1):43-48.
[178] Lamancusa J S. Numerical optimization techniques for structural-acoustic design ofrectangular panels[J]. Computers&structures,1993,48(4):661-675.
[179] Williams E G. Fourier acoustics: Sound radiation and nearfield acoustic holography [M].London: Academic Press.1999.
[180] Maynard J D, Williams E G, Lee Y. Near-field acoustic holography: I. theory of generalizedholography and development of NAH[J]. The Journal of the Acoustic Society of America,1985,78(4):1395-1413.
[181] Veronesi W A, Maynard J D. Near-field acoustic holography (NAH) II. Holographicreconstruction algorithms and computer implemention[J]. The Journal of the Acoustic Societyof America,1987,81(5):1307-1322.
[182] Bi C X, Chen X Z, Zhou R, et al. Landweber iterative regularization for nearfield acousticholography[J]. Chinese Science Bulletin.2006,51(11):1374-1380.
[183] Tikhonov A N. Solution of incorrectly formulated problems and the regularization method[J].Dokl. Acad. Nawk. USSR,1963,151(3):501-504.
[2]杨莉.客车车身结构动力学、声学CAE关键技术研究[D].2005.
[3]张军.声学_结构灵敏度及结构_声学优化设计研究[D].2006.
[4]程昊.基于边界元法的声学灵敏度分析若干关键问题研究[D].2010.
[5]刘宝山.结构振动声辐射灵敏度分析及优化设计研究[D].2010.
[6]郑昌军.三维声学灵敏度分析的宽频快速多级边界元法研究[D].2011.
[7]李善德.大规模声学问题的快速多极边界元方法研究[D].2011
[8]何作镛，赵玉芳.声学理论基础.北京：国防工业出版社，1981.
[9] Lee C., Benkeser P.J. A computationally efficient method for the calculation of the transientfield of acoustic radiators[J]. Journal of the Acoustical Society of America.1994,96(1):545-551.
[10] Mitzner K M. Numerical solutions for transient scattering from a hard surface of arbitraryshape—retarded potential technical[J]. Journal of the Acoustical Society of America.1967,42:1305-1313.
[11] Hu Q, Wu S F. Sound radiation from a finite cylinder[C], Proceedings of the ASME NoiseControl and Acoustics Division,1996,22:39-45.
[12] Hu Q, Wu S F. An explicit integral formulation for transient acoustic radiation[J]. The Journalof the Acoustical Society of America.1998,104(6):3251-3258.
[13]余爱萍.瞬态声振耦合问题的边界元分析和实验研究[D].1988.
[14]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,1989,23(3):82-89.
[15] Wu T W, Ciskowski R D, Seybert A F. Vectorization and parallelization of the acousticboundary element code BEMAP on the IBM ES/3090VF[J]. Engineering Analysis withBoundary Element,1992,10(1):17-26.
[16] Harris P J, Amini S. On the Burton and Miller boundary integral formulation of the exterioracoustic problem[J]. Transactions of the ASME.1992,114:540-545.
[17]赵键,汪鸿振,朱物华.边界元方法计算已知振速封闭面的声辐射[J].声学学报,1989,14(4):250-257.
[18]王有成,刘钊,吴约.边界元技术中的全特解场方法[C].第四届全国工程中的边界元方法学术会议论文集,南京:河海大学出版社,1994.
[19]高耀南,韩玉雄,沈文钧.关于时域边界元方法的若干研究[J].应用力学学报,1993,l0(4):60-64.
[20] Bitsie F. The Structural-Acoustic Energy Finite Element Method and Energy BoundaryElement Method[D].1996.
[21] Zienkiewicz O C, Taylor R L. The finite element method [M]. London: McGraw-hill,1977.
[22] Reddy J N. An introduction to the finite element method[M]. New York: McGraw-Hill,2006.
[23] Dhatt G, Touzot G. Finite Element Method[M]. John Wiley&Sons,2012.
[24] Smith R R, Hunt J T, Barach D. Finite element analysis of acoustically radiating structureswith application to sonar transducers[J]. The Journal of the Acoustical Society of America,1973,54:1277-1288.
