基于表面振动监测的大型水下结构辐射噪声预报研究
|
摘要
水下结构辐射噪声预报是水声领域一项重要研究内容,是定量声学设计、减振降噪设计等工作的理论基础与重要依据。对于潜艇这类大型水下结构而言,辐射噪声的实时监测或者快速预报是提高其战斗力与生存力的有力保障。因此,辐射声场预报研究具有重要的理论价值和广泛的应用背景。本文以大型结构辐射噪声的快速预报为目标,遵循理论研究和工程应用相结合的研究思路,开展了辐射声场快速预报的理论与试验研究。
深入分析了表面振动与辐射声场之间的传递规律,声场声压等于表面振速向量与声传递向量的内积,声传递向量的元素等于与辐射面共形的刚性障板表面对应活塞以单位速度振动时的辐射声压。讨论了以规则障板表面活塞辐射声场近似实际障板表面活塞辐射声场的合理性。对于实际障板尺度远小于或者远大于声波波长的情况,其表面活塞的辐射可以分别看作点声源或者平面波的辐射。即便规则障板与实际障板拟合程度不高,拟合前后表面活塞的辐射声场差别很小。对于实际障板尺度与声波波长可比拟的情况,其表面活塞的辐射声场主要取决于以活塞为中心、尺度与声波波长相当的局部障板形状,规则障板与该局部障板的拟合程度决定了声场预报精度。只要保证对辐射声场起主要贡献的单元所对应的声传递向量元素是准确的,便可以较好地近似总辐射声场。最终,建立了一个具有坚实理论基础、可应用于大型水下结构辐射噪声快速预报的理论算法——单元辐射叠加法。该方法没有非唯一性、奇异积分以及高维矩阵求逆等问题的困扰,计算速度远远高于边界元等其它数值积分方法。一系列算例表明,该方法的计算结果从甚低频直至高频均与解析数值解或者边界元结果符合得很好。
从理论上分析了平面、圆柱面两类典型辐射面表面振动空间采样所引起的声场预报误差问题。将平面、圆柱面振速分布分别变换到二维波数域或者轴向、周向波数域,建立变换谱与辐射声场之间的对应关系,再根据空间采样后变换谱的混叠程度确定辐射声场的预报误差。对于固定观察方位与分析频率,平面辐射面声场预报精度是由空间采样前、后表面振速的二维波数谱在特定波数上的比值决定的;圆柱辐射面声场预报精度是由空间采样前、后表面振速的轴向、周向波数谱在特定轴向波数上、特定周向波数范围内的比值决定的。数值分析了简支矩形板、简支圆柱壳表面振动空间采样间隔与辐射声场预报误差之间的关系,并将有关结论推广到一般矩形板、圆柱壳表面振动空间采样情况。
与国内有关单位联合开展了水下多舱段壳体结构振动声辐射的试验研究。针对试验中出现的振动相位信息缺失情况讨论了辐射噪声的工程预报问题,因为这种情况具有实际意义。根据声场叠加原理,将辐射声压级表示为表面单元独立振动时辐射声压级与修正因子之和的形式,其中修正因子反映了由于表面振动的相位关系引起的辐射声压相关性。再通过理论和试验研究,分析了修正因子与观察距离、表面振速插值密度等因素之间的关系。对于距离足够远的同一观察方位而言,修正因子与测量距离无关;随着表面插值、细化单元的增多,修正因子相应增大。在此基础上,提出了一种基于特定工况修正因子预报其它工况辐射噪声的工程预报方法。对于在工作频段或者源强度上可以区分的多台设备激励情况,根据设备全开工况的修正因子可以预报其它工况的辐射噪声;对于多台设备在工作频段、强度上无法区分的情况,根据特定工况的修正因子在某些频率范围内可以预报其它工况的辐射噪声。
本文对表面振动与辐射声场之间传递规律进行了较深入的理解和阐述。提出了一种新的辐射声场预报方法,适用于大型水下结构辐射噪声的快速预报,为定量声学设计或者减振降噪控制提供了新的理论依据。从空间信号的离散与重建角度,分析了表面振动空间采样与辐射声场预报精度之间的关系,对于表面振动测点布放方案的设计与评估具有一定指导意义。讨论了表面振动相位信息未知情况下辐射噪声预报的试验修正方法,为解决辐射噪声工程预报中实际问题提供了新思路。
The prediction of noise radiated by underwater structures is one of the most important research contents in the field of underwater acoustics. It is regarded as the theoretical foundation and the important criterion for quantitative acoustic design and vibration-noise control. For the large underwater structures such as submarines, fast prediction or real-time monitoring of noise is crucial in improving the fighting and survival capacities. Therefore, the research on prediction of noise radiated by underwater structures has important theoretical value and wide engineering application. In this dissertation, fast prediction of noise radiated by large underwater structures is focused on. Theoretical and experimental investigations are implemented following the principle of theoretical research combined with engineering application.
The physical essence of transfer law between the surface vibration and the acoustic field has been analyzed deeply. The acoustic pressure equals the inner product of two vectors, namely, surface velocity vector and Acoustic Transfer Vector (ATV). The element of ATV equals the acoustic pressure radiated by the corresponding piston vibrating in unit speed on the rigid baffle coinciding with the vibrating surface. The discussion is focused on the rationality of the acoustic pressure radiated by the piston on the actual baffle approximated by the analytical solution of that on the regular baffle. In the case of the dimension of the actual baffle far larger or less than the acoustic wavelength, the radiation of the piston can be regarded as that of a point source or a planar wave, respectively. Although the regular baffle does not fit the actual baffle well, the difference of the acoustic pressure radiated by the piston before and after fitting can be ignored. In the case of the dimension of the actual baffle comparable with the acoustic wavelength, the acoustic pressure is mainly determined by the shape of the neighboring baffle on the acoustic wavelength scale. The error is mainly determined by the fitting degree between the regular baffle and the actual baffle. As long as the elements of ATV dominating the whole acoustic pressure are accurate, a satisfying prediction can be obtained. Finally, a method named Element Radiation Superposition Method (ERSM) is established which has profound theoretical foundation and can be applied to the fast prediction of noise radiated by large underwater structures. It succeeds to avoid the problems of non-uniqueness, singularity integral and high-dimensional matrix inverse. Consequently, it has a larger advantage in calculating speed than the numerical integration methods. A series of numerical analysis prove that the results of ERSM are in satisfactory agreement with those of analytical solutions or BEM either in low frequency or in high frequency.
The relationships between the prediction precision of acoustic pressure and the spatial sampling interval on surface vibration are analyzed theoretically for two typical surfaces, namely, plane and cylinder. The distributions of surface vibration are transformed to two-dimensional wavenumber domain or axial circumferential wavenumber domain respectively. The mappings between the transformed spectrums and the acoustic pressures are established. The prediction error is totally determined by the degree of aliasing in the corresponding transformed domains resulted from spatial sampling. For the fixed observed bearing and analyzing frequency, the prediction precision of acoustic pressure radiated by a vibrating plane is determined by the ratio of the two-dimensional wavenumber spectrums at the specific wavenumber before and after spatial sampling. The prediction precision of acoustic pressure radiated by a vibrating cylinder is mainly decided by the ratio of the axial circumferential wavenumber spectrums at the specific axial wavenumber and below the specific circumferential wavenumber before and after spatial sampling. The spatial sampling interval required by the designated acoustic pressure prediction precision on the simply supported rectangular plate and that on the simply supported cylindrical shell are analyzed numerically. Some conclusions are extended to the cases of spatial sampling on the generally supported rectangular plate and that on the generally supported cylindrical shell.
