瞬态近场声全息理论和实验研究
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摘要
近场声全息技术(NAH)是近二十多年来发展起来的一种具有强大的噪声源识别定位和声场可视化功能的声学前沿技术,它可以为产品的噪声控制、低噪声及声质量设计等提供重要依据。目前,国内外学者提出了多种全息算法,然而这些算法大多在频域内进行,且只适用于稳态声场。在实际工程中,很多情况下声场为瞬态声场,若将NAH应用到瞬态声场,获得声场随时间的变化规律,必将极大地扩展其工程应用范围。正是在这一背景下,瞬态近场声全息(TNAH)被提出来。本文在分析TNAH的研究意义和研究进展的基础上,将已有的TNAH按照全息面声压信号处理方式的不同分为四类：基于三维变换的TNAH、基于二维变换的TNAH、基于一维变换的TNAH和无需变换的TNAH。本文对这四类TNAH中存在的问题进行了深入地研究和探讨,并提出了相应的解决方法。在基于三维变换的TNAH研究中,提出了基于Laplace变换的瞬态声场质点振速重建方法,用于解决基于Fourier变换的时域声全息在重建质点振速时出现的奇异性问题；在基于二维变换的TNAH研究中,推导出全息面声压到重建面质点振速之间的脉冲响应函数,并结合实时声全息的思想提出了基于该脉冲响应函数的质点振速重建方法；在无需变换的TNAH研究方面,提出了两种新的全息方法：基于时域平面波叠加法的TNAH和基于插值时域等效源法(ESM)的TNAH;最后提出一种瞬态声场分离方法,实现了TNAH在非自由声场条件下的运用。本文具体研究内容如下：
第一章首先阐述了TNAH的研究意义,然后通过论述国内外有关瞬态声辐射计算的研究进展为TNAH的研究提供借鉴和思路,最后通过回顾目前国内外已有的TNAH方法,并分析其存在的问题,确立了本文的主要研究内容。
第二章研究了基于三维变换的时域声全息。首先推导了基于Fourier变换的时域声全息的声压重建公式,并从理论上分析了声压重建过程中的误差及其控制办法。为了解决基于Fourier变换的时域声全息在重建质点振速时出现的奇异性问题,提出了基于Laplace变换的瞬态声场质点振速重建方法,并通过以固定在障板上的活塞为声源的数值仿真验证了所提出方法的有效性。
第三章分析了基于二维变换的实时声全息。首先从速度势波动方程和Neumann边界条件出发,运用Laplace变换推导了全息面声压到重建面声压之间的脉冲响应函数,并阐述了基于该脉冲响应函数的声压重建过程。为了能够实现声场中质点振速的实时重建,运用Laplace变换推导了全息面声压到重建面质点振速之间的脉冲响应函数,并结合实时声全息的思想提出了基于该脉冲响应函数的质点振速重建方法,最后通过以障板上的圆形活塞为声源的数值仿真检验了该方法的有效性。
第四章基于波叠加法的思想,提出了两种无需对全息面声压进行任何变换的TNAH:基于时域平面波叠加法的TNAH和基于插值时域ESM的TNAH。两者均避开了二维空间Fourier变换的使用,从而避免了二维空间Fourier变换所带来的限制；而且两者的重建过程均在时域内进行,因而具有实时重建声场的能力。首先推导了基于时域平面波叠加法的TNAH的重建公式,详述了其重建过程,并通过数值仿真和实验验证了其有效性,进一步与时域声全息和实时声全息相比较阐述了其优越性。随后推导了基于插值时域ESM的TNAH的重建公式,阐述了其重建过程,并通过三例具有不同形状声源的仿真阐述了该方法不仅具有TNAH常规的功能,而且不受声源形状的限制,因此该方法具有更加广阔的应用范围。
第五章将TNAH扩展到非自由声场。首先基于声波在时域波数域的传播原理,推导了瞬态声场分离公式,提出了一种适用于非自由声场条件下的瞬态声场分离方法。该方法不仅可以在空间域,而且可以在时域,很好地移除干扰声源的影响,分离出只有目标声源辐射的声场；继而可以将分离出来的目标声源辐射声场与TNAH联合起来,实现非自由声场条件下的声场重建。
第六章总结了本文的主要研究成果,提出了需要进一步研究和解决的问题。
Nearfield acoustic holography (NAH), developed in recent over20years, is an advanced acoustic technique with the powerful abilities of identifying noise sources and visualizing sound fields. It can provide the important guidance for the noise control, as well as the low-noise and sound quality design of product. Up to now, the domestic and foreign scholars have proposed a number of holography methods. However, these methods almost proceed in the frequency domain, and are only applied to stationary sound fields. In practice, sound fields are usually transient. If the NAH is used in transient sound fields to obtain the varying patterns of sound fields with time, it will be applied to the engineering more widely. Therefore, transient nearfield acoustic holography (TNAH) is developed. On the basis of analyzing the research significance and development of TNAH, it is divided into four kinds in accordance with the processing mode of pressure signals on the hologram surface:TNAH based on three-dementional transform, based on two-dementional transform, based on one-dementional transform, and without any transform.