[25] Tetambe R P, Rajakumar C. A simplified finite element method for studying acousticcharacteristics inside a car cavity[J]. Journal of Sound and Vibration,1979,63(1):61-72.
[26] Nefske D J, Wolf J A, HowellL J. Structural-acoustic finite element analysis of the automobilepassenger compartment: a review of current practice[J]. Journal of Sound and Vibration,1982,80(3):247-266.
[27] Kagawa Y, Yamabuchi T, Sugihara K., et al. Loudspeaker characteristic calculation by thefinite element method—Comparison with measured results[J]. Journal of Sound and Vibration,1983,91(4):604-607.
[28] Tetambe R P, Rajakumar C. Estimation of error in finite element acoustic analysis[J].Computers&Structures,1996,61(1):13-19.
[29] Thompson L L. A review of finite-element methods for time-harmonic acoustics[J]. Journal ofthe Acoustical Society of America,2006,119(3):1315-1330.
[30] Harari I. A survey of finite element methods for time-harmonic acoustics[J]. ComputerMethods in Applied Mechanics and Engineering,2006,195(13-16):1594-1607.
[31]朱才朝,秦大同,李润方.车身结构振动与车内噪声声场混合分析与控制[J].机械工程学报,2002,38(8):54-58.
[32]杨莉,孙庆鸿.自由阻尼处理结构的有限元建模及声辐射分析[J].振动工程学报,2004,17(3):306-310.
[33]陈军明,陈应波,黄玉盈.水中双向正交加肋圆柱壳体声辐射的有限元法[J].武汉理工大学学报,2004,26(4):74-76.
[34] Kirkup S. The boundary element method in acoustics[M]. Hebden Bridge: Integrated SoundSoftware,1998.
[35] Wu T W. Boundary element acoustics: fundamentals and computer codes[M]. Southampton,UK; Boston: WIT Press,2000.
[36] Schanz M, Steinbach O. Boundary Element Analysis[M]. New York: Springer-Verlag BerlinHeidelberg,2007.
[37] Beer G, Smith I M, Duenser C. The boundary element method with programming: forengineers and scientists[M]. Wien; New York: Springer,2008.
[38]王元淳.边界元法基础[M].上海:上海交通大学出版社,1988.
[39]杜庆华.边界积分方程方法-边界元法[M].北京:高等教育出版社,1989.
[40]申光宪.边界元法[M].北京:机械工业出版社,1998.
[41] Chen L H, Schweikert D G. Sound Radiation from an Arbitrary Body[J]. The Journal of theAcoustical Society of America,1963,35(10):1626-1632.
[42] Chertock G. Sound Radiation from Vibrating Surfaces[J]. The Journal of the AcousticalSociety of America,1964,36(7):1305-1313.
[43] Schenck H A. Improved integral formulation for acoustic radiation problems[J]. The Journal ofthe Acoustical Society of America,1968,44(1):41-58.
[44] Seybert A F, Rengarajan T K. The use of CHIEF to obtain unique solutions for acousticradiation using boundary integral equations[J]. The Journal of the Acoustical Society ofAmerica,1987,81(5):1299-1306.
[45] Wu T W, Seybert A F. A weighted residual formulation for the CHIEF method in acoustics [J].The Journal of the Acoustical Society of America,1991,90(3):1608-1614.
[46] Lee L, Wu T W. An enhanced CHIEF method for steady-state elastodynamics[J]. EngineeringAnalysis with Boundary Element,1993,12(2):75-83.
[47] Juhl P. A numerical study of the coefficient matrix of the boundary element method nearcharacteristic frequencies[J]. Journal of Sound and Vibration,1994,175(1):39-50.
[48] Li W L, Wu T W, Seybert A F. A half-space boundary element method for acoustic problemswith a reflecting plane of arbitrary impedance[J]. Journal of Sound and Vibration,1994,171(2):173-184.
[49] Park J M, Eversman W. A Boundary Element Method For Propagation Over AbsorbingBoundaries[J]. Journal of Sound and Vibration,1994,175(2):197-218.
[50] Burton A J, Miller G F. The Application of Integral Equation Methods to the NumericalSolution of Some Exterior Boundary-Value Problems [J]. Proceedings of the Royal Society ofLondon Series A-Mathematical and Physical Sciences,1971,323(1553):201-210.