Experimental research on vibration and radiation of underwater multi-compartmented shell structure is performed together with the related Institute. An engineering method of noise prediction is discussed to solve the problem of vibration phase missing in this experiment. According to the superposition principle of acoustic field, the acoustic pressure level can be expressed as the sum of the acoustic pressure level radiated by the surface elements vibrating independently and a modifying factor. Therein, the modifying factor reflects the correlation between the acoustic pressures arising from the phase inconsistency of the surface vibration. Through the theoretical and experimental studies, the influences of the observation distance and the surface vibration interpolation degree on the modifying factor are analyzed. For the far observers in the same bearing, the modifying factor has nothing with the observation distance and increases with the number of surface elements in the interpolation process. On the basis, an engineering method is put forward to predicting the noise with the modifying factor obtained in the specific case. If the vibration equipments work in different frequency or in different intensity, the noise can be predicted by the modifying factor obtained in the case of all vibration equipments working. If not, the noise can be predicted in some frequency band by the modifying factor obtained in the specific case.
The study in this dissertation provides some further understanding on the rule between vibration and radiation. A new method is put forward to predicting the noise radiated by large underwater structures and providing theoretical foundation for quantitative acoustic design and vibration-noise control. In view of the sampling and reconstruction of spatial signal, the relationships between the spatial sampling on surface vibration and the prediction error of acoustic pressure are analyzed. Some conclusions are of certain guiding significance in designing and evaluating the laying scheme of surface vibration measurements. The prediction method in the case of vibration phase missing has been discussed and provides a new way to solve the actual problems in engineering noise prediction.
深入分析了表面振动与辐射声场之间的传递规律,声场声压等于表面振速向量与声传递向量的内积,声传递向量的元素等于与辐射面共形的刚性障板表面对应活塞以单位速度振动时的辐射声压。讨论了以规则障板表面活塞辐射声场近似实际障板表面活塞辐射声场的合理性。对于实际障板尺度远小于或者远大于声波波长的情况,其表面活塞的辐射可以分别看作点声源或者平面波的辐射。即便规则障板与实际障板拟合程度不高,拟合前后表面活塞的辐射声场差别很小。对于实际障板尺度与声波波长可比拟的情况,其表面活塞的辐射声场主要取决于以活塞为中心、尺度与声波波长相当的局部障板形状,规则障板与该局部障板的拟合程度决定了声场预报精度。只要保证对辐射声场起主要贡献的单元所对应的声传递向量元素是准确的,便可以较好地近似总辐射声场。最终,建立了一个具有坚实理论基础、可应用于大型水下结构辐射噪声快速预报的理论算法——单元辐射叠加法。该方法没有非唯一性、奇异积分以及高维矩阵求逆等问题的困扰,计算速度远远高于边界元等其它数值积分方法。一系列算例表明,该方法的计算结果从甚低频直至高频均与解析数值解或者边界元结果符合得很好。
从理论上分析了平面、圆柱面两类典型辐射面表面振动空间采样所引起的声场预报误差问题。将平面、圆柱面振速分布分别变换到二维波数域或者轴向、周向波数域,建立变换谱与辐射声场之间的对应关系,再根据空间采样后变换谱的混叠程度确定辐射声场的预报误差。对于固定观察方位与分析频率,平面辐射面声场预报精度是由空间采样前、后表面振速的二维波数谱在特定波数上的比值决定的;圆柱辐射面声场预报精度是由空间采样前、后表面振速的轴向、周向波数谱在特定轴向波数上、特定周向波数范围内的比值决定的。数值分析了简支矩形板、简支圆柱壳表面振动空间采样间隔与辐射声场预报误差之间的关系,并将有关结论推广到一般矩形板、圆柱壳表面振动空间采样情况。
与国内有关单位联合开展了水下多舱段壳体结构振动声辐射的试验研究。针对试验中出现的振动相位信息缺失情况讨论了辐射噪声的工程预报问题,因为这种情况具有实际意义。根据声场叠加原理,将辐射声压级表示为表面单元独立振动时辐射声压级与修正因子之和的形式,其中修正因子反映了由于表面振动的相位关系引起的辐射声压相关性。再通过理论和试验研究,分析了修正因子与观察距离、表面振速插值密度等因素之间的关系。对于距离足够远的同一观察方位而言,修正因子与测量距离无关;随着表面插值、细化单元的增多,修正因子相应增大。在此基础上,提出了一种基于特定工况修正因子预报其它工况辐射噪声的工程预报方法。对于在工作频段或者源强度上可以区分的多台设备激励情况,根据设备全开工况的修正因子可以预报其它工况的辐射噪声;对于多台设备在工作频段、强度上无法区分的情况,根据特定工况的修正因子在某些频率范围内可以预报其它工况的辐射噪声。
本文对表面振动与辐射声场之间传递规律进行了较深入的理解和阐述。提出了一种新的辐射声场预报方法,适用于大型水下结构辐射噪声的快速预报,为定量声学设计或者减振降噪控制提供了新的理论依据。从空间信号的离散与重建角度,分析了表面振动空间采样与辐射声场预报精度之间的关系,对于表面振动测点布放方案的设计与评估具有一定指导意义。讨论了表面振动相位信息未知情况下辐射噪声预报的试验修正方法,为解决辐射噪声工程预报中实际问题提供了新思路。
The prediction of noise radiated by underwater structures is one of the most important research contents in the field of underwater acoustics. It is regarded as the theoretical foundation and the important criterion for quantitative acoustic design and vibration-noise control. For the large underwater structures such as submarines, fast prediction or real-time monitoring of noise is crucial in improving the fighting and survival capacities. Therefore, the research on prediction of noise radiated by underwater structures has important theoretical value and wide engineering application. In this dissertation, fast prediction of noise radiated by large underwater structures is focused on. Theoretical and experimental investigations are implemented following the principle of theoretical research combined with engineering application.
The physical essence of transfer law between the surface vibration and the acoustic field has been analyzed deeply. The acoustic pressure equals the inner product of two vectors, namely, surface velocity vector and Acoustic Transfer Vector (ATV). The element of ATV equals the acoustic pressure radiated by the corresponding piston vibrating in unit speed on the rigid baffle coinciding with the vibrating surface. The discussion is focused on the rationality of the acoustic pressure radiated by the piston on the actual baffle approximated by the analytical solution of that on the regular baffle. In the case of the dimension of the actual baffle far larger or less than the acoustic wavelength, the radiation of the piston can be regarded as that of a point source or a planar wave, respectively. Although the regular baffle does not fit the actual baffle well, the difference of the acoustic pressure radiated by the piston before and after fitting can be ignored. In the case of the dimension of the actual baffle comparable with the acoustic wavelength, the acoustic pressure is mainly determined by the shape of the neighboring baffle on the acoustic wavelength scale. The error is mainly determined by the fitting degree between the regular baffle and the actual baffle. As long as the elements of ATV dominating the whole acoustic pressure are accurate, a satisfying prediction can be obtained. Finally, a method named Element Radiation Superposition Method (ERSM) is established which has profound theoretical foundation and can be applied to the fast prediction of noise radiated by large underwater structures. It succeeds to avoid the problems of non-uniqueness, singularity integral and high-dimensional matrix inverse. Consequently, it has a larger advantage in calculating speed than the numerical integration methods. A series of numerical analysis prove that the results of ERSM are in satisfactory agreement with those of analytical solutions or BEM either in low frequency or in high frequency.