In this dissertation, problems existing in these four kinds of TNAH were investigated and discussed deeply, and then the corresponding solutions were provided. In the research of TNAH based on three-dementional transform, a method based on the Laplace transform for reconstructing the particle velocity in transient sound fields was proposed to solve the singularity appeared in time domain acoustic holography with the Fourier transform. In TNAH based on two-dementional transform, the impulse response function between pressure on the hologram surface and particle velocity on the reconstruction surface was deduced, based on which real-time acoustic holography processed the ability of reconstructing particle velocity. With respect to TNAH without any transform, two new approaches were presented:one is based on time domain plane wave superposition method, and the other adopted an interpolated time-domain equivalent source method (ESM). To realize the use of TNAH in nonfree sound fields, a separation technique of transient sound fields was developed. The detailed research contents of this dissertation are summarized as follows:
In chapter one, the significance of TNAH was first elaborated, and then the development of calculating transient acoustic radiation at home and abroad was discussed to provide references and ideas for TNAH, finally by reviewing existing approaches of TNAH and analyzing their defects, the main research contents of this dissertation were determined.
In chapter two, time domain acoustic holography based on three-dementional transform was investigated. Its reconstruction formulas of sound pressure were deduced based on Fourier transform, and its reconstruction errors as well as the corresponding control methods were analyzed in theory. To solve the singularity appeared in the process of reconstructing the particle velocity by time domain acoustic holography based on the Fourier transform, a method using the Laplace transform was proposed, whose validity was also confirmed by a numerical simulation with a baffled piston as source.
In chapter three, real-time acoustic holography based on two-dementional transform was analyzed. The impulse response function between sound pressure on the hologram plane and sound pressure on the reconstruction plane was first deduced by Laplace transform from the wave equation of velocity potential and Neumann boundary condition, and then based on it the reconstruction process of sound pressure was shown. To reconstruct the particle velocity in real time, the impulse response function between sound pressure on the hologram plane and particle velocity on the reconstruction plane was also deduced by Laplace transform, and then based on it a reconstruction method of particle velocity using real-time acoustic holography was proposed and verified by a numerical simulation with a baffled circular piston as source.
In chapter four, two approaches of TNAH without any transform were proposed by using the wave superposition idea:one is based on time domain plane wave superposition method, and the other based on an interpolated time domain ESM. They both avoided the use of two-dementional spatial Fourier transform, thus removing restrictions brought by two-dementional spatial Fourier transform. Besides, their reconstructions were proceeding in the time domain, which provided the ability of reconstructing sound fields in real time. The formulas of TNAH based on time domain plane wave superposition method were first deduced, and then its reconstruction process was elaborated, finally its validity and advantages were demonstrated respectively by numerical simulations and experiments, and by comparisons with time domain acoustic holography and real-time acoustic holography. Similarly, the formulas of TNAH based on an interpolated time domain ESM were deduced, and its reconstruction process was elaborated. Three simulation cases with different shape sources were carried out to demonstrate that TNAH based on an interpolated time domain ESM not only processed conventional abilities of TNAH, but also got rid of the limit from source shapes, thus having more wide application range.