[51] Chien C C, Rajiyah H, Atluri S N. An effective method for solving the hyper-singular integralequations in3-D acoustics[J]. Journal of the Acoustical Society of America,1990,88(2):918-937.
[52] Yan Z Y, Hung K C, Zheng H. Solving the hypersingular boundary integral equation inthree-dimensional acoustics using a regularization relationship[J]. Journal of the AcousticalSociety of America,2003,113(5):2674-2683.
[53] Kress R. Minimizing the condition number of boundary integral operators in acoustic andelectromagnetic scattering[J]. The Quarterly Journal of Mechanics and Applied Mathematics,1985,38(2):323-341.
[54] Amini S. On the chose of the coupling parameter in boundary integral formulations of theexterior acoustic problem[J]. Applicable analysis,1990,35(1-4):75-92.
[55] Cunefare K A, Koopmann G, Brod K. A boundary element method for acoustic radiation validfor all wavenumbers[J]. The Journal of the Acoustical Society of America,1989,85(1):39-48.
[56] Meyer W L, Bell W A, Zinn B T, et al. Boundary integral solutions of three dimensionalacoustic radiation problems[J]. Journal of Sound and Vibration,1978,59(2):245-262.
[57] Reut Z. On the boundary integral methods for the exterior acoustic problem[J]. Journal ofSound and Vibration,1985,103(2):297-298.
[58] Tobocman W. Extension of the Helmholtz integral equation method to shorter wavelengths[J].The Journal of the Acoustic Society of America.1986,80(6):1828-1837.
[59] Amini S. Harcis P J. A comparison between various boundary integral formulations of theexterior acoustic problem[J]. Computer Methods in Applied Mechanics Engineering,1990,84(1):59-75.
[60] Marburg S, Amini S. Cat's eye radiation with boundary elements: Comparative study ontreatment of irregular frequencies[J]. Journal of Computational Acoustics,2005,13(1):21-45.
[61] Cheng C Y R, Seybert A F, Wu T W. Multidomain boundary element solution for silencer andmuffler performance prediction[J]. Journal of Sound and Vibration,1991,151(1):119-129.
[62] Wu T W, Wan G C. Muffler performance studies using a direct mixed-body boundary elementmethod and a three-point method for evaluating transmission loss[J]. Journal of Vibration andAcoustics,1996,118(3):479-484.
[63] Wu T W, Cheng C Y R, Zhang P. A direct mixed-body boundary element method for packedsilencers[J]. The Journal of the Acoustical Society of America,2002,111(6):2566-2572.
[64] Pan K L, Chu C I, Wu T W. A direct mixed-body boundary element method for mufflers withinternal thin components covered by lining and a perforated panel[J]. Journal of ComputationalAcoustics,2007,15(1):145-157.
[65] Liu Y. Fast multipole boundary element method: theory and applications in engineering[M].Cambridge; New York: Cambridge University Press,2009.
[66] Chen Z S, Waubke H, Kreuzer W. A formulation of the fast multipole boundary elementmethod for acoustic radiation and scattering from three-dimensional structures[J]. Journal ofComputational Acoustics,2008,16(2):303-320.
[67] Fischer M, Gaul L. Application of the fast multipole bem for structural-acoustic simulations[J].Journal of Computational Acoustics,2005,13(1):87-98.
[68]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,2000,40(4):391-394.
[69]闰再友,姜揖,严明.利用边界元法计算无界声场中结构体声辐射[J].上海交通大学学报,2000,34(4):520-523.
[70]王秀峰,陈心昭.进一步改进边界元方法以克服振动声辐射计算中解的非唯一性[J].应用声学,2001,21(3):2-5.
[71]王炳和,相敬林.舰船水下声场边界元法建模与计算机模拟[J].计算机工程与应用,2004,40(7):217-210.
[72]李宏伟,文立华,陈克安.非光滑结构表面声学边界元法中奇异积分计算方法[J].西北工业大学学报,2006,24(4):498-500.
[73] Coyette J P, Fyfe K R. Improved formulation for acoustic eigenmode extraction from boundaryelement models[J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design,1990,112(3):392-397.