The relationships between the prediction precision of acoustic pressure and the spatial sampling interval on surface vibration are analyzed theoretically for two typical surfaces, namely, plane and cylinder. The distributions of surface vibration are transformed to two-dimensional wavenumber domain or axial circumferential wavenumber domain respectively. The mappings between the transformed spectrums and the acoustic pressures are established. The prediction error is totally determined by the degree of aliasing in the corresponding transformed domains resulted from spatial sampling. For the fixed observed bearing and analyzing frequency, the prediction precision of acoustic pressure radiated by a vibrating plane is determined by the ratio of the two-dimensional wavenumber spectrums at the specific wavenumber before and after spatial sampling. The prediction precision of acoustic pressure radiated by a vibrating cylinder is mainly decided by the ratio of the axial circumferential wavenumber spectrums at the specific axial wavenumber and below the specific circumferential wavenumber before and after spatial sampling. The spatial sampling interval required by the designated acoustic pressure prediction precision on the simply supported rectangular plate and that on the simply supported cylindrical shell are analyzed numerically. Some conclusions are extended to the cases of spatial sampling on the generally supported rectangular plate and that on the generally supported cylindrical shell.
Experimental research on vibration and radiation of underwater multi-compartmented shell structure is performed together with the related Institute. An engineering method of noise prediction is discussed to solve the problem of vibration phase missing in this experiment. According to the superposition principle of acoustic field, the acoustic pressure level can be expressed as the sum of the acoustic pressure level radiated by the surface elements vibrating independently and a modifying factor. Therein, the modifying factor reflects the correlation between the acoustic pressures arising from the phase inconsistency of the surface vibration. Through the theoretical and experimental studies, the influences of the observation distance and the surface vibration interpolation degree on the modifying factor are analyzed. For the far observers in the same bearing, the modifying factor has nothing with the observation distance and increases with the number of surface elements in the interpolation process. On the basis, an engineering method is put forward to predicting the noise with the modifying factor obtained in the specific case. If the vibration equipments work in different frequency or in different intensity, the noise can be predicted by the modifying factor obtained in the case of all vibration equipments working. If not, the noise can be predicted in some frequency band by the modifying factor obtained in the specific case.
The study in this dissertation provides some further understanding on the rule between vibration and radiation. A new method is put forward to predicting the noise radiated by large underwater structures and providing theoretical foundation for quantitative acoustic design and vibration-noise control. In view of the sampling and reconstruction of spatial signal, the relationships between the spatial sampling on surface vibration and the prediction error of acoustic pressure are analyzed. Some conclusions are of certain guiding significance in designing and evaluating the laying scheme of surface vibration measurements. The prediction method in the case of vibration phase missing has been discussed and provides a new way to solve the actual problems in engineering noise prediction.
引文
[1]王磊,常书刚.潜艇噪声与综合降噪技术的应用.航海技术. 2007, 2: 44-47.
[2]崔维成,刘水庚,顾继红等.国外潜艇设计和性能研究的一些新动态.船舶力学. 2004, 4(2): 65-80.
[3]姜来根. 21世纪海军舰船.北京:国防工业出版社. 1998.
[4]中国舰船研究科技情报研究所.海军装备和舰船新技术进展研究—“十五”科技发展计划参考资料. 1999.
[5]Beattie G A, Cotterill P A. The integrated management and assessment of submarine radiated and sonar self noise performance. UDT. 1995.
[6]Cotterill P A, Barzier S P R. The propagation of vibrational energy along an irregularly reinforced submarine hull. UDT. 1995.
[7]Wittekind D. Practical and theoretical limits in noise reduction of submarines. UDT. 1996.
[8]Giangreco C, Nguyen R. Prediction of self noise on flank array on submarine. UDT. 1995.
[9]周春凯,张均平.潜艇自噪声监测系统.国外舰船工程. 2002, 1: 77-81.
[10]Laulagnet B. Model analysis of a shell’s acoustic radiation in light and heavy fluids. Journal of Sound and Vibration. 1989, 131(3): 397-415.
[11]Stepanishen P R. Modal coupling in the vibration of fluid-loaded cylindrical shells. Journal of the Acoustical Society of America. 1982, 71(4): 813-823.
[12]Photiais D M. The relationships of singular value decomposition to wave-vector by the three-dimensional structures. Journal of the Acoustical Society of America. 1990, 88(4): 1152-1159.
[13]Laulagnet B, Guyader J L. Sound radiation by finite cylindrical ring stiffened shells. Journal of Sound and Vibration. 1990, 138(2): 173–191.
[14]Burroughs C B. Acoustic radiation from fluid-loaded infinite circular cylinders with doubly periodic ring supports. Journal of the Acoustical Society of America. 1984, 75(3): 714-722.
[15]Everstine G C. Finite element formulations of structural acoustics problems. Computers and Structures. 1997, 65: 307-321.
[16]Hunt J T, Knittel M R, Barach D. Finite element approach to acoustic radiation from elastic structures. Journal of the Acoustical Society of America. 1974, 55(2): 269-280.
[17]Astley R J. Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. International Journal for Numerical Methods in Engineering. 2000, 49: 951-976.
[18]Deraemaeker A, Babuska I, Bouillard P. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. International Journal for Numerical Methods in Engineering. 1999, 46: 471-499.
[19]Craggs A. An acoustic finite element approach for studying boundary flexibility and sound transmission between irregular enclosures. Journal of Sound and Vibration. 1973, 39(3): 343-357.
[20]Bell W, Meyer W, Zinn B. Predicting the acoustics of arbitrarily shaped bodies using an integral approach. AIAA Journal. 1977, 15(6): 813-820.
[21]Bell W, Meyer W, Zinn B. Boundary integral solutions of three dimensional acoustic radiation problems. Journal of the Acoustical Society of America. 1978, 59(2): 245-262.
[22]Kleinman R E, Roach G F. Boundary integral equations for the three-dimensional Helmholtz equation. SIAM Review. 1974, 16(2):214-216.
[23]Amini S, Kirkup S M. Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods. Journal of Computational Physics. 1995, 118: 208-221.
[24]Everstine G C, Henderson F M. Coupled finite element/boundary element approach for fluid-structure interaction. Journal of the Acoustical Society of America. 1990, 78: 1938-1947.
[25]Chertock G. Sound Radiation from Vibrating Bodies. Journal of the Acoustical Society of America. 1964, 36(7): 1305-1313
[26]Richard H L. Statistical energy analysis of dynamical systems: theory and application. USA: MIT Press. 1975.
[27]Burroughs C B, Fischer R W, Kern F R. An introduction to statistical energy analysis. Journal of the Acoustical Society of America. 1997, 101(4): 1779-1789.
[28]Woodhouse J. An approach to the theoretical background of statistical energy analysis applied to structural vibration. Journal of the Acoustical Society of America. 1981, 69(6): 1695-1709.
[29] Desmet W. Mid-frequency vibro-acoustic modelling: challenges and potentialsolutions. Proceedings of ISMA. 2002, 2: 835-862.
[30]Nefske D J, Sung S H. Power flow finite element analysis of dynamic systems: basic theory and application to beams. Journal of Vibration, Acoustics, Stress and Reliability in Design. 1989, 111: 94-100.
[31]Carcaterra A, Sestieri A. Energy density equations and power flow in structures. Journal of Sound and Vibration. 1995, 188: 269-282.
[32]Bernhard R J, Huff J E. Structural-acoustic design at high frequency using the energy finite element method. Journal of Vibration and Acoustics. 1999, 121: 295-301.
[33]Mace B R, Shorter P J. Energy flow models from finite element analysis. Journal of Sound and Vibration. 2000, 233: 369-389.
[34]Chen L H, Schweikert D G. Sound radiation from an arbitrary body. Journal of the Acoustical Society of America. 1963, 35(10): 1626-1632.
[35]Kupradze V D, Aleksidze M A. The method of functional equations for the approximate solution of certain boundary value problems. Computational Mathematics and Mathematical Physics. 1964, 4: 82-126.
[36]Schenck H A. Improved integral formulation for acoustic radiation problems. Journal of the Acoustical Society of America. 1968,43: 44-51
[37]Benthien G W, Schenck H A. Nonexistence and non uniqueness problems associated with integral equation methods in acoustics. Computers and Structures. 1997, 65(3): 295～305.
