声障板对矢量传感器指向性的影响研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
近年來,由于声矢:E传感器可以同时拾取声场的标量和矢量信息,被广泛地应用于水声技术的各个领域。随着矢量传感器性能的提高和信号处理技术的发展,其在拖曳线列阵、浮标、低噪声测量系统的应用円益成熟。但是,在这些应用中,矢量传感器都工作于自由场中,并没有受到邻近边界条件的影响。矢量传感器如果安装在舰艇壳体,水下无人航行体时,不可避免的会受到边界衍射的影响,从而影响矢量传感器的测量效果,
     本文分析了不同频率下球形、长旋转椭球形、有限长圆柱障板对矢量传感器指向性的影响,在此基础上研究了障板的尺寸和形状对矢量传感器指向性的影响’给出了优化的障板结构,并提出了矢量传感器指向性重建技术。本文研究内容主要有以下儿点:
     ].推导了阻抗球和弹性球壳散射声场声压和振速的数学表达式,分析了不同频率、阻抗条件下阻抗球以及不同频率下内充空气弹性球壳散射声场声压和振速的指向性的特点。对阻抗球而言,阻抗对散射声场的影响由散射背景项决定,分析丁矢量传感器声E和振速的指向性随阻抗的变化规律以及绝对软球和刚?球的散射场和入射场的幅值、相位差随频率的变化关系.对内充空气弹性球壳而言,散射声场可视为刚硬球散射声场和球壳作弹性振动时辐射声场的代数和,分析了不同频率下弹性球壳障板下矢量传感器指向性的变化规律以及散射场和入射场的幅倍、相位差随频率的变化关系。
     2.推导了软长旋转椭球和硬长旋转椭球散射场声IE和振速的数学表达式,分析了不同频率下软长旋转椭球和硬长旋转椭球障板下矢量传感器声压和振速指向性的特点以及散射场和入射场的幅度、相位差随频率和入射角的变化规律。
     3.利用有限元和边界元法计算了不同频率下软有限长圆柱,硬有限长圆柱,内充空气的弹性有限长圆柱壳的散射声压场和振速场,分析了不同频率下软有限长圆柱,硬有限长圆柱,内充空气的弹性有限长圆柱壳障板下矢量传感器指向性的变化规律以及散射场和入射场的幅度和相位差随频率变化关系。
     4.矢I传感器的指向性与障板的尺寸和形状有密切关系。分析了不同频率下.拉有相同纵向和横向尺寸的球,长旋转椭球,有限长圆柱障板对矢量传感器指向性的影响,在此基础上,设计合理的障板结构,减小障板散射声场对矢量传感器指性的影响。
     5.矢量传感器在障板上的安装位置对其指向性有很大影响。选择合理的矢蒉传感器安装位置,可减小散射场对矢量传感器指向性的影响。
     6.根据仿真进行实验验证。在千岛湖进行了障板对矢跫传感器指向性影响的相关实验,分析比较仿真与实验结果。
     7.提出了障板条件下矢贽传感器指向性重建技术。合理的障板形状和尺寸以及合理的矢量传感器安装位K只能减小散射声场对矢量传感器指向性的影响.而很难从根本上消除散射声场带來的影响。提出釆用声场分离的方法将散射波和入射波分离,重建矢量传感器的指向性。
In recent years, since it could simultaneously pick up the scalar and vectorinformation of the sound field, acoustic vector sensor is widely used in underwateracoustic technical fields. In many applications the vector sensor works in the rfee ifeldwith no effects of the boundary conditions. If the vector sensor is installed on shipshell or unmanned underwater vehicle, it will be inevitably affected by the sounddiffraction, thus affecting its measuring results.
     This paper analyzes effects of the directivity of vector sensor under the conditionof baffle in shape of sphere, prolate spheroid, finite cylinder at different frequencies.Based on that, it studies the effects of the shape and size of the baffle on thedirectivity of vector sensor, and gives out the optimized shape of the baffle, andproposes the reconstructing technique of the directivity of vector sensor. The keycontributions are:
     1. This paper deduces the mathematical expression of sound pressure andvibration velocity in the scatting fields of impedance sphere and elastic spherical shellIt also analyzes characteristic of the directivity of pressure and vibration velocity ofthe impedance sphere at different frequencies and impedance conditions, as well asthat of the scatting field of air-filled elastic spherical shell at different frequencies. Interms of impedance ball, the effect of impedance on scatting field is determined by thescattering background. The paper analyzes the change law of the directivity ofpressure and vibration velocity of vector sensor with the impedance and the changerelationship between frequencies and the amplitude as well as the phase difference ofincident and scatting fields of absolute soft sphere and rigid sphere,For the elasticspherical shell iflled with air, the scatting field can be seen as the algebra addition ofrigid sphere scatting field and vibrating elastic spherical shell radiating field Thepaper analyzes the change law of directivity of vector sensor under the condition ofelastic spherical shell baffle at different frequencies, together with the changerelationship between frequencies and the amplitude as well as the phase difference ofscatting and incident ifelds.