[74]赵志高.结构声辐射的机理与数值方法研究[D].2005.
[75] Lyon R H. Statistical energy analysis of dynamical systems: theory and applications[M].Cambridge, MA: MIT press,1975.
[76] Langley R S. A derivation of the coupling loss factors used in statistical energy analysis [J].Journal of Sound and Vibration,1990,141(2):207-219.
[77] Ren W, Keith A. Prediction of sound fields in rooms using statistical energy analysis[J].Applied Acoustics,1991,34(3):207-220.
[78] Chen H. Statistical Energy Analysis Modeling of a Passenger Vehicle[C]. Proc. Inter-Noise95,Newport Beach, CA.1239-1242,1995.
[79] Renji K. On the number of modes required for statistical energy analysis-based calculations [J].Journal of Sound and Vibration,2004,269(3-5):1128-1132.
[80] Wang C, Lai J C S. Discussions on “On the number of modes required for statistical energyanalysis-based calculations”[J]. Journal of Sound and Vibration,2005,281(1-2):475-480.
[81] Mace B R. Statistical energy analysis: coupling loss factors, indirect coupling and systemmodes[J]. Journal of Sound and Vibration,2005,279(1-2):141-170.
[82] Zhou R. Crocker M J. Sound transmission loss of foam-filled honeycomb sandwich panelsusing statistical energy analysis and theoretical and measured dynamic properties[J]. Journal ofSound and Vibration,2010,329(6):673-686.
[83] Cotoni V. Shorter P. Numerical and experimental validation of a hybrid finiteelement-statistical energy analysis method[J]. The Journal of the Acoustical Society ofAmerica,2007,122(1):259-270.
[84]王绍茹,高淑英.统计能量法预测题录声屏障的降噪效果[J].西南交通大学学报,2001,36(6):645-647.
[85]张建润,孙庆鸿,陈南.轿车声学建模的统计能量法[J].中国机械工程,2004,15(20):1865-1868.
[86]伍先俊,朱石坚.统计能量法及其在船舶声振预测中的应用综述[J].武汉理工大学学报(交通科学与工程版),2004,28(2):212-215.
[87]马纪军,张军,兆文忠.统计能量法及其在提速客车噪声预测中的应用[J].大连铁道学院学报,2005,26(1):53-56.
[88]伍先俊,翁雪涛,朱石坚.基于有限元法对比的统计能量法研究[J].振动与冲击,2005,24(1):58-62.
[89]丁少春,朱石坚,楼京俊.运用统计能量法研究壳体的振动与声辐射特性[J].船舶工程,2007,29(6):30-32.
[90]和卫平,陈美霞,高菊,等.基于统计能量法的环肋圆柱壳中、高频振动与声辐射性能数值分析[J].中国舰船研究,2008,3(6):7-12.
[91]陈书明,王登峰,曹晓琳等.车内噪声FE-SEA混合建模及分析方法[J].振动工程学报,2010,23(2):140-144.
[92] Vlahopoulos N, Zhao X. An Approach for Evaluating Power Transfer Coefficients forSpot-Welded Joints in an Energy Finite Element Formulation[J]. Journal of Sound andVibration,1999,220(1):135-154.
[93] Bernhard R J, Huff J E. Structural-Acoustic design at high frequency using the energy finiteelement method [J]. Journal of vibration of acoustics,1999,121(3):295-301.
[94] Borlase G A, Vlahopoulos N. An energy finite element optimization process for reducinghigh-frequency vibration in large-scale structures[J]. Finite elements in analysis and design,2000,36(1):51-67.
[95] Zhang W, Wang A, Vlahopoulos N. Validation of the EFEA Method through Correlation withConventional FEA and SEA Results[J].2001SAE Noise and Vbration Conference, SAE PaperNo.2001-01-1618,2001.
[96] Wang S. Theory and Applications of a Simplified Energy Finite Element Method and ItsSimilarity to SEA[J]. Noise Control Engineering Journal,2002,50(2):63-72.