[38] Seybert A F, Rengarajan T K. The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations. Journal of the Acoustical Society of America. 1987, 81(5):1299-1306.
[39]王清,徐博侯.关于Helmholtz外问题的边界积分方程解的唯一性问题.应用数学与力学. 1990, 11(10): 903～909.
[40] Wu T W, Seybert A F. A weighted residual formulation for the CHIEF method in acoustics. Journal of the Acoustical Society of America. 1991, 90(3): 395-402.
[41]张胜勇,陈心昭.分布源边界点法及其在振动体声辐射计算中的应用.声学学报. 1999, 24(2): 149-154.
[42]Zhang S Y, Chen X Z. The volume source boundary point method and its application to an acoustic radiation calculation. Journal of Vibration Engineering. 1998, 11(4): 395-400.
[43]Zhang S Y, Chen X Z, Wang Y C. The distributed source boundary point method(DSBPM) and its application to the calculation for acoustic radiation caused by vibrating body. Acta Acustica. 1999, 24(2): 149-154.
[44]Burton A J, Miller G F. The application of integral equation methods to the numerical solution of some exterior boundary value problems. Proceedings of the Royal Society of London. 1971, 323: 201-210.
[45]Kirkup S M, Henwood D J. Methods for speeding up the boundary element solution of acoustic radiation problems. Journal of Vibration and Acoustics, Transactions of the ASME. 1992, 114(4): 374～380.
[46]Ingber M S, Hickox C E. A modified Burton-Miller algorithm for treating the uniqueness of representation problem for exterior acoustic radiation and scattering problems. Engineering Analysis Boundary Elements. 1992, 9(4): 323-329.
[47]Koopmann G H, Song L, Fahnline J. A method for computing acoustic fields based on the principle of wave superposition. Journal of the Acoustical Society of America. 1989, 86(5): 2433-2438.
[48] Colton D, Kress R. Integrel Equation Methods in Scattering Theory. New York: Wiley Intescience Publication. 1983.
[49]Jeans R, Mathews I C.The wave superposition method as a robust technique for computing acoustic fields[J]. Journal of the Acoustical Society of America. 1992, 92(2): 1156-1166.
[50]Wilton D T, Mathews I C, Jeans R A. A clarification of nonexistence problems with superposition method. Journal of the Acoustical Society of America. 1993, 94(3) :1676～1680.
[51]Hwang J Y, Chang S C. A retracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers, Journal of the Acoustical Society of America. 1991, 90(2): 1167-1180.
[52] Yang S A. An integral equation approach to three-dimensional acoustic radiation and scattering problems. Journal of the Acoustical Society of America. 2004, 116 (3): 1372-1380.
[53]向宇,黄玉盈.基于复数矢径的波叠加法解声辐射问题.固体力学学报. 2004, 25(1): 35-40.
[54]Borgiotti G V. The power radiated by a vibrating body in an acoustic fluid and its determination from boundary measurements. Journal of the Acoustical Society of America. 1990, 88:1884-1893.
[55]Photiadis D M. The relationship of singular value decomposition to wave-vector filtering in sound radiation problems. Journal of the Acoustical Society of America, 1990, 88(2): 1152-1159.
[56]Cunefare K A, Currey M N. On the exterior acoustic radiation modes of structures. Journal of the Acoustical Society of America. 1994, 96: 2302-2312.
[57]Bouchet L B, Loyau T, Hamzaoui N, Boisson C. Calculation of acoustic radiation. using equivalent-sphere methods, J Acoust Soc America, 2000, 107(5): 2387-2397
[58]Sarkissian A. Acoustic radiation from finite structures. Journal of the Acoustical Society of America. 1991, 90(1): 574–578.
[59]毛崎波,姜哲.通过声辐射模态研究结构声辐射的有源控制.声学学报. 2001, 26(3): 277-281.
[60]黎胜,赵德有.结构声辐射的振动模态分析和声辐射模态分析研究.声学学报. 2004, 29(3): 200-208.
[61]李双,陈克安.结构振动模态和声辐射模态之间的对应关系及其应用.声学学报. 2007, 32(2): 171-177.
[62]Pilon A R, Lyrintzis A S. An Improved Kirchhoff Method for Jet Aeroacoustics. AIAA Journal. 1998, 36(5): 783-790.
[63]Hu Q, Wu S F. System and method for predicting sound radiation and scattering from an arbitrarily shaped object. Journal of the Acoustical Society of America. 2000, 107(4): 1811.
[64]汤渭霖.用物理声学方法计算非硬表面的声散射.声学学报. 1993, 18(1): 45-53.
[65]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. 1999, 24(1):1-5.
[66]胡家雄,伏同先. 21世纪常规潜艇声隐身技术发展动态.舰船科学技术. 2001, 4: 2-5.
[67]汤渭霖,范军.水中弹性球壳的共振声辐射理论.声学学报. 2000, 25(4): 308-312
[68]刘涛,范军,汤渭霖.水中弹性圆柱壳的共振声辐射.声学学报. 2002, 27(1): 62-66
[69]汤渭霖,何兵蓉.水中有限长加肋圆柱壳体振动和声辐射近似解析解.声学学报. 2001, 26(1): 1-5.
[70]商德江,何祚镛.加肋双层圆柱壳振动声辐射数值计算分析.声学学报. 2001, 26(3): 193-201.
[71]骆东平,张玉红.环肋增强柱壳振动特性分析,中国造船. 1989, 1: 64-74.
[72]严谨.水下复杂圆柱壳振动能量流和声辐射特性研究[博士论文].武汉:华中科技大学. 2006 .
[73]谢官模,李军向,罗斌等.环肋、舱壁和纵骨加强的无限长圆柱壳在水下的声辐射特性.船舶力学. 2004, 8(2): 101-108.
[74]陈美霞.有限长加筋双层圆柱壳声辐射性能分析[博士学位论文].武汉:华中科技大学. 2003.
[75]姚熊亮,刘庆杰,翁强等.水下加筋圆柱壳体的振动与近场声辐射研究.中国舰船研究. 2006, 1(2): 13-16.
[76]陈美霞,邱昌林,骆东平.基于FEM /BEM法的内部声激励水下圆柱壳声辐射计算中国舰船研究. 2007, 2(6): 50-54.
[77]童宗鹏,王国治,张志谊等.水下航行器声振特性的统计能量法研究.噪声与振动控制. 2005, 1: 29-32.
[78]盛美萍.杂耦合系统的统计能量分析及其应用.中国工程科学. 2002, 4(6): 77-84.
[79]孙丽萍.能量有限元法研究及其应用[博士论文].哈尔滨工程大学. 2004.
[80]何祚镛.实船设备结构振动和水声声强测试分析及噪声源的识别.中国造船. 2003, 44(2): 50-58.
[81]骆东平,谢官模,谭林森.环肋柱壳在流场中的声辐射性能实验报告.武汉造船. 1997, (5): 43-46.
[82]曾革委,吴崇健.加肋圆柱壳舱段水下声辐射试验研究.中国舰船研究. 2006, 1(1): 13-16.
[83]Chen M, Wang B, Cao W. Experimental research on vibration and acoustic radiation of the submerged complicated shell structure with multiple excitations. Journal of Ship Mechanics. 2008.
[84]Morse M P, Feshbach H. Methods of theoretical physics. New York: McGraw Hill. 1953.
[85]Seybert A F, Soenarko B, Rizzo F J, etc. Application of the BIE method to sound radiation problems using an isoparametric element. Journal of Vibration, Acoustics, Stress, and Reliability in Design. 1984, 106: 414-419.
[86]Tong Z, Zhang Y, Zhang Z, etc.. Dynamic behavior and sound transmission analysis of a fluid–structure coupled system using the direct-BEM/FEM. Journal of Sound and Vibration. 2007, 299(3): 645-655.