     2, The paper deduces the mathematical expression of sound pressure andvibration velocity in the scatting ifelds of soft and rigid prolate spheroid. It alsoanalyzes characteristic of the directivity of pressure and vibration velocity of vectorsensor under the condition of soft and rigid prolate spheroidal baffle at different frequencies, together with the change law between the incident angle and theamplitude as well as the phase difference of scatting and incident ifelds.
     3. Using the method of infinite and boundary elements, the paper calculates thescatting pressure and vibration velocity fields of soft ifnite cylinder, rigid finitecylinder and air-filled elastic finite cylindrical shell at different frequencies. It givesout the change law of characteristic of the directivity of vector sensor under thecondition of soft finite cylinder, rigid finite cylinder and air-iflled elastic finitecylindrical shell baflfe at different frequencies, together with the change relationshipbetween frequencies and the amplitude as well as the phase difference of scatting andincident ifelds.
     4. The size and shape of the balffe are closely related to the directivity of vectorsensor. The paper analyzes effects of the directivity of vector sensor under thecondition of balffe in shape of the sphere with the same vertical and hoirzontaldimensions, long rotating ellipsoid, finite cylinder. Based on that, the paper designsthe reasonable baffle structure to reduce the effects of the scatting field on thedirectivity of vector sensor.
     5. The position where the vector sensor is installed on the baffle has great effectson its directivity. Choosing the reasonable position to install the vector sensor canreduce the effects of the scatting ifeld on the vector sensor.
     6. The paper gives the expeirmental verification on basis of the simulation. InThousand Island Lake the expeirments of the effects of balffe on the vector sensor arecarried out,and the paper analyzes the comparison of the simulation and experimentalresults.
     7. The paper proposes the reconstructing technique of the directivity of vectorsensor under the condition of balffe. Reasonable shape and size of the baffle andreasonable position where the vector sensor is installed on the baffle can only reducethe effects of the directivity of vector sensor in the scatting ifeld, while it is diiffcult tofundamentally eliminate the impacts of the scatting field. The paper proposes thesound field separation method to separate the scatting ifeld from the incident ifeld andreconstruct the directivity of vector sensor.
引文
[1]孙贵青,李启虎.声矢量传感器研究进展,声学学报,Vol.29, No.6, Nov.,2004:481-490
    [2]姚直象.单矢量传感器及矢量阵信号处理研究,哈尔滨工程大学博士学位论文,2006
    [3]孙贵青.矢量水听器检测技术研究,哈尔滨工程大学博士学位论文,2001
    [4] Benjamin A. Cray, West Kingston, RI(US). Acoustic Vector Sensor, United StatesPatent, Apr.9,2002
    [5] Ken kan Deng, Potomac,MD(US). Acoustic Vector Sensor, United States Patent,Feb.17,2005
    [6]陈洪娟.矢量传感器,哈尔滨工程大学,2006
    [7] C. B. Leslie, J. M. Kendall, and J. L. Jones.Hydrophone for measuring particlevelocity, J. Acoust. Soc. Am., Vol.28, No.4, July,1956,711-715
    [8] Boyer G L.. Instrumentation for measuring underwater acoustic intensity, J. Acoust.Soc. Am., Vol.32,1960,1519
    [9]时胜国.矢量水听器及其在平台上的应用研究,哈尔滨工程大学博士学位论文,2006
    [10]何祚镛,赵玉芳.声学理论基础,国防工业出版社,1992
    [11]贾志富.全面感知水声信息的新传感器技术—矢量水听器及其应用,物理,Vol.38,No.3, March.2009,157-168
    [12] Shipps. J.C, Abraham. B.M. The use of vector sensors for underwater port andwaterway security. Sensors for Industry Conference,2004
    [13] Michael H. Davis. Target Strength Estimation using Finite Element Analysis.DSTO-TN-0395. Australia.2001.9
    [14] Shchurov V.A..The properties of the vertical and horizontal power flows of theunderwater ambient, J. Acoust. Soc. Am., vol.90, No.2,1992,1002-1004
    [15] Shchurov V.A..Coherent and diffusive fields of underwater acoustic ambient noise, J.Acoust. Soc. Am, vol.90, No.2,1991,991-1001
    [16] Shchurov V.A..The interaction of energy flows of underwater ambient and a localsource, Natural Physical Sources of Underwater Sound, Kluwer Academic Publishers,1993,93-109
    [17] Shchurov V.A..Ambient noise energy motion in the near-surface octan layer, RecentAdvances in Underwater Acoustics, Proc.I.O.A. vol.13, part3. Weymouth, UK.250-256,1991.