In chapter five, TNAH was extended to the nonfree sound fields. In the case of nonfree sound fields, a transient sound field separation technique was first developed to remove the influence of disturbing sources and separate out the sound field only radiated by objective sources in both time and space domains, and its separation formulas were deduced based on the propagation principle of sound pressure in the time-wavenumber domain. Then by utilizing the separated sound field radiated by objective sources and combining TNAH, the reconstruction could be realized in the case of nonfree sound fields.
In chapter six, all the investigations in this dissertation were summarized, and the topics studied further in the future were proposed.
第一章首先阐述了TNAH的研究意义,然后通过论述国内外有关瞬态声辐射计算的研究进展为TNAH的研究提供借鉴和思路,最后通过回顾目前国内外已有的TNAH方法,并分析其存在的问题,确立了本文的主要研究内容。
第二章研究了基于三维变换的时域声全息。首先推导了基于Fourier变换的时域声全息的声压重建公式,并从理论上分析了声压重建过程中的误差及其控制办法。为了解决基于Fourier变换的时域声全息在重建质点振速时出现的奇异性问题,提出了基于Laplace变换的瞬态声场质点振速重建方法,并通过以固定在障板上的活塞为声源的数值仿真验证了所提出方法的有效性。
第三章分析了基于二维变换的实时声全息。首先从速度势波动方程和Neumann边界条件出发,运用Laplace变换推导了全息面声压到重建面声压之间的脉冲响应函数,并阐述了基于该脉冲响应函数的声压重建过程。为了能够实现声场中质点振速的实时重建,运用Laplace变换推导了全息面声压到重建面质点振速之间的脉冲响应函数,并结合实时声全息的思想提出了基于该脉冲响应函数的质点振速重建方法,最后通过以障板上的圆形活塞为声源的数值仿真检验了该方法的有效性。
第四章基于波叠加法的思想,提出了两种无需对全息面声压进行任何变换的TNAH:基于时域平面波叠加法的TNAH和基于插值时域ESM的TNAH。两者均避开了二维空间Fourier变换的使用,从而避免了二维空间Fourier变换所带来的限制；而且两者的重建过程均在时域内进行,因而具有实时重建声场的能力。首先推导了基于时域平面波叠加法的TNAH的重建公式,详述了其重建过程,并通过数值仿真和实验验证了其有效性,进一步与时域声全息和实时声全息相比较阐述了其优越性。随后推导了基于插值时域ESM的TNAH的重建公式,阐述了其重建过程,并通过三例具有不同形状声源的仿真阐述了该方法不仅具有TNAH常规的功能,而且不受声源形状的限制,因此该方法具有更加广阔的应用范围。
第五章将TNAH扩展到非自由声场。首先基于声波在时域波数域的传播原理,推导了瞬态声场分离公式,提出了一种适用于非自由声场条件下的瞬态声场分离方法。该方法不仅可以在空间域,而且可以在时域,很好地移除干扰声源的影响,分离出只有目标声源辐射的声场；继而可以将分离出来的目标声源辐射声场与TNAH联合起来,实现非自由声场条件下的声场重建。
第六章总结了本文的主要研究成果,提出了需要进一步研究和解决的问题。
Nearfield acoustic holography (NAH), developed in recent over20years, is an advanced acoustic technique with the powerful abilities of identifying noise sources and visualizing sound fields. It can provide the important guidance for the noise control, as well as the low-noise and sound quality design of product. Up to now, the domestic and foreign scholars have proposed a number of holography methods. However, these methods almost proceed in the frequency domain, and are only applied to stationary sound fields. In practice, sound fields are usually transient. If the NAH is used in transient sound fields to obtain the varying patterns of sound fields with time, it will be applied to the engineering more widely. Therefore, transient nearfield acoustic holography (TNAH) is developed. On the basis of analyzing the research significance and development of TNAH, it is divided into four kinds in accordance with the processing mode of pressure signals on the hologram surface:TNAH based on three-dementional transform, based on two-dementional transform, based on one-dementional transform, and without any transform.