[87]赵键,汪鸿振,朱物华.边界元法计算已知振速封闭面的声辐射.声学学报, 1989; 14(4): 250-257.
[88] Terai T. On calculation of sound fields around three dimensional objects by integral equation methods. Journal of Sound and Vibration. 1980, 69(1): 71-100.
[89]何祚镛,赵玉芳.声学理论基础.北京:国防工业出版社. 1981.
[90]Vlahopoulos N, Raveendra S T. Formulation, implementation and validation of multiple connection and free edge constraints in an indirect boundary element formulation. Journal of Sound and Vibration. 1998, 210(1): 137-152.
[91]Banerjee P K. The Boundary Element Methods in Engineering. New York: McGraw Hill. 1994.
[92]Cickowski R D, Brebbia C A. Boundary Element Methods in Acoustics. Southampton Boston: Computational Mechanics Publications. 1991.
[93]LMS International, SYSNOISE Users Manual, 1998
[94]Estorff V O. Efforts to reduce computation time in numerical acoustics - An overview. Acta Acustica. 2003, 89(1): 1-13.
[95]黄其柏,赵志高. Helmholtz边界积分方程的多频计算.声学学报. 2005, 30(3): 255-263.
[96]宁德志,滕斌,勾莹.快速多极子展开技术在高阶边界元方法中的实现.计算力学学报. 2005, 22(6): 700-704.
[97]雷霆,姚振汉,王海涛.三维快速多极边界元高性能并行计算.清华大学学报. 2007, 47(2): 280-283.
[98]Michel Tran Van Nhieu. An approximate solution to sound radiation from slender bodies. Journal of the Acoustical Society of America. 1994, 96(2): 1070-1079.
[99]Utschig M, Achenbach J D, Igusa T. Reduction to parts: A semianalytical approach to the structural acoustics of a cylindrical shell with hemispherical endcaps. Journal of the Acoustical Society of America. 1996; 100 (2): 871-881.
[100]王斌,汤渭霖,范军.一种辐射声场预报方法——单元辐射叠加法.声学学报. 2008, 33(3): 226-230.
[101]范军,汤渭霖.声纳目标强度(TS)计算在板块元方法.声学技术. 1999,增刊: 31-32.
[102]李建鲁,范军,汤渭霖.水下简单形状目标回声的近远场过渡特性.上海交通大学学报. 2001, 12: 86-90.
[103]范军,李建鲁,汤渭霖.水下复杂形状目标回声的近、远场过渡特性.上海交通大学学报. 2002, 02: 21-24.
[104]Junger M C, Feit D. Sound, Structures, and Their Interaction. Cambridge MA: MIT Press, 1986.
[105]刘涛.水中复杂壳体的声振特性研究[博士论文].上海交通大学. 2002.
[106]Kincaid D, Cheney W. Numerical Analysis Mathematics of Scientific Computing (Third Edition). USA: Thomson. 2003.
[107]Dobroveolskii Y Y. Mutual radiation impedance of small pistons in a convex baffle. Soviet physics acoustics. 1971, 14(4): 440-443.
[108]Lee J, Seo I. Radiation impedance computations of a square piston in a rigid infinite baffle. Journal of Sound and Vibration. 1996, 198(3): 299-312.
[109]KAN S, JUN Y, GAN W S. A simple calculation method for the self- and mutual- radiation impedance of flexible rectangular patches in a rigid infinite baffle. Journal of sound and vibration. 2005, 282(1): 179-195.
[110]Kim M J, Kim C D, Ha K L. A new calculation method of radiation impedance for Vibrating Surfaces with an Arbitrary Shape. Japan society of applied physics. 2000, 39(5): 3174-3179.
[111]Arase E M. Mutual Radiation Impedance of Square and Rectangular Pistons in a Rigid Infinite Baffie. J. Acoust. Soc. Am.1964, 36(8): 1521-1525.
[112]Greenspon J E, Sherman C H. Mutual-radiation impedance and near field pressure for pistons on a cylinder. Journal of the Acoustical Society of America. 1964, 36(1): 149-153.
[113]Kim J S, Kim M J, Ha K L, etc. Improvement of calculation for radiation impedance of the vibrators with cylindrical baffle. Japan society of applied physics. 2004, 43(5): 3188-3192.
[114]Shenman C H. Mutual radiation impedance of sources on a sphere. Journal of the Acoustical Society of America. 1959, 31(7): 947-952.
[115]Van Boisvert J E, Buren A L V. Acoustic radiation impedance and directional response of rectangular pistons on elliptic cylinders. Journal of the Acoustical Society of America 2005, 118(1): 104-112.
[116]Machens, Kai-Ulrich. On radiation from elliptic-cylinder geometries, Acta Acustica, 1999,85(4): 449-463.
[117]Van Boisvert J E, Buren A L V. Acoustic radiation impedance of rectangular pistons on prolate spheroids. Journal of the Acoustical Society of America. 2002, 111(2): 867-874.
[118]Gutierrez-Vega J C, Rodriguez-Dagnino R M, Meneses-Nava M A, etc. Mathieu functions, a visual approach. American Journal of Physics. 2003, 71(3): 233-241.
[119]Lindner A, Freese H. A new method to compute Mathieu functions. American Journal of Physics. 1994, 27: 5565-5571.
[120]Frenkel D, Portugal R. Algebraic methods to compute Mathieu functions. American Journal of Physics. 2001, 34: 3541-3551.
[121]Van Buren A L, Boisvert J E. Accurate calculation of prolate spheroidal radial functions of the first kind and their first derivatives. Quarterly of Applied Mathematics. 2002, 60(3): 589-599.
[122]Van Buren A L, Boisvert J E. Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives. Quarterly of Applied Mathematics. 2004, 62(3): 493-507.
[123]Wang C, Lai J C S. The sound radiation efficiency of finite length acoustically circular cylindrical shells under mechanical excitation II: limitations of the infinite length model. Journal of Sound and Vibration. 2001, 241(5): 825-838.
[124]Drumheller D M, Gilroy L E, Hazen M G. The Bistatic Acoustic Simple Integrated Structure (BASIS) Target Strength Model. Technical Report. US Naval Research Laboratory. 2002.
[125]Gilroy L E, Brennan D P. Predicting Acoustic Target Strength with AVAST. DRDC Atlantic. 2001.
[126]Fiedler C, Schneider H G. BeTSSi-Sub Benchmark Target Strength Simulation Submarine. Technical Report. Germany. 2002.
[127]Burroughs C B, Hallander J E. Acoustic radiation from fluid-loaded, ribbed cylindrical shells excited by different types of concentrated mechanical drives. Journal of the Acoustical Society of America. 1992, 91(5):2721-2739.
[128] Harari A, Sandman B E, Zaldonis J A. Analytical and experimental determination of the vibration and pressure radiation from a submerged cylindrical shell with two end plates. Journal of the Acoustical Society of America. 1994, 95(6): 3360-3368.
[129]Bonilha M W, Fahy F J. On the vibration field correlation of randomly excited flat plate structures, I: Theory. Journal of Sound and Vibration. 1998, 214(3): 443-467.
[130]Bonilha M W, Fahy F J. On the vibration field correlation of randomly excited flat plate structures, II: Experimental verification. Journal of Sound and Vibration. 1998, 214(3): 469-496.
[131]Anton H, Jan E, Harald P, etc. Experimental and numerical investigation of a complex submerged structure. Part I: modal analysis. Acta Acustica. 2003, 89 (1): 61-70.
[132]Anton H, Jan E, Harald P, etc. Experimental and numerical investigation of a complex submerged structure. Part II: sound radiation. Acta Acustica. 2003, 89(1): 71-77.