    [18] Shchurov V.A., Ilyichev V.I., Khvorostov Y.A..Ambient noise anisotropy in horizontalplane, Proc. ICA-14, El-10.1992, Beijing, China.
    [19] Shchurov V.A.et. al..The ambient noise energy motion in the near-surface in oceanwake-guide, Journal de Physique IV, colloque C5, supplement au Journal de PhysiqueIII. France.1994. V.4. C-P.1273.
    [20]陈志刚.基于矢量水听器的舰船辐射噪声测量技术研究,哈尔滨工程大学硕士学位论文,2008
    [21]孙贵青,杨德森,张林,何元安,张揽月.矢量水听器在水下目标低频辐射噪声测量中的应用,哈尔滨工程大学学报,Vol.22, No.5, Oct.,2001,5-11
    [22] Shchurov V.A. et al. Apossible mechanism of dynamic ambient ocean noise horizontalenergy flow forming, Proc. I.O.A. Arrays and Beamforming in Sonar. University ofBristol. UK.1996, P.121-127.
    [23] Shchurov V.A. et al. Peculiarities of forming underwater combined acoustic receivernoise immunity, Natural Physical Processes Associated with Sea Surface Sound.University of Southampton, UK.1997. P.28-35.
    [24] Shchurov V.A. Up-to-Date State and Outlook for the Intensity Measurement Methodin Underwater Acoustics, Proc.16-th Intern. Congr. On Acoust./2aUW21, USA.1998.P.989-990.
    [25]嵇建飞.被动式水声定位系统浮标无线电节点设计,哈尔滨工程大学硕士学位论文,2008
    [26] Ye. L. Gordienko.Study of the ocean noise field anisotropy, Akusticheskie sredstva imetody osvoyeniya okeana, Vladivostok: DVGU,1981, pp.122-126.
    [27] V. P. Dzyuba.Statistical properties of the acoustic noise field, Tez. Dokl.14-i Vsesoyuz.Shkoly-seminara opstatisticheskoi gidroakustike(SG-14). Nauka, Moscow,1986, pp.32-36(in Russian).
    [28] V. A. Shchurov.Investigation of the acoustic noise field in the ocean using thevector-phase techniques, in Utilization of the Vector-Phase Technique in OceanAcousticss, edited by V. A. Shchurov (DVO AN SSSR, Vladivostok,1989), pp.5-47(in Russian)
    [29]陈托.水平阵海底地层参数反演研究,哈尔滨工程大学硕士学位论文,2008
    [30] E.Ermolaeva, B.Goncharenko, V.Gordienko. VectorPhase methods of bottomreflectingproperties research in shallow shelf area, Acoustic08Paris,1889-1894
    [31] Anthony P. Lyons. Sediment sound speed measurements using buried vector sensors,J.Acoust.Soc.Am.,Vol.119, No.5, Pt.2, May.2006,3444
    [32]李凤华,孙梅,张仁和.由矢量水听器阵反演海底地声参数,哈尔滨工程大学学报,Vol.31, No.7, Jul.,2010,895-902
    [33] Li Fenghua, Zhang Renhe. Geoacoustic inversion based on a vector hydrophone array,J.Acoust.Soc.Am.,Vol.123, No.5, Pt.2, May2008,3351
    [34] PENG Han-Shu, LI Feng-Hua. Geoacoustic inversion based on a vector hydrophonearray, CHIN. PHYS. LETT., Vol.24, No.7, Jan.,2007,1977-1981
    [35]伍先俊,翁雪涛,朱石坚.基于有限元法对比的统计能量研究,振动与冲击,Vol.24,No.1,Jan,2005,58-63
    [36]汤渭霖.用物理声学方法计算界面附近目标的回波,声学学报,Vol.24,No.1,Jan,1999,1-5
    [37]汤渭霖.用物理声学方法计算非硬表面的声散射,声学学报,Vol.18,No.1,Jan,1993,45-53
    [38]汤渭霖.声呐目标回波的亮点模型,声学学报,Vol.19,No.2,Mar,1994,92-100
    [39]冯玉田.水中目标声散射特性研究-FDTD及Fourier衍射定理的应用,上海大学博士学位论文,2006
    [40]曹开朗,李伟.薄壳理论用于干式柔膜密封储气罐的计算,煤气与热力,Vol.19,No.5, Sep.,1999,24-28