[97] Zhang W, Wang A, Vlahopoulos N. A vibration analysis of stiffened plates under heavy fluidloading by an energy finite element analysis formulation[J]. Finite elements in analysis anddesign,2005,41(11):1056-1078.
[98] Zhang W, Vlahopoulos N, Wu K. An energy finite element formulation for high-frequencyvibration analysis of externally fluid-loaded cylindrical shells with periodic circumferentialstiffeners subjected to axi-symmetric excitation[J]. Journal of sound and vibration,2005,282(3):679-700.
[99] Yan X. Energy finite element analysis developments for high frequency vibration analysis ofcomposite structures[D].2008.
[100] Vlahopoulos N, Wu K, Medyanik S. Energy Finite Element Analysis for Structural-AcousticDesign of Naval Vehicles[J]. Journal of Ship Production and Design,2012,28(1):42-48.
[101]孙丽萍.能量有限元法研究及其应用[D].2004.
[102]吴轶钢.零阶能量有限元方法及其在船舶结构声辐射中的应用研究[D].2008.
[103]孙丽萍,聂武.能量有限元法在船舶结构中的应用[J].哈尔滨工业大学学报,2008,40(9):1491-1494.
[104]游进,李鸿光,孟光.耦合板结构随机能量有限元分析[J].振动与冲击,2009,28(11):43-46.
[105] Xie M X, Chen H L, Wu J H, et al. Application of energy finite element method tohigh-frequency structural-acoustic coupling of an aircraft cabin with truncated conical shape[J]. Computer Modeling in Engineering&Sciences (CMES),2010,61(1):1-22.
[106] Xie M, Li Y, Chen H. Prediction of High-frequency Vibro-acoustic Coupling in AnechoicChamber Using Energy Finite Element Method and Energy Boundary Element Method[J].Computer Modeling in Engineering&Sciences (CMES),2012,85(1):65-78.
[107] Wang A, Vlahopoulos N, Wu K. An energy boundary element formulation for sound radiationat high frequency[C]. The International Congress and Exposition on Noise ControlEngineering, ASME paper No.2002-405,2002.
[108] Wang A, Vlahopoulos N, Zhu J, et al. An Energy Boundary Element Formulation forPredicting the Acoustic Field around a Vehicle at High Frequencies due to Airborne NoiseSources[J]. Proceedings of ASME IMECE, ASME Paper No. IMECE2003-55334,2003.
[109] Wang A, Vlahopoulos N, Wu K. Development of an energy boundary element formulation forcomputing high-frequency sound radiation from incoherent intensity boundary conditions [J].Journal of Sound and Vibration,2004,278(1):413-436.
[110] Zhang G, Vlahopoulos N. An Energy Based Boundary Element Method for Computing theAcoustic Field around a Vehicle[J]. Ann Arbor,1001:48109-2145.
[111] Zhang G, Vlahopoulos N. Combining an energy boundary element analysis with an energyfinite element analysis for computing airborne noise inside a flexible structure due to anexterior acoustic source[J]. The Journal of the Acoustical Society of America,2006,119(5):3418.
[112] Ma Z D, Hagiwara I. Sensitivity analysis methods for coupled acoustic-structural systems partI. Modal sensitivities[J]. AIAA Journal,1991,29(11):1787-1795.
[113] Ma Z D, Hagiwara I. Sensitivity analysis methods for coupled acoustic-structural systems partII. Direct frequency response and its sensitivities[J]. AIAA Journal,1991,29(11):1796-1801.
[114] Hagiwara I, Kozukue W, Ma Z D. The development of eigenmode sensitivity analysis methodsfor coupled acoustic-structural systems and their application to reduction of vehicle interiornoise[J]. Finite elements in analysis and design,1993,14(2):235-248.
[115] Ma Z D, Hagiwara I. Development of Eigenmode and Frequency Response SensitivityAnalysis Methods for Coupled Acoustic-Structrual Systems[J]. JSME International Journal,SeriesⅢ,1995,35(2):229-235.
[116] Gates A A, Accorsi M L. Automatic shape optimization of three-dimensional shell structureswith large shape changes[J]. Computers&structures,1993,49(1):167-178.