In this dissertation, problems existing in these four kinds of TNAH were investigated and discussed deeply, and then the corresponding solutions were provided. In the research of TNAH based on three-dementional transform, a method based on the Laplace transform for reconstructing the particle velocity in transient sound fields was proposed to solve the singularity appeared in time domain acoustic holography with the Fourier transform. In TNAH based on two-dementional transform, the impulse response function between pressure on the hologram surface and particle velocity on the reconstruction surface was deduced, based on which real-time acoustic holography processed the ability of reconstructing particle velocity. With respect to TNAH without any transform, two new approaches were presented:one is based on time domain plane wave superposition method, and the other adopted an interpolated time-domain equivalent source method (ESM). To realize the use of TNAH in nonfree sound fields, a separation technique of transient sound fields was developed. The detailed research contents of this dissertation are summarized as follows:
In chapter one, the significance of TNAH was first elaborated, and then the development of calculating transient acoustic radiation at home and abroad was discussed to provide references and ideas for TNAH, finally by reviewing existing approaches of TNAH and analyzing their defects, the main research contents of this dissertation were determined.
In chapter two, time domain acoustic holography based on three-dementional transform was investigated. Its reconstruction formulas of sound pressure were deduced based on Fourier transform, and its reconstruction errors as well as the corresponding control methods were analyzed in theory. To solve the singularity appeared in the process of reconstructing the particle velocity by time domain acoustic holography based on the Fourier transform, a method using the Laplace transform was proposed, whose validity was also confirmed by a numerical simulation with a baffled piston as source.
In chapter three, real-time acoustic holography based on two-dementional transform was analyzed. The impulse response function between sound pressure on the hologram plane and sound pressure on the reconstruction plane was first deduced by Laplace transform from the wave equation of velocity potential and Neumann boundary condition, and then based on it the reconstruction process of sound pressure was shown. To reconstruct the particle velocity in real time, the impulse response function between sound pressure on the hologram plane and particle velocity on the reconstruction plane was also deduced by Laplace transform, and then based on it a reconstruction method of particle velocity using real-time acoustic holography was proposed and verified by a numerical simulation with a baffled circular piston as source.
In chapter four, two approaches of TNAH without any transform were proposed by using the wave superposition idea:one is based on time domain plane wave superposition method, and the other based on an interpolated time domain ESM. They both avoided the use of two-dementional spatial Fourier transform, thus removing restrictions brought by two-dementional spatial Fourier transform. Besides, their reconstructions were proceeding in the time domain, which provided the ability of reconstructing sound fields in real time. The formulas of TNAH based on time domain plane wave superposition method were first deduced, and then its reconstruction process was elaborated, finally its validity and advantages were demonstrated respectively by numerical simulations and experiments, and by comparisons with time domain acoustic holography and real-time acoustic holography. Similarly, the formulas of TNAH based on an interpolated time domain ESM were deduced, and its reconstruction process was elaborated. Three simulation cases with different shape sources were carried out to demonstrate that TNAH based on an interpolated time domain ESM not only processed conventional abilities of TNAH, but also got rid of the limit from source shapes, thus having more wide application range.
In chapter five, TNAH was extended to the nonfree sound fields. In the case of nonfree sound fields, a transient sound field separation technique was first developed to remove the influence of disturbing sources and separate out the sound field only radiated by objective sources in both time and space domains, and its separation formulas were deduced based on the propagation principle of sound pressure in the time-wavenumber domain. Then by utilizing the separated sound field radiated by objective sources and combining TNAH, the reconstruction could be realized in the case of nonfree sound fields.
In chapter six, all the investigations in this dissertation were summarized, and the topics studied further in the future were proposed.