    [41]朱韬.水中目标低频声散射特性研究,上海交通大学硕士学位论文,2008
    [42]姜琳.板壳结构的声散射数值及实验分析,大连理工大学博士学位论文,2008
    [43]李建鲁,范军,万琳,汤渭霖.利用近场板块元法计算水下简单目标的近场瞬态回波,中国声学学会2001年青年学术会议论文集,2001
    [44]朱凤芹.内部填充流体的弹性壳体的声散射特性研究,哈尔滨工程大学硕士学位论文,2008
    [45]范军,汤渭霖.声纳目标强度计算的板块元方法,中国声学学会青年学术会议论文集,1999年
    [46]卓凯琳,范军,汤渭霖. FEM-BEM耦合方法分析弹性体目标的声散射问题,上海交通大学学报,Vol.43, No.8,Aug.2009,1258-1262
    [47]姚振汉,王海涛.边界元法,高等教育出版社,2010
    [48]王勖成.有限单元法,清华大学出版社,2003
    [49]刘青山.边界元法在试井分析中的方法研究,西南石油学院硕士学位论文,2004
    [50] J.J.Lobdill.Surface reflections: Their effects on earl simulated in target strengthdetermination, AD.1962
    [51]姜俊奇.有限长加肋弹性柱壳的振动及声辐射研究,哈尔滨工程大学硕士论文,2005
    [52]孙磊.轻外壳对双层壳体结构水下辐射声影响研究,哈尔滨工程大学硕士论文,2007
    [53] Zheng Guoyin, Fan jun, Tang Weilin. Acoustic scattering from fluid-filled finitecylindrical shell in water: II. Experiment, Chinese Journal of Acoustics, Vol.30, No.3,March,2011,301-312
    [54] Zheng Guoyin, Fan jun, Tang Weilin. Acoustic scattering from fluid-filled finitecylindrical shell in water: I. Theory, Chinese Journal of Acoustics, Vol.30, No.3,March,2011,288-310
    [55] Sun yang, Xu haiting. Sound scattering from partially water-filled elastic sphericalshell with an internal elastic plate, Vol.27, No.2, Feb.,2008,111-118
    [56] B. M. Brown. Extension of the target strength tudes.AD.1972
    [57] Gautan Sengupta. Numerical simulation of acoustic scattering fromsubmarines.Computational Acoustics-Volumes I. Elsevier Science Publishers.1993
    [58] Joseph Shirron. Computational simulation of elastic scattering. NavalResearchLaboratory. Washington D.C.
    [59] M.Almegron, M. Nodin.Acoustics target strength of submarines. PRAO’S,1991
    [60] Christopher W. Nell, L. E. Gilroy. An improved BASIS model for theBeTSSisubmarine. DRDC TR2003-199. Defence R&D Canada.2003.11
    [61] L. E. Gilroy, D. P. Brennan. Predicting acoustics target strength with AVAST.DRDCTM2001-071. Defence R&D Canada.2001
    [62] L. E. Gilroy, J. Fawcett. Comparison of three-dimensional and axisymmetricsoftwarefor predicting acoustics target strength. DRDC TM2001-018. Defence R&DCanada.2001.11
    [63]赵日昌.潜艇反射物理模型和数学模型,中国船舶科技报告,760研究所,1995
    [64]马忠诚,范景理.水下模型散射声场模型,中国船舶科技报告,760研究所,1995
    [65]范军.潜艇回波特性预报,1997年青年声学会议论文集,1997
    [66]汤渭霖,范军,孙辉.潜艇回波特性预报模型,中国船舶科技报告,哈尔滨工程大学,1998
    [67]范军,孙辉.潜艇回波特性预报软件说明,中国船舶科技报告,哈尔滨工程大学,1995
    [68]叶伟.声纳目标谐振区回声特性研究,上海交通大学硕士学位论文,2005
    [69]徐海亭等.水下目标回波特性,中国船舶科技报告,中科院声学研究所北站,1995
    [70] WIENER F M. Sound diffraction by rigid spheres and circular cylinders. J Acoust SocAm.,Vol.19, No.3,1947,444-451
    [71] BERANEK L.Acoustic measurements, New York, McGraw Hill,1949
    [72] Kang Kim. Investigation of an underwater acoustic intensity vector sensor, P.H.D.thesis in Acoustic, The Pennsylvania State University,2002
    [73]生雪莉,郭龙翔,梁国龙.球形软障板矢量传感器指向性研究,中国声学学会全国声学学术会议论文集,2002
    [74]李春旭.声压、振速联合信息处理.哈尔滨工程大学博士学位论文,2000.