[117] Hambric S.A. Sensitivity Calculations for Broad-Band Acoustic Radiated Noise DesignOptimization Problems[J]. Journal of Vibration and Acoustics,1996,118(3):529-532.
[118] Choi K K, Shim I, Wang S. Design sensitivity analysis of structure-induced noise and vibration[J]. Journal of Vibration and Acoustics,1997,119(3):173-179.
[119] Wang S. Design Sensitivity Analysis of Noise, Vibration, and Harshness of Vehicle BodyStructure[J]. Journal of Structural Mechanics,1999,27(3):317-335.
[120] Scarpa F. Parametric sensitivity analysis of coupled acoustic-structural systems [J]. Journal ofVibration and Acoustics,2000,122(2):109-115.
[121]王登峰,殷涌光,程悦荪,等.拖拉机驾驶室内部噪声响应的灵敏度分析[J].农业机械学报,1993,24(1):25-30.
[122] Wang H W, Gu Y X, Gao J. Sensitivity Analysis and Design Optimization for Sound PressureLevel Integral of Structure-Acoustics System[C]. Proceeding of the Fourth World Congress ofStructural and Multidisciplinary Optimization, June4-8,2001, Dalian, China:120-121.
[123]高剑.声场与结构耦合系统的模态分析与灵敏度计算[D].2002.
[124]王海文.声场结构耦合系统的有限元分析及灵敏度计算[D].2004.
[125]张军,兆文忠,谢素明,等.结构耦合系统声压响应优化设计研究[J].振动工程学报，2005,18(4):519-523.
[126]张军,兆文忠,张维英.声场-结构耦合系统声压约束下板重量优化设计研究[J].应用力学学报,2006,23(4):568-571.
[127]陈钢,赵国忠,顾元宪.声场-结构耦合系统灵敏度分析及优化设计研究[J].振动与冲击,2007,26(4):86-89.
[128]赵冠军,刘更,吴立言.汽车驾驶室声固祸合系统的灵敏度分析[J].机械设计,2008,25(1):53-55.
[129]赵志高,黄其柏,何锃,等.有限元与声辐射模态的薄板声辐射灵敏度分析[J].声学技术,2008,27(3):464-468.
[130] Kane J H, Mao S, Everstine G C. A boundary element formulation for acoustic shapesensitivity analysis[J]. The Journal of the Acoustical Society of America,1991,90(1):561-573.
[131] Grabacki J. Boundary integral equations in sensitivity analysis[J]. Applied mathematicalmodeling,1991,15(4):170-181.
[132] Smith D C, Bernhard R J. Computation of Acoustic Shape Design Sensitivity Using aBoundary Element Method[J]. Journal of Vibration and Acoustics-transactions of The ASME,1992,114(1):127-132.
[133] Vlahopoulos N. Boundary element formulations for acoustic sensitivities with respect tostructural design variable and acoustic impedance[C]. Recent Developments in Air-andStructure-Borne Sound and Vibration,1992,1:1019-1026.
[134] Cunefare K A, Koopmann G H. Acoustic design sensitivity for structural radiators[J]. ASMETransactions Journal of Vibration Acoustics,1992,114(2):178-186.
[135] Matsumoto T, Tanaka M, Miyagawa M, et al. Optimum design of cooling lines in injectionmoulds by using boundary element design sensitivity analysis[J]. Finite elements in analysisand design,1993,14(2):177-185.
[136] Matsumoto T, Tanaka M, Yamada Y. Design sensitivity analysis of steady-state acousticproblems using boundary integral equation formulation[J]. JSME international journal. Ser. C,Dynamics, control, robotics, design and manufacturing,1995,38(1):9-16.
[137] Burczyński T, Kane J H, Balakrishna C. Shape design sensitivity analysis via materialderivative‐adjoint variable technique for3‐D and2‐D curved boundary elements[J].International journal for numerical methods in engineering,1995,38(17):2839-2866.
[138] Koo B U. Shape design sensitivity of acoustic problem using a boundary element method[J].Computers&Structures,1997,65(5):713-719.
[139] Koo B U. Acoustic shape sensitivity analysis using boundary integral equation[J]. The Journalof the Acoustical Society of America,1998,104(5):2851-2860.