引文
[1]Maynard J D, Williams E G, Lee Y. Nearfield acoustic holography:Ⅰ. Theory of generalized holography and the development of NAH. J. Acoust. Soc. Am.,1985,78(4):1395-1413
[2]Maynard J D, Veronesi W A. Nearfield acoustic holography (NAH) Ⅱ. Holographic reconstruction algorithms and computer implementation. J. Acoust. Soc. Am.,1987,81(5): 1307-1322
[3]Naval Research Laboratory. Generalized nearfield acoustical holography. Report No. NRL/PU1001-99-393, March 2000
[4]Williams E G, Maynard J D. Holographic imaging without the wavelength resolution limit. Phys. Rev. Lett.,1980,45:554-557
[5]Williams E G, Maynard J D. Numerical evaluation of the Rayleigh integral for planar radiators using the FFT. J. Acoust. Soc. Am.,1982,72(6):2020-2030
[6]Williams E G, Dardy H D, Fink R G Nearfield acoustical holography using an underwater, automated scanner. J. Acoust. Soc. Am.,1985,78(2):789-798
[7]Williams E G Fourier Acoustics:Sound Radiation and Nearfield Acoustical Holography. Academic Press, San Diego,1999
[8]Veronesi W A, Maynard J D. Digital holography reconstruction of sources with arbitrarily shaped surfaces. J. Acoust. Soc. Am.,1989,85(2):588-598
[9]Kim G T, Lee B T.3-D sound source reconstruction and field reproduction using Helmholtz integral equation. J. Sound. Vib.,1990,136:245-261
[10]Sarkissian A. Reconstruction of the surface acoustic field on radiating structures. J. Acoust. Soc. Am.,1992,92(2):825-830
[11]Kim B K, Ih J G On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method. J. Acoust. Soc. Am.,1996,105(5): 3003-3016
[12]Valdivia N, Williams E G Implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography. J. Acoust. Soc. Am.,2004,116(3): 1559-1572
[13]Zhang Z, Vlahopoulos N, Raveendra S T, et al. A computational acoustic field reconstruction process based on an indirect boundary element formulation. J. Acoust. Soc. Am.,2008, 108(5):2167-2178
[14]Chappell D J, Harris P J. A Burton-Miller inverse boundary element method for near-field acoustic holography. J. Acoust. Soc. Am.,2009,126(1):149-157
[15]毕传兴,陈剑,陈心昭等.分布源边界点在声场全息重建和预测中的应用.机械工程学报,2003,39(8)：81-85
[16]毕传兴,陈剑,陈心昭.基于分布源边界点法的多源声场全息重建和预测技术理论研究.中国科学(E辑),2004,34(1)：111-120
[17]毕传兴,陈剑,陈心昭.半自由场的全息重建和预测实验研究.物理学报,2004,53(12)：4268-4276
[18]李卫兵,陈剑,毕传兴等.基于分布源边界点法的声散射场全息重建和预测理论.2005,23(4)：384-388
[19]毕传兴,袁燕,贺春东等.基于分布源边界点法的局部近场声全息技术.2010,59(12)；8646-8654
[20]Koopmann G H, Song L M, Fahnline J. A method for computing acoustic fields based on the principle of wave superposition. J. Acoust. Soc. Am.,1989,86(6):2433-2438
[21]Song L M, Koopmann G H, Fahnline J. Numerical errors associated with the method of superposition for computing acoustic fields. J. Acoust. Soc. Am.,1991,89(6):2625-2633
[22]Sarkissian A. Extension of measurement surface in near-field acoustic holography. J. Acoust. Soc. Am.,2004,115(4):1593-1596
[23]于飞,陈剑,李卫兵等.腔体内三维声场重构和预测的波叠加方法.自然科学进展,2005,15(1)：90-96
[24]薛玮飞,陈进,李加庆.机械噪声源识别的混合波叠加法.中国机械工程,2006,23；2503-2507
[25]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,2008,57(1)：313-321
[26]毕传兴,陈心昭,陈剑等.基于等效源法的声全息技术.中国科学(E辑),2005,35(5)；535-548
[27]Valdivia N P, Williams E G. Study of the comparison of the methods of equivalent sources and boundary element methods for near-field acoustic holography. J. Acoust. Soc. Am.,2006, 120(6):3694-3705