    [75] KOSOBRODOV R A, NEKRASOV V N. Effect of thediffraction of sound by thecarrier of hydroacoustic equipment on the results of measurements,AcoustPhys,Vol.47, No.3,2001,382–388
    [76] Malcolm Hawkes,Arye Nehorai.Acoustic Vector-Sensor Processing in thePresence ofa Reflecting Boundary.IEEE Transactions on Singenal Processing,Vol.48, No.11, Nov.,2000,2981-2993
    [77]侯玉敏,毛卫宁.刚性曲面障板散射对多模球形水听器测向的影响,声学技术,Vol.24, No.2, Feb.,2005,94-97
    [78]时胜国,杨德森.弹性球壳声散射对矢量水听器测向影响研究,声学技术,Vol.27,No.5, Oct.,2008,642-648
    [79]时胜国,杨德森,王三德.弹性球壳声衍射对矢量传感器测量影响,哈尔滨工程大学学报,Vol.27, No.1,Feb.2006,84-89
    [80]陈亚林,杨博,马远良.复杂边界条件下矢量传感器的指向性分析及实验研究,Vol.25, No.4, Aug.,2006,381-387
    [81]张揽月,杨德森,张巍.刚硬球型障板声散射对矢量线阵的性能影响,声学技术,Vol.28, No.2,Pt.3,Apr.,2009,103-104
    [82]冀邦杰,杨宝民,王海陆.有限平面障板对低频指向性的影响,声学技术,Vol.26,No.4,Aug.,2007,588-591
    [83] Javad Ahmadi-Shokouh, Hengameh Keshavarz. A Vector-Hydrophone’s MinimalComposition for Finite Estimation-Variance in Direction-Finding Near/Without aReflecting Boundary. IEEE Transactions on Signal Processing, Vol.55, No.6, June,2007,2785-2794
    [84]宋晓雪.曲面障板近场声散射对矢量水听器测向影响,哈尔滨工程大学硕士学位论文,2008
    [85]李海霞.有限障板对矢量水听器测向的影响,哈尔滨工程大学硕士学位论文,2010
    [86]何勤.有限障板下矢量水听器性能的研究,哈尔滨工程大学硕士学位论文,2010
    [87]张巍.有障板时矢量声场特性与矢量信号处理技术研究,哈尔滨工程大学硕士学位论文,2010
    [88] B.R.Rapids and G.C.Lauchle. Vector intensity field scattered by a rigidprolatespheroid.J.Acoust.Soc.Am.2006,120(1):38-48
    [89]沈杰罗夫.水声学中的波动问题,国防工业出版社,1983
    [90]何祚镛.结构振动与声辐射,哈尔滨工程大学,2001
    [91]吴崇试.数学物理方法,北京大学出版社,2003
    [92]郭敦仁.数学物理方法,高等教育出版社,1991
    [93]王竹溪,郭敦仁.特殊函数概论,北京大学出版社,2000
    [94]杨永发,徐勇.向量分析与场论(第二版),南开大学出版社,2006
    [95] Zhenye, Emile Hoskinson, Richard K. Dewey, Li Ding, David M. Farmer. A methodfor acoustic scattering by slender bodies. I.Theory and vecification, J.Acoust.Soc.Am,Vol.102, No.4, Oct.1997,1964-1976
    [96] Li Ding,Zhen ye. A method for acoustic scattering by slender bodies. I.Comparsionwith laboratory measurements, J.Acoust.Soc.Am, Vol.102, No.4, Oct.1997,1977-1982
    [97] Tomoo Kamakura, Tsuneo lshiwata, Kazuhisa Matsuda. A new theoretical approach tothe analysis of nonlinear sound beams using the oblate spheroidal coordinate system,J.Acoust.Soc.Am., Vol.105,No.6,June,1999,3083-3087
    [98] A.L.Van Buren, B.J.King. Acoustic Radiation from two spheroids, J.Acoust.Soc.Am.,Vol.52,No.1,1972,364-372
    [99] A.L.Van Buren. Acoustic radiation impedance of caps and rings on prolate spheroids,J.Acoust.Soc.Am., Vol.50,No.5(part2),1971,1343-1356
    [100] Roland V. Baier. Acoustic radiation impedance of caps and rings on oblate spheroidalbaffles, J.Acoust.Soc.Am., Vol.51,No.5(part2),1972,1705-1716
    [101] Roger H.Hackman, Douglas G.Todoroff. An application of thespheroidal-coordinate-based transition matrix: The acoustic scattering from highaspect ratio solids, J.Acoust.Soc.Am., Vol.78,No.3,Sept.1985,1058-1071
    [102] A.Germon, G.C.Lauchle. Axisymmetric scattering of spherical waves by a prolatespheroid, J.Acoust.Soc.Am., Vol.65,No.5, May,1979,1322-1327
    [103] Alexander Silbiger. Scattering of sound by an elastic prolate spheroid,J.Acoust.Soc.Am., Vol.35,No.4,1963,564-570
    [104] Lang Jen, ChuanShuihu. Spheroidal wave functions of large frequency parametersc=kf and the radiation fields of a metallic prolate spheroid excited by anycircumferential slot, IEEE Transactions on antennas and propagation, Vol. AP-31,No.2, March1983,382-389