[133]于沨,陈宗岐,蒋行海等.潜艇噪声振动同时基测量与噪声源分析技术.舰船科学技术. 2002, 24(1): 24-26.
[134]于沨,那健,朱练军等.水下目标振动噪声监测.测试技术学报. 2002, 16(z1): 485-488.
[135]王怀应;朱练军;杨松等.利用ICP振动加速度计进行潜艇振动监测.舰船科学技术. 2002, 24(1): 27-29.
[136]Tao J, Ge H L, Qiu X. A new rule of vibration sampling for predicting acoustical radiation from rectangular plates. Journal of Sound and Vibration. 2006, 67(8): 756-770.
[137]Bert C W, Malik M. Frequency equations and modes of free vibration of rectangular plate with various edges condition. Proc Institution Mechanical Engineer (Part C). 1994, 208: 307-319.
[138]Frank F, Palol G. Sound and structural vibration. New York: Academic. 1987.
[139]Szechenyi E. Modal densities and radiation efficiencies of unstiffened cylinders using statistical methods. Journal of Sound and Vibration. 1971, 19(1): 65-81.
[140]李新民,张景绘.水下圆柱壳体固有频率的近似计算分析.应用力学学报. 2008, 25(2): 326-331.
[2]崔维成,刘水庚,顾继红等.国外潜艇设计和性能研究的一些新动态.船舶力学. 2004, 4(2): 65-80.
[3]姜来根. 21世纪海军舰船.北京:国防工业出版社. 1998.
[4]中国舰船研究科技情报研究所.海军装备和舰船新技术进展研究—“十五”科技发展计划参考资料. 1999.
[5]Beattie G A, Cotterill P A. The integrated management and assessment of submarine radiated and sonar self noise performance. UDT. 1995.
[6]Cotterill P A, Barzier S P R. The propagation of vibrational energy along an irregularly reinforced submarine hull. UDT. 1995.
[7]Wittekind D. Practical and theoretical limits in noise reduction of submarines. UDT. 1996.
[8]Giangreco C, Nguyen R. Prediction of self noise on flank array on submarine. UDT. 1995.
[9]周春凯,张均平.潜艇自噪声监测系统.国外舰船工程. 2002, 1: 77-81.
[10]Laulagnet B. Model analysis of a shell’s acoustic radiation in light and heavy fluids. Journal of Sound and Vibration. 1989, 131(3): 397-415.
[11]Stepanishen P R. Modal coupling in the vibration of fluid-loaded cylindrical shells. Journal of the Acoustical Society of America. 1982, 71(4): 813-823.
[12]Photiais D M. The relationships of singular value decomposition to wave-vector by the three-dimensional structures. Journal of the Acoustical Society of America. 1990, 88(4): 1152-1159.
[13]Laulagnet B, Guyader J L. Sound radiation by finite cylindrical ring stiffened shells. Journal of Sound and Vibration. 1990, 138(2): 173–191.
[14]Burroughs C B. Acoustic radiation from fluid-loaded infinite circular cylinders with doubly periodic ring supports. Journal of the Acoustical Society of America. 1984, 75(3): 714-722.
[15]Everstine G C. Finite element formulations of structural acoustics problems. Computers and Structures. 1997, 65: 307-321.
[16]Hunt J T, Knittel M R, Barach D. Finite element approach to acoustic radiation from elastic structures. Journal of the Acoustical Society of America. 1974, 55(2): 269-280.
[17]Astley R J. Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. International Journal for Numerical Methods in Engineering. 2000, 49: 951-976.
[18]Deraemaeker A, Babuska I, Bouillard P. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. International Journal for Numerical Methods in Engineering. 1999, 46: 471-499.
[19]Craggs A. An acoustic finite element approach for studying boundary flexibility and sound transmission between irregular enclosures. Journal of Sound and Vibration. 1973, 39(3): 343-357.
[20]Bell W, Meyer W, Zinn B. Predicting the acoustics of arbitrarily shaped bodies using an integral approach. AIAA Journal. 1977, 15(6): 813-820.
[21]Bell W, Meyer W, Zinn B. Boundary integral solutions of three dimensional acoustic radiation problems. Journal of the Acoustical Society of America. 1978, 59(2): 245-262.
[22]Kleinman R E, Roach G F. Boundary integral equations for the three-dimensional Helmholtz equation. SIAM Review. 1974, 16(2):214-216.
[23]Amini S, Kirkup S M. Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods. Journal of Computational Physics. 1995, 118: 208-221.
[24]Everstine G C, Henderson F M. Coupled finite element/boundary element approach for fluid-structure interaction. Journal of the Acoustical Society of America. 1990, 78: 1938-1947.
[25]Chertock G. Sound Radiation from Vibrating Bodies. Journal of the Acoustical Society of America. 1964, 36(7): 1305-1313
[26]Richard H L. Statistical energy analysis of dynamical systems: theory and application. USA: MIT Press. 1975.
[27]Burroughs C B, Fischer R W, Kern F R. An introduction to statistical energy analysis. Journal of the Acoustical Society of America. 1997, 101(4): 1779-1789.
[28]Woodhouse J. An approach to the theoretical background of statistical energy analysis applied to structural vibration. Journal of the Acoustical Society of America. 1981, 69(6): 1695-1709.
[29] Desmet W. Mid-frequency vibro-acoustic modelling: challenges and potentialsolutions. Proceedings of ISMA. 2002, 2: 835-862.
[30]Nefske D J, Sung S H. Power flow finite element analysis of dynamic systems: basic theory and application to beams. Journal of Vibration, Acoustics, Stress and Reliability in Design. 1989, 111: 94-100.
[31]Carcaterra A, Sestieri A. Energy density equations and power flow in structures. Journal of Sound and Vibration. 1995, 188: 269-282.
[32]Bernhard R J, Huff J E. Structural-acoustic design at high frequency using the energy finite element method. Journal of Vibration and Acoustics. 1999, 121: 295-301.
[33]Mace B R, Shorter P J. Energy flow models from finite element analysis. Journal of Sound and Vibration. 2000, 233: 369-389.
[34]Chen L H, Schweikert D G. Sound radiation from an arbitrary body. Journal of the Acoustical Society of America. 1963, 35(10): 1626-1632.
[35]Kupradze V D, Aleksidze M A. The method of functional equations for the approximate solution of certain boundary value problems. Computational Mathematics and Mathematical Physics. 1964, 4: 82-126.
[36]Schenck H A. Improved integral formulation for acoustic radiation problems. Journal of the Acoustical Society of America. 1968,43: 44-51
[37]Benthien G W, Schenck H A. Nonexistence and non uniqueness problems associated with integral equation methods in acoustics. Computers and Structures. 1997, 65(3): 295～305.
[38] Seybert A F, Rengarajan T K. The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations. Journal of the Acoustical Society of America. 1987, 81(5):1299-1306.
[39]王清,徐博侯.关于Helmholtz外问题的边界积分方程解的唯一性问题.应用数学与力学. 1990, 11(10): 903～909.
[40] Wu T W, Seybert A F. A weighted residual formulation for the CHIEF method in acoustics. Journal of the Acoustical Society of America. 1991, 90(3): 395-402.
[41]张胜勇,陈心昭.分布源边界点法及其在振动体声辐射计算中的应用.声学学报. 1999, 24(2): 149-154.
[42]Zhang S Y, Chen X Z. The volume source boundary point method and its application to an acoustic radiation calculation. Journal of Vibration Engineering. 1998, 11(4): 395-400.
[43]Zhang S Y, Chen X Z, Wang Y C. The distributed source boundary point method(DSBPM) and its application to the calculation for acoustic radiation caused by vibrating body. Acta Acustica. 1999, 24(2): 149-154.
[44]Burton A J, Miller G F. The application of integral equation methods to the numerical solution of some exterior boundary value problems. Proceedings of the Royal Society of London. 1971, 323: 201-210.