[28]毕传兴,陈心昭,徐亮等.基于等效源法的Patch近场声全息.中国科学(E辑),2007,37(9)：1205-1213
[29]Wang Z, Wu S F. Helmholtz equation-least-squares method for reconstructing the acoustic pressure field. J. Acoust. Soc. Am.,1997,102(4):2020-2032
[30]Wu S F, Yu J. Reconstructing interior acoustic pressure fields via Helmholtz equation least-squares method. J. Acoust. Soc. Am.,1998,104(4):2054-2060
[31]Rayess N, Wu S F. Experimental validation of the HELS method for reconstructing acoustic radiation from a complex vibrating structure. J. Acoust. Soc. Am.,2000,107(6):2955-2964
[32]Wu S F, Zhao X. Combined Helmholtz equation-least squares method for reconstructing the acoustic radiation from arbitrarily shaped objects. J. Acoust. Soc. Am.,2002,112(1): 179-188
[33]Wu S F. Hybrid near-field acoustic holography. J. Acoust. Soc. Am.,2004,115(1):207-217
[34]Zhao X, Wu S F. Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography. J. Acoust. Soc. Am.,2005,117(2):555-565
[35]Wu S F. Methods for reconstructing acoustic quantities based on acoustic pressure measurements. J. Acoust. Soc. Am.,2008,124(5):2680-2697
[36]Morse P M. Vibration and Sound. McGraw-Hill, New York,1948
[37]Fischer F A. Die Abstrahlung von Impulsen durch ebene Kolbenmembranen in starrer Wand. Acustica,1951,1:35-39
[38]Miles J W. Transient Loading of a Baffled Piston. J. Acoust. Soc. Am.,1953,25:200-203
[39]Oberhettinger F. On Transient Solutions of the 'Baffled Piston' Problem. J. Res. Nat. Bur. Stand.,1961,65B:1-6
[40]Kozina O G, Makarov G I. Transient Processes in the Acoustic Fields Generated by a Piston Membrane of Arbitrary Shape. Sov. Phys. Acoust.,1961,7:39-43
[41]Sherman D, Moran D A. Transient Sound Field of Simple Arrays of Circular Pistons. Scl. Rep. No.1, Parke Math. Labs., Carlisle, MA,1966
[42]Stepanishen P R. An Approach to Computing Time-Dependent Interaction Forces and Mutual Radiation Impedances between Pistons in a Rigid Planar Baffle. J. Acoust. Soc. Am.,1971, 49(1):283-292
[43]Stepanishen P R. The Time-Dependent Force and Radiation Impedance on a Piston in a Rigid Infinite Planar Baffle. J. Acoust. Soc. Am.,1971,49(3):841-849
[44]Stepanishen P R. Transient Radiation from Pistons in an Infinite Planar Baffle. J. Acoust. Soc. Am.,1971,49(5):1629-1638
[45]Lockwood J C, Willette J G High-speed method for computing the exact solution for the pressure variations in the nearfield of a baffled piston. J. Acoust. Soc. Am.,1973,53(3): 735-741
[46]Stepanishen P R. Impulse response and radiation impedance of an annular piston. J. Acoust. Soc. Am.,1974,56(2):283-292
[47]Robinson D E, Lees S, Bess L. Near Field Transient Radiation Patterns for Circular Pistons. IEEE Trans. Acoust Speech Sig. Proc.,1974, ASSP-22:395-403
[48]Auphan M, Dormont H. Pulsed acoustic radiation of plane damped transducers. Ultrasonics, 1977,15:159-168
[49]Stepanishen P R, Fisher G. Experimental verification of the impulse response method to evaluate transient acoustic fields. J. Acoust. Soc. Am.,1981,69(6):1610-1617
[50]Harris G R. Review of transient field theory for a baffled planar piston. J. Acoust. Soc. Am., 1981,70(1):10-20
[51]Stepanishen P R. Acoustic transients from planar axisymmetric vibrators using the impulse response approach. J. Acoust. Soc. Am.,1981,70(4):1176-1181
[52]Harris G R. Transient field of a baffled planar piston having an arbitrary vibration amplitude distribution. J. Acoust. Soc. Am.,1981,70(1):186-204
[53]Naze Tj(?)tta J N, Tjotta S. Nearfield and farfield of pulsed acoustic radiators. J. Acoust. Soc. Am.,1982,71:824-834
[54]Lasota H, Salamon R, Delannoy B. Acoustic diffraction analysis by the impulse response method:A line impulse response approach. J. Acoust. Soc. Am.,1984,76(1):280-290
[55]Piwakowsakli B, Delannoy B. Method for computing spatial pulse response:Time domain approach. J. Acoust. Soc. Am.,1989,86(6):2422-2432
[56]Jensen J A. Ultrasound fields from triangular apertures. J. Acoust. Soc. Am.,1996,100(4): 2049-2056
[57]Jensen J A. A new calculation procedure for spatial impulse responses in ultrasound. J. Acoust. Soc. Am.,1999,105(6):3266-3274
[58]McGough R J, Kelly J F. A fast time-domain method for calculating the nearfield pressure generated by a pulsed circular piston. IEEE Trans. Ultrason. Ferroelectr. Freq. Control,2006, 53:1150-1159
[59]Chen D, McGough R J. A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons. J. Acoust. Soc. Am.,2008,124(3):1526-1537
[60]Miles J W. On Radiation and Scattering from Small Cylinders. J. Acoust. Soc. Am.,1953, 25(6):1087-1089
[61]Barakat R G. Propagation of Acoustic Pulses from a Circular Cylinder, J. Acoust. Soc. Am., 1961,33(12):1759-1764
[62]Ebenezer D D, Stepanishen P R. Wave-vector-time domain and Kirchhoff integral equation methods to determine the transient acoustic radiation loading on circular cylinders. J. Acoust. Soc. Am.,1991,89(1):39-51
[63]Brillouin J. Rayonnement transitoire des sources sonores et problemes connexes. Ann. Telecommun.,1950,5:160-172,179-194
[64]Kozina O G, Makarov G I, Shaposhnikov N N. Transient Processes in the Acoustic Fields Generated by a Vibrating Spherical Segment. Sov. Phys. Acoust.,1962,8:53-57
[65]Junger M C, Thompson W. Oscillatory Acoustic Transients Radiated by Impulsively Accelerated Bodies. J. Acoust. Soc. Am.,1965,38(6):978-986
[66]Wu S F. Transient sound radiation from impulsively accelerated bodies. J. Acoust. Soc. Am., 1993,94(1):542-553
[67]Hamilton J A, Astley R J. Exact solutions for transient spherical radiation. J. Acoust. Soc. Am.,2001,109(5):1848-1858
[68]Faure P, Cathignol D, Chapelon J Y, et al. On the pressure field of a transducer in the form of a curved strip. J. Acoust. Soc. Am.,1994,95(2):628-637
[69]Baek D B, Jensen J A, Willatzen M. Spatial impulse response of a rectangular double curved transducer. J. Acoust. Soc. Am.,2012,131(4):2730-2741
[70]Quaegebeur N, Chaigne A, Lemarquand G. Transient modal radiation of axisymmetric sources:Application to loudspeakers. Applied Acoustics,2010,71:335-350
[71]Ferris H G Computation of Farfield Radiation Patterns by Use of a General Integral Solution to the Time-Dependent Scalar Wave Equation. J. Acoust. Soc. Am.,1967,41(2):394-400
[72]Mitzner K M. Numerical solution for transient scattering from a hard surface of arbitrary shape-Retarded potential technique. J. Acoust. Soc. Am.,1967,42(2):391-397
[73]Farn C L S, Huang H. Transient acoustic fields generated by a body of arbitrary shape. J. Acoust. Soc. Am.,1968,43(2):252-257
[74]Thompson L L, Pinsky P M. A Space-Time Finite Element Method for the Exterior Acoustics Problem. J. Acoust. Soc. Am.,1996,99(6):3297-3311