    [105] R.D.Spence, Sara Granger. The scattering of sound from a prolate spheroid,J.Acoust.Soc.Am., Vol.23,No.6, Nov.,1951,701-706
    [106] J.A.Roumeliotis, A.D.Kotsis, and G.Kolezas. Acoustic scattering by an impenetrablespheroid, Acoustical Physics, Vol.53, No.4,2007,436-477
    [107] J.P.Barton, L.W.Nicholas, Haifeng Zhang and Constantine Tarawneh. Near-fieldcalculations for a rigid spheroid with an arbitrary incident acoustic field. J.Acoust.Soc.Am.2003,113(3):1216-1222
    [108]韩一平.椭球粒子对高斯波束的散射,西安电子科技大学博士学位论文,2000
    [109] Carson Flammer. Spheroidal wave functions, Stanford university press,1957
    [110] Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong. Spheroidal wave functions inelectromagnetic theory, A Wiley-Interscience Publication John Wilet&sons, inc.,2002
    [111] M. Abramowitz and I.A. Stegun, eds. Handbook of Mathematical Functions, Dover,New York,1964.
    [112]彭芳麟.数学物理方程的MATLAB解法与可视化,清华大学出版社,2004
    [113](美)斯蒂芬·沃尔夫雷姆.Mathematica全书(第四版),西安交通大学出版社,2002
    [114] Stephen Wolfram. Mathamatica Book(5th Edition), Wolfram Media,2003
    [115] A.L.Van Buren, R.V.Baier, S.Hanish, and B.J.King. Calculation of spheroidal wavefunctions,J.Acoust.Soc.Am. Vol.51, No.1(part2),1972,414-416
    [116] Le-Wei Li, Mook-Seng Leong, Tat-Soon Yeo, Pang-shyanKooi, and Kian-Yong Tan.Compuations of spheroidal harmonics with complex arguments: A review with analgorithm, PHYSICAL REVIEW E, Vol.58, No.5, Nov.1998
    [117] D.B.Hodge. Eigenvalues and Elgenfunctions of the spheroidal wave equation, Journalof mathematical physics, Vol.11,No.8,Aug.1970,2308-2312
    [118] D.W.Lozier, F.W.J.Olver. Numerical evaluation of special functions,http://math.nist.gov/nesf/., Dec.2000
    [119] B.D.B.Figueiredo, M.Novello. Solutions to spheroidal wave equation,J.Math.Phys.,Vol.34, No.7, July,1993,3121-3132
    [120] N.Aquino, E.Castano. Spheroidal functions revisited: matrix evaluation and generatingfunctions, Rev.Mex.Fis.,Vol.48,No.3,2002,277-282
    [121] P.E.Falloon, P.C.Abbott, and J.B.Wang. Theory and computation of spheroidal wavefunctions, Journal of physics A: Mathematical and General, Vol.36,2003,5477-5495
    [122] KedarKhare, Nicholas George. Sampling theory approach to prolate spheroidal wavefunctions, Journal of physics A: Mathematical and General, Vol.36,2003,10011-10021
    [123] E.W.Leaver. Solutions to a generalized spheroidal wave equation: Teukolsky’sequations in general relativity, and the two-center problem in molecular quantummechanics, J.Math.Phys.Vol.27,No.5, May,1986,1238-1265
    [124] G.Walter, T.Soleski. A new friendly method of computing prolate spheroidal wavefunctions and wavelets,
    [125]曾学刚,阮成礼,林为干.长旋转椭球波函数本征值的精确计算,电子科技大学学报,Vol.21, No.1,Feb.,1992,7-10
    [126]张善杰.旋转椭球函数的数值计算,电子学报,Vol.2, No.12, Dec.,1993,72-77
    [127] Janet B.Jones-Oliveira, Hans R. Fischer. Absolute and uniform convergence ofalternate forms of the prolate spheroidal radial wave functions, Advances in AppliedMathematics, Vol.29,2002,311-327
    [128] A.A.Abramov, S.V.Kurochkin. Highly accurate calculation of radial spheroidalfunctions, Computational mathematics and mathematical physics, Vol.46, No.6,2006,949-954.