[45]Kirkup S M, Henwood D J. Methods for speeding up the boundary element solution of acoustic radiation problems. Journal of Vibration and Acoustics, Transactions of the ASME. 1992, 114(4): 374～380.
[46]Ingber M S, Hickox C E. A modified Burton-Miller algorithm for treating the uniqueness of representation problem for exterior acoustic radiation and scattering problems. Engineering Analysis Boundary Elements. 1992, 9(4): 323-329.
[47]Koopmann G H, Song L, Fahnline J. A method for computing acoustic fields based on the principle of wave superposition. Journal of the Acoustical Society of America. 1989, 86(5): 2433-2438.
[48] Colton D, Kress R. Integrel Equation Methods in Scattering Theory. New York: Wiley Intescience Publication. 1983.
[49]Jeans R, Mathews I C.The wave superposition method as a robust technique for computing acoustic fields[J]. Journal of the Acoustical Society of America. 1992, 92(2): 1156-1166.
[50]Wilton D T, Mathews I C, Jeans R A. A clarification of nonexistence problems with superposition method. Journal of the Acoustical Society of America. 1993, 94(3) :1676～1680.
[51]Hwang J Y, Chang S C. A retracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers, Journal of the Acoustical Society of America. 1991, 90(2): 1167-1180.
[52] Yang S A. An integral equation approach to three-dimensional acoustic radiation and scattering problems. Journal of the Acoustical Society of America. 2004, 116 (3): 1372-1380.
[53]向宇,黄玉盈.基于复数矢径的波叠加法解声辐射问题.固体力学学报. 2004, 25(1): 35-40.
[54]Borgiotti G V. The power radiated by a vibrating body in an acoustic fluid and its determination from boundary measurements. Journal of the Acoustical Society of America. 1990, 88:1884-1893.
[55]Photiadis D M. The relationship of singular value decomposition to wave-vector filtering in sound radiation problems. Journal of the Acoustical Society of America, 1990, 88(2): 1152-1159.
[56]Cunefare K A, Currey M N. On the exterior acoustic radiation modes of structures. Journal of the Acoustical Society of America. 1994, 96: 2302-2312.
[57]Bouchet L B, Loyau T, Hamzaoui N, Boisson C. Calculation of acoustic radiation. using equivalent-sphere methods, J Acoust Soc America, 2000, 107(5): 2387-2397
[58]Sarkissian A. Acoustic radiation from finite structures. Journal of the Acoustical Society of America. 1991, 90(1): 574–578.
[59]毛崎波,姜哲.通过声辐射模态研究结构声辐射的有源控制.声学学报. 2001, 26(3): 277-281.
[60]黎胜,赵德有.结构声辐射的振动模态分析和声辐射模态分析研究.声学学报. 2004, 29(3): 200-208.
[61]李双,陈克安.结构振动模态和声辐射模态之间的对应关系及其应用.声学学报. 2007, 32(2): 171-177.
[62]Pilon A R, Lyrintzis A S. An Improved Kirchhoff Method for Jet Aeroacoustics. AIAA Journal. 1998, 36(5): 783-790.
[63]Hu Q, Wu S F. System and method for predicting sound radiation and scattering from an arbitrarily shaped object. Journal of the Acoustical Society of America. 2000, 107(4): 1811.
[64]汤渭霖.用物理声学方法计算非硬表面的声散射.声学学报. 1993, 18(1): 45-53.
[65]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. 1999, 24(1):1-5.
[66]胡家雄,伏同先. 21世纪常规潜艇声隐身技术发展动态.舰船科学技术. 2001, 4: 2-5.
[67]汤渭霖,范军.水中弹性球壳的共振声辐射理论.声学学报. 2000, 25(4): 308-312
[68]刘涛,范军,汤渭霖.水中弹性圆柱壳的共振声辐射.声学学报. 2002, 27(1): 62-66
[69]汤渭霖,何兵蓉.水中有限长加肋圆柱壳体振动和声辐射近似解析解.声学学报. 2001, 26(1): 1-5.
[70]商德江,何祚镛.加肋双层圆柱壳振动声辐射数值计算分析.声学学报. 2001, 26(3): 193-201.
[71]骆东平,张玉红.环肋增强柱壳振动特性分析,中国造船. 1989, 1: 64-74.
[72]严谨.水下复杂圆柱壳振动能量流和声辐射特性研究[博士论文].武汉:华中科技大学. 2006 .
[73]谢官模,李军向,罗斌等.环肋、舱壁和纵骨加强的无限长圆柱壳在水下的声辐射特性.船舶力学. 2004, 8(2): 101-108.
[74]陈美霞.有限长加筋双层圆柱壳声辐射性能分析[博士学位论文].武汉:华中科技大学. 2003.
[75]姚熊亮,刘庆杰,翁强等.水下加筋圆柱壳体的振动与近场声辐射研究.中国舰船研究. 2006, 1(2): 13-16.
[76]陈美霞,邱昌林,骆东平.基于FEM /BEM法的内部声激励水下圆柱壳声辐射计算中国舰船研究. 2007, 2(6): 50-54.
[77]童宗鹏,王国治,张志谊等.水下航行器声振特性的统计能量法研究.噪声与振动控制. 2005, 1: 29-32.
[78]盛美萍.杂耦合系统的统计能量分析及其应用.中国工程科学. 2002, 4(6): 77-84.
[79]孙丽萍.能量有限元法研究及其应用[博士论文].哈尔滨工程大学. 2004.
[80]何祚镛.实船设备结构振动和水声声强测试分析及噪声源的识别.中国造船. 2003, 44(2): 50-58.
[81]骆东平,谢官模,谭林森.环肋柱壳在流场中的声辐射性能实验报告.武汉造船. 1997, (5): 43-46.
[82]曾革委,吴崇健.加肋圆柱壳舱段水下声辐射试验研究.中国舰船研究. 2006, 1(1): 13-16.
[83]Chen M, Wang B, Cao W. Experimental research on vibration and acoustic radiation of the submerged complicated shell structure with multiple excitations. Journal of Ship Mechanics. 2008.
[84]Morse M P, Feshbach H. Methods of theoretical physics. New York: McGraw Hill. 1953.
[85]Seybert A F, Soenarko B, Rizzo F J, etc. Application of the BIE method to sound radiation problems using an isoparametric element. Journal of Vibration, Acoustics, Stress, and Reliability in Design. 1984, 106: 414-419.
[86]Tong Z, Zhang Y, Zhang Z, etc.. Dynamic behavior and sound transmission analysis of a fluid–structure coupled system using the direct-BEM/FEM. Journal of Sound and Vibration. 2007, 299(3): 645-655.
[87]赵键,汪鸿振,朱物华.边界元法计算已知振速封闭面的声辐射.声学学报, 1989; 14(4): 250-257.
[88] Terai T. On calculation of sound fields around three dimensional objects by integral equation methods. Journal of Sound and Vibration. 1980, 69(1): 71-100.
[89]何祚镛,赵玉芳.声学理论基础.北京:国防工业出版社. 1981.
[90]Vlahopoulos N, Raveendra S T. Formulation, implementation and validation of multiple connection and free edge constraints in an indirect boundary element formulation. Journal of Sound and Vibration. 1998, 210(1): 137-152.
[91]Banerjee P K. The Boundary Element Methods in Engineering. New York: McGraw Hill. 1994.
[92]Cickowski R D, Brebbia C A. Boundary Element Methods in Acoustics. Southampton Boston: Computational Mechanics Publications. 1991.
[93]LMS International, SYSNOISE Users Manual, 1998
[94]Estorff V O. Efforts to reduce computation time in numerical acoustics - An overview. Acta Acustica. 2003, 89(1): 1-13.