[140] Crane S P, Cunefare K A, Engelstad S P, et al. Comparison of design optimization formulationsfor minimization of noise transmission in a cylinder[J]. Journal of aircraft,1997,34(2):236-243.
[141] Christensen S T. Design sensitivity analysis in structural acoustics[C].7thAIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St.Louis, MO: AIAA,1998.
[142] Hahn S R, Ferri A A. Sensitivity analysis of coupled structural-acoustic problems usingperturbation techniques[J]. The Journal of the Acoustical Society of America,1997,101(2):918-918.
[143] Allen M J, Sbzagio R, Vlahopoulos N. Structural/acoustic Sensitivity Analysis of a StructrueSubject to Stochastic Excitation [J]. AIAA Journal,2001,39(7):1270-1279.
[144] Wang S, Lee J. Acoustic design sensitivity analysis and optimization for reduced exterior noise[J]. AIAA journal,2001,39(4):574-580.
[145] Ricardo S. A three-dimensional formulation for deriving the acoustic shape sensitivity usingthe boundary element method[D]. Ann Arbor: University of Michigan,2001.
[146] Marburg S. Efficient optimization of a noise transfer function by modification of a shellstructure geometry–Part I: Theory[J]. Structural and Multidisciplinary Optimization,2002,24(1):51-59.
[147] Zhang Z D, Vlahopoulos N, Raveendra S T. Formulation of a numerical process for acousticimpedance sensitivity analysis based on the indirect boundary element method[J]. Engineeringanalysis with boundary elements,2003,27(7):671-681.
[148] Lee J, Wang S. Shape design sensitivity analysis for the radiated noise from the thin-body[J].Journal of sound and vibration,2003,261(5):895-910.
[149] Kim N H, Dong J, Choi K K, et al. Design sensitivity analysis for sequentialstructural–acoustic problems[J]. Journal of Sound and Vibration,2003,263(3):569-591.
[150] Kim N H, Dong J. Shape sensitivity analysis of sequential structural–acoustic problems usingFEM and BEM[J]. Journal of sound and vibration,2006,290(1):192-208.
[151] Sar gül A S, Secgin A. A study on the applications of the acoustic design sensitivity analysis ofvibrating bodies[J]. Applied Acoustics,2004,65(11):1037-1056.
[152] Dong J, Choi K K, Kim N H. Design optimization for structural-acoustic problems usingFEA-BEA with adjoint variable method[J]. Journal of Mechanical Design,2004,126(3):527-533.
[153] Choi J H, Won J H, Yoon J M. Boundary Method for Shape Design Sensitivity Analysis in theOptimization of Three-Dimensional Elastostatics[C].6thWorld Congresses of Structural andMultidisciplinary Optimization, Rio de Janeiro, Brazil,2005.
[154] Fritze D, Marburg S, Hardtke H J. FEM–BEM-coupling and structural–acoustic sensitivityanalysis for shell geometries[J]. Computers&structures,2005,83(2):143-154.
[155] Rus G, Gallego R. Boundary integral equation for inclusion and cavity shape sensitivity inharmonic electrodynamics[J]. Engineering analysis with boundary elements,2005,29(1):77-91.
[156] Arai Y, Tanaka M, Matsumoto T. A new design sensitivity analysis of acoustic problems basedon BEM avoiding fictitious Eigen frequency issue[J]. Transactions of the Japan Society ofMechanical Engineers Series C,2007,73(729):1392-1399.
[157] Yu Y, Kwak B M. Design sensitivity analysis of acoustical damping and its application todesign of musical bells[J]. Structural and Multidisciplinary Optimization,2011,44(3):421-430.
[158] Brancati A, Aliabadi M H, Mallardo V. A BEM sensitivity formulation for three‐dimensionalactive noise control[J]. International Journal for Numerical Methods in Engineering,2012,90(9):1183-1206.
[159]白杨,汪鸿振.声学-结构设计灵敏度分析[J].振动与冲击,2003,22(03):43-46.
[160]赵志高.结构声辐射的机理与数值方法研究[D].2005.
[161]张军，兆文忠.结构声辐射有限元/边界元法声学一结构灵敏度研究[J].振动工程学报.2005,18(3):366-370.