    [129]卓琳凯,范军,汤渭霖.FEM-BEM耦合方法分析弹性目标的声散射问题,上海交通大学学报,2009.8.vol.43(8)
    [130] G.C.Everstine, F.M.Henderson. Coupled finite element/boundary element approachfor fluid-structure interaction, J.A.S.A., Vol.7, No.5,1990,1938-1947
    [131] Miguel.C.Junger, David Fei. Sound, structure and their interaction, The MIT Press,1972
    [132] O.C.ZIENKIEWICZ, R.L.TAYLOR&J.Z.ZHU THE FINITE ELEMENT METHOD:ITS BASIS&FUNDAMENTALS(Sixth edition),, Elsevier(Singapore) Pte Ltd,2008
    [133](英) O.C.Zienkiewicz,(美)R.L.Taylor著,曾攀译.有限单元法(第五版),第1卷:基本原理,清华大学出版社,2008
    [134]黄克智,薛明德,陆明万.张量分析,清华大学出版社,2003
    [135]杨德全,赵忠生.边界元理论及应用,北京理工大学出版社,2006
    [136]祝家麟,袁正强.边界元分析,科学出版社,2009
    [137]易大义,沈云宝,李有法.计算方法(第二版),浙江大学出版社,2002
    [138]王远坤.边界元法分析声场及功能梯度涂层结构,合肥工业大学硕士学位论文,2007
    [139]刘扬.水下弹性壳体结构声辐射快速预报方法研究,哈尔滨工程大学硕士学位论文,2007
    [140]牛忠荣,周焕林,王秀喜,张晨利.边界积分方程中近边界点几乎奇异积分的计算,合肥工业大学学报(自然科学版),Vol.23, No.1, Feb.,2000,86-90
    [141]牛忠荣,王秀喜,周焕林.边界元法中计算几乎奇异积分的一种无奇异算法,应用力学学报,Vol.18, No.4, Dec.,2001,1-9
    [142] Tanaka M, Sladek V, Sladek J. Regularization techniques applied to BEM. Appl.Mech. Rev., Vol.47, No.10,1994,457-499
    [143] NiuZhongrong,Wendland W L,Wang Xiuxi,et a1.A new semi-analytical algorithmfor the evaluation of the nearly singular integrals in three-dimensional, ComputerMethods of Applied Mechanics and Engineering, Vol.195,2005,1057-1074.
    [144] Wu T W. Boundary Element Acoustics Fundamentals and Computer Codes, USA:WIT Press,2000,51-66.
    [145] Ma H, Kamiya N. A general algorithm for the numerical evaluation of nearly singularboundary integrals of various orders for two and three dimensional elasticity,Computational Mechanics, Vol.29,2002,277-288.
    [146] Davey K, Rasgado M T A, Rosindale I. The3D elastodynamic boundary elementmethod: Semi-analytical integration for linear isoparametric triangular elements, Int JNumber Methods Eng, Vol.44,1999,1031-1054.
    [147] Li H B, et al., Anew method for evaluating singular integrals in stress analysis of solidby the direct boundary element method, Int. J. Num. Meth. Engng, Vol.21,1985,2071-2098
    [148] Yu De-hao. The numerical computation of hypersingular integrals and its applicationin BEM, Advances in Engineering software, Vol.18,1993,103-109
    [149] Sladek V, Sladek J, Tanaka M. Optimal transformations of the integration variables incomputation of singular integrals in BEM, Int. J. Numer Methods Eng, Vol.47,2000,1263-1283
    [150] Ma H, Kamiya N. A general algorithm for accurate computation of field variables andits derivatives near the boundary in BEM, Engineering Analysis with BoundaryElements, Vol.25,2001,833-841
    [151] Huang Q, Cruse TA. Some notes on singular integral techniques BE analysis, Int. J.Numer Methods Eng, Vol.36, No.15,1993,2643-2659
    [152]刘勇辉,陆鑫森.边界元法中奇异积分计算的极坐标变换法,应用数学和力学,Vol.9, No.10, Oct.,1988,899-908
    [153]牛忠荣,王左辉,胡宗军,周焕林.二维边界元法中几乎奇异积分的解析法,工程力学,Vol.21, No.6, Dec.,2004,113-117