[75]Wu S F, Hu Q. An alternative formulation for predicting sound radiation from a vibrating object. J. Acoust. Soc. Am.,1998,103(4):1763-1774
[76]Hu Q, Wu S F. An explicit integral formulation for transient acoustic radiation. J. Acoust. Soc. Am.,1998,104(6):3251-3258
[77]Mansur W J. A Time-Stepping technique to solve wave propagation problems using the boundary Element Method. PhD thesis, University of Southampton,1983
[78]Bluck M, Walker S P. Analysis of three-dimensional transient acoustic wave propagation using the boundary integral equation method. Int. J. Numer. Methods Eng.,1996,39(9): 1419-1431
[79]Wu T W. Boundary Element Acoustics Fundamentals and Computer Codes. WIT Press, Billerica,2001
[80]Chappell D J, Harris P J, Henwood D, et al. A stable boundary element method for modeling transient acoustic radiation. J. Acoust. Soc. Am.,2006,120(1):74-80
[81]Kropp W, Svensson U P. Time domain formulation of the method of equivalent sources. Acta Acustica,1995,3:67-73
[82]Kropp W, Svensson U P. Application of the time domain formulation of the method of equivalent sources to radiation and scattering problems. Acustica,1995,81:528-543
[83]孙同晶,李桂娟,王科俊.基于Kirchhoff积分的瞬态声场计算方法.计算机仿真,2007,24(10)：319-321
[84]Hald J. Time domain acoustical holography. Proceedings of Inter-noise 1995, Newport Beach, USA,1995:1349-1354
[85]Saemann E U, Hald J. Transient tyre noise measurements using time domain acoustical holography. Proceedings of SAE,1997:1423-1429
[86]Hald J. Non-stationary STSF. B&K Technical Review,2000
[87]Hald J. Time domain acoustical holography and its applications. Sound and Vibration,2001, 35:16-24
[88]La Rochefoucauld O D, Melon M, Garcia A. Time domain holography:Forward projection of simulated and measured sound pressure fields. J. Acoust. Soc. Am.,2004,116(1):142-153
[89]La Rochefoucauld O D, Melon M, Garcia A. Time domain acoustic holography:Influence of filtering on localisation of non stationary source. Proceedings of the 17 International Congress on Acoustics, Rome, Italy,2001
[90]Blais J F, Ross A. Forward projection of transient sound pressure fields radiated by impacted plates using numerical Laplace transform. J. Acoust. Soc. Am.,2009,125(5):3120-3128
[91]Blais J F, Ross A. Backward propagation of sound fields radiated by impacted plates using a transient acoustical holography approach. Proceedings of Inter-noise 2009, Ottawa, Canada, 2009
[92]Parka C S, Kim Y H. Time domain visualization using acoustic holography implemented by temporal and spatial complex envelope (L). J. Acoust. Soc. Am.,2009,126(4):1659-1662
[93]Deblauwe F, Leuridan J, Chauray J L, et al. Acoustic holography in transient conditions. Sixth International Congress on Sound and Vibration, Copenagen,1999:899-906
[94]Deblauwe F. Transient holography-what is possible for engines. Proceedings of SPIE-The International Society for Optical Engineering,2000:1052-1055
[95]Thomas J H, Grulier V, Paillasseur S, et al. Real-time nearfield acoustic holography (RT-NAH):A technique for time-continuous reconstruction of a source signal. Proceedings of Novem 2005, Saint-Raphael, France,2005
[96]Thomas J H, Grulier V, Paillasseur S, et al. Real-Time Nearfield Acoustic Holography: Implementation of the