[162]程昊,高煜,张永斌,等.振动体声学灵敏度分析的边界元法[J].机械工程学报,2008,44(7):45-51.
[163]刘宝山,赵国忠,王剑.基于设计灵敏度分析的圆柱壳声辐射优化[J].大连理工大学学报,2011,51(5):313–319.
[164] Bitsie F, Bernhard R J. Sensitivity Calculations for Structural-Acoustic EFEM Predictions[J].Noise Control Engineering,1998,46(3):91-96.
[165] Bernhard R J, Huff J E. Structural-Acoustic Design at High Frequency Using the Energy FiniteElement Method[J]. Journal of Vibration and Acoustics,1999,121(3):295-301.
[166] Borlase G A, Vlahopoulos N. An Energy Finite Element Optimization Process for ReducingHigh-Frequency Vibration in Large-Scale Structures[J]. Finite Elements in Analysis andDesign,2000,36(1):51-67.
[167] Kim N H, Dong J, Choi K K. Energy flow analysis and design sensitivity of structuralproblems at high frequencies[J]. Journal of sound and vibration,2004,269(1):213-250.
[168] Dong J, Choi K K, Wang A, et al. Parametric design sensitivity analysis of high‐frequencystructural–acoustic problems using energy finite element method[J]. International journal fornumerical methods in engineering,2005,62(1):83-121.
[169] Dong J. Design sensitivity analysis and optimization of high frequency structural-acousticproblems using energy finite element method and energy boundary element method[D].2004.
[170] Dong J, Choi K K, Vlahopoulos N, et al. Sensitivity analysis and optimization using energyfinite element and boundary element methods[J]. AIAA journal,2007,45(6):1187-1198.
[171] Zhang S Y and Chen X Z. The Boundary point method for the calculation of exterior acousticradiation problem[J]. Journal of Sound and Vibration,1999,228(4):761-772.
[172]张胜勇,陈心昭,王有成.分布源边界点法及其在振动体声辐射计算中的应用[J].声学学报,1999,24(2):149-154.
[173]毕传兴.基于分布源边界点法的近场声全息理论与实验研究[D].2004.
[174] Bi C X, Chen J, Chen X Z. Reconstruction and prediction of multi-source acoustic field withthe distributed source boundary point method based nearfield acoustic holography[J]. Sciencein China Series E: Technological Sciences,2004,47(2):216-228.
[175] Bi C X, Chen J, Chen X Z. Distributed Source Boundary Point Method-Based NearfieldAcoustic Holography for Reconstructing the Acoustic Radiation from Arbitrarily ShapedObjects[J]. Journal of Computational Acoustics,2006,14(04):379-395.
[176] Bi C X, Chen X Z, Zhou R, et al. Reconstruction and separation in a semi-free field by usingthe distributed source boundary point method-based nearfield acoustic holography[J]. Journalof vibration and acoustics,2007,129(3):323-329.
[177] Salagame R R, Belegundu A D, Koopman G H. Analytical sensitivity of acoustic powerradiated from plates[J]. Journal of vibration and acoustics,1995,117(1):43-48.
[178] Lamancusa J S. Numerical optimization techniques for structural-acoustic design ofrectangular panels[J]. Computers&structures,1993,48(4):661-675.
[179] Williams E G. Fourier acoustics: Sound radiation and nearfield acoustic holography [M].London: Academic Press.1999.
[180] Maynard J D, Williams E G, Lee Y. Near-field acoustic holography: I. theory of generalizedholography and development of NAH[J]. The Journal of the Acoustic Society of America,1985,78(4):1395-1413.
[181] Veronesi W A, Maynard J D. Near-field acoustic holography (NAH) II. Holographicreconstruction algorithms and computer implemention[J]. The Journal of the Acoustic Societyof America,1987,81(5):1307-1322.
[182] Bi C X, Chen X Z, Zhou R, et al. Landweber iterative regularization for nearfield acousticholography[J]. Chinese Science Bulletin.2006,51(11):1374-1380.
[183] Tikhonov A N. Solution of incorrectly formulated problems and the regularization method[J].Dokl. Acad. Nawk. USSR,1963,151(3):501-504.