    [154]邬吉明,余德浩.三维Helmholtz方程外问题的自然积分方程及其数值解,计算物理,Vol.16, No.5, Sep.,1999,449-456
    [155]胡宗军,牛忠荣,程长征,周焕林.三维Helmholtz积分方程外问题几乎奇异积分的半解析算法,应用力学学报,Vol.27, No.3, Sep.,2010,532-538
    [156]牛忠荣,王秀喜,周焕林.三维边界元法中几乎奇异积分的正则化算法,力学学报,Vol.36, No.1, Jan.,2004,49-56
    [157]胡宗军,牛忠荣,程长征,周焕林.三维声场问题边界元法中几乎奇异积分的正则化,中国科学技术大学学报, Vol.39, No.6. Jun.,2009,638-643
    [158]周焕林,牛忠荣,王秀喜.三维位势问题边界元法中几乎奇异积分的正则化,计算物理,Vol.22, No.6. Nov.,2005,501-506
    [159]张效松,叶天麒.三维位势问题边界元奇异积分分析,数值计算与计算机应用,No.4. Dec.,1998,271-275
    [160]周焕林,王秀喜,牛忠荣.位势问题边界元法中几乎奇异积分的完全解析算法,中国科学技术大学学报,Vol.33, No.4.Aug.,2003,431-437
    [161]李增刚,詹福良.Virtual.Lab Acoustics声学仿真计算高级应用实例,国防工业出版社,2010
    [162] Du Qinghua, Yao Zhenhan, Cen Zhangzhi. Some application of boundary elementmethods, boundary element finite coupling techniques in elastic stress analysis, Amechanica solid sinica, Vol.3, No.3,1990,327-340
    [163]何元安.大型水下结构近场声全息的理论与实验研究,哈尔滨工程大学博士学位论文,2000
    [164]于飞.基于波叠加方法的声全息技术与声学灵敏度分析,合肥工业大学出版社,2008
    [165]徐亮.Patch近场声全息及近场声全息分辨率增强方法,合肥工业大学博士学位论文,2009
    [166]毕传心.基于分布源边界点法的近场声全息理论及实验研究,合肥工业大学博士学位论文,2004
    [167]李加庆.基于声全息的故障特征提取技术研究,上海交通大学博士学位论文,2008
    [168]李卫兵.基于统计最优和波叠加方法的近场声全息技术研究,合肥工业大学博士学位论文,2006
    [169]陈晓东.近场平面声全息的测量和重构误差研究,合肥工业大学博士学位论文,2004
    [170]张海滨.循环平稳声场的非共形面近场声全息理论与实验研究,上海交通大学博士学位论文,2008
    [171] MingsianR.Bai. Application of BEM(boundary element method)-based acousticholography to radiation analysis of sound sources with arbitrarily shaped geometries,J.Acoust.Soc.Am.92(1),July1992
    [172] Angie Sarkissian. Extension of measurement surface in near-field acoustic holography,J.Acoust.Soc.Am.115(4),April2004
    [173] E.G. Williams, and Y. Lee. Nearfield acoustic holography: I. Theory of generalizedholography and the development of NAH, J.D.Maynard, J.Acoust.Soc.Am.78(4),October1985
    [174] W.A.Veronesi, J.D. Maynard. Nearfield acoustic holography: II. Holographicreconstruction algorithms and computer implementation, J.Acoust.Soc.Am.81(5),May1987
    [175]何元安,何祚镛,商德江等.基于平面声全息的全空间场变换:II.水下大面积平面发射声基阵的近场声全息实验,声学学报,Vol.28, No.1, Jan.,2003
    [176]何元安,何祚镛.基于平面声全息的全空间场变换:I.原理与算法,声学学报,Vol.27, No.6, Nov.,2002
    [177]于飞,陈心昭,李卫兵,陈剑.空间声场全息重建的波叠加方法研究,物理学报,Vol.53, No.8, August,2004
    [178]张海滨,蒋伟康,万泉.适用于循环平稳声场的基于波叠加法的近场声全息技术,物理学报,Vol.57, No.1, January,2008
    [179] Cheng M T, Mann J A, Pate A. Wave-number domain separation of the incident andscattered sound field in Cartesian and cylindrical coordinates. J AcoustSoc Am, Vol.97, No.4,1995,2293-2303
    [180] SaijYou K, Ueda M, Youshikawa W. Application of generalized near-field acousticalholography to scattering problem. Jpn. J ApplPhys, Vol.33,3120-3135
    [181] Li WeiBing, Lian MeiZhuan, Bi ChuanXing, Chen Jian, Chen XinZhao. Separationtheory of the incident and scattered sound fields in spherical coordinate, Science inChina Series E: Technology Sciences, Vol.50, No.3, June,2007,361-370

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700