[95]黄其柏,赵志高. Helmholtz边界积分方程的多频计算.声学学报. 2005, 30(3): 255-263.
[96]宁德志,滕斌,勾莹.快速多极子展开技术在高阶边界元方法中的实现.计算力学学报. 2005, 22(6): 700-704.
[97]雷霆,姚振汉,王海涛.三维快速多极边界元高性能并行计算.清华大学学报. 2007, 47(2): 280-283.
[98]Michel Tran Van Nhieu. An approximate solution to sound radiation from slender bodies. Journal of the Acoustical Society of America. 1994, 96(2): 1070-1079.
[99]Utschig M, Achenbach J D, Igusa T. Reduction to parts: A semianalytical approach to the structural acoustics of a cylindrical shell with hemispherical endcaps. Journal of the Acoustical Society of America. 1996; 100 (2): 871-881.
[100]王斌,汤渭霖,范军.一种辐射声场预报方法——单元辐射叠加法.声学学报. 2008, 33(3): 226-230.
[101]范军,汤渭霖.声纳目标强度(TS)计算在板块元方法.声学技术. 1999,增刊: 31-32.
[102]李建鲁,范军,汤渭霖.水下简单形状目标回声的近远场过渡特性.上海交通大学学报. 2001, 12: 86-90.
[103]范军,李建鲁,汤渭霖.水下复杂形状目标回声的近、远场过渡特性.上海交通大学学报. 2002, 02: 21-24.
[104]Junger M C, Feit D. Sound, Structures, and Their Interaction. Cambridge MA: MIT Press, 1986.
[105]刘涛.水中复杂壳体的声振特性研究[博士论文].上海交通大学. 2002.
[106]Kincaid D, Cheney W. Numerical Analysis Mathematics of Scientific Computing (Third Edition). USA: Thomson. 2003.
[107]Dobroveolskii Y Y. Mutual radiation impedance of small pistons in a convex baffle. Soviet physics acoustics. 1971, 14(4): 440-443.
[108]Lee J, Seo I. Radiation impedance computations of a square piston in a rigid infinite baffle. Journal of Sound and Vibration. 1996, 198(3): 299-312.
[109]KAN S, JUN Y, GAN W S. A simple calculation method for the self- and mutual- radiation impedance of flexible rectangular patches in a rigid infinite baffle. Journal of sound and vibration. 2005, 282(1): 179-195.
[110]Kim M J, Kim C D, Ha K L. A new calculation method of radiation impedance for Vibrating Surfaces with an Arbitrary Shape. Japan society of applied physics. 2000, 39(5): 3174-3179.
[111]Arase E M. Mutual Radiation Impedance of Square and Rectangular Pistons in a Rigid Infinite Baffie. J. Acoust. Soc. Am.1964, 36(8): 1521-1525.
[112]Greenspon J E, Sherman C H. Mutual-radiation impedance and near field pressure for pistons on a cylinder. Journal of the Acoustical Society of America. 1964, 36(1): 149-153.
[113]Kim J S, Kim M J, Ha K L, etc. Improvement of calculation for radiation impedance of the vibrators with cylindrical baffle. Japan society of applied physics. 2004, 43(5): 3188-3192.
[114]Shenman C H. Mutual radiation impedance of sources on a sphere. Journal of the Acoustical Society of America. 1959, 31(7): 947-952.
[115]Van Boisvert J E, Buren A L V. Acoustic radiation impedance and directional response of rectangular pistons on elliptic cylinders. Journal of the Acoustical Society of America 2005, 118(1): 104-112.
[116]Machens, Kai-Ulrich. On radiation from elliptic-cylinder geometries, Acta Acustica, 1999,85(4): 449-463.
[117]Van Boisvert J E, Buren A L V. Acoustic radiation impedance of rectangular pistons on prolate spheroids. Journal of the Acoustical Society of America. 2002, 111(2): 867-874.
[118]Gutierrez-Vega J C, Rodriguez-Dagnino R M, Meneses-Nava M A, etc. Mathieu functions, a visual approach. American Journal of Physics. 2003, 71(3): 233-241.
[119]Lindner A, Freese H. A new method to compute Mathieu functions. American Journal of Physics. 1994, 27: 5565-5571.
[120]Frenkel D, Portugal R. Algebraic methods to compute Mathieu functions. American Journal of Physics. 2001, 34: 3541-3551.
[121]Van Buren A L, Boisvert J E. Accurate calculation of prolate spheroidal radial functions of the first kind and their first derivatives. Quarterly of Applied Mathematics. 2002, 60(3): 589-599.
[122]Van Buren A L, Boisvert J E. Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives. Quarterly of Applied Mathematics. 2004, 62(3): 493-507.
[123]Wang C, Lai J C S. The sound radiation efficiency of finite length acoustically circular cylindrical shells under mechanical excitation II: limitations of the infinite length model. Journal of Sound and Vibration. 2001, 241(5): 825-838.
[124]Drumheller D M, Gilroy L E, Hazen M G. The Bistatic Acoustic Simple Integrated Structure (BASIS) Target Strength Model. Technical Report. US Naval Research Laboratory. 2002.
[125]Gilroy L E, Brennan D P. Predicting Acoustic Target Strength with AVAST. DRDC Atlantic. 2001.
[126]Fiedler C, Schneider H G. BeTSSi-Sub Benchmark Target Strength Simulation Submarine. Technical Report. Germany. 2002.
[127]Burroughs C B, Hallander J E. Acoustic radiation from fluid-loaded, ribbed cylindrical shells excited by different types of concentrated mechanical drives. Journal of the Acoustical Society of America. 1992, 91(5):2721-2739.
[128] Harari A, Sandman B E, Zaldonis J A. Analytical and experimental determination of the vibration and pressure radiation from a submerged cylindrical shell with two end plates. Journal of the Acoustical Society of America. 1994, 95(6): 3360-3368.
[129]Bonilha M W, Fahy F J. On the vibration field correlation of randomly excited flat plate structures, I: Theory. Journal of Sound and Vibration. 1998, 214(3): 443-467.
[130]Bonilha M W, Fahy F J. On the vibration field correlation of randomly excited flat plate structures, II: Experimental verification. Journal of Sound and Vibration. 1998, 214(3): 469-496.
[131]Anton H, Jan E, Harald P, etc. Experimental and numerical investigation of a complex submerged structure. Part I: modal analysis. Acta Acustica. 2003, 89 (1): 61-70.
[132]Anton H, Jan E, Harald P, etc. Experimental and numerical investigation of a complex submerged structure. Part II: sound radiation. Acta Acustica. 2003, 89(1): 71-77.
[133]于沨,陈宗岐,蒋行海等.潜艇噪声振动同时基测量与噪声源分析技术.舰船科学技术. 2002, 24(1): 24-26.
[134]于沨,那健,朱练军等.水下目标振动噪声监测.测试技术学报. 2002, 16(z1): 485-488.
[135]王怀应;朱练军;杨松等.利用ICP振动加速度计进行潜艇振动监测.舰船科学技术. 2002, 24(1): 27-29.
[136]Tao J, Ge H L, Qiu X. A new rule of vibration sampling for predicting acoustical radiation from rectangular plates. Journal of Sound and Vibration. 2006, 67(8): 756-770.
[137]Bert C W, Malik M. Frequency equations and modes of free vibration of rectangular plate with various edges condition. Proc Institution Mechanical Engineer (Part C). 1994, 208: 307-319.
[138]Frank F, Palol G. Sound and structural vibration. New York: Academic. 1987.
[139]Szechenyi E. Modal densities and radiation efficiencies of unstiffened cylinders using statistical methods. Journal of Sound and Vibration. 1971, 19(1): 65-81.
[140]李新民,张景绘.水下圆柱壳体固有频率的近似计算分析.应用力学学报. 2008, 25(2): 326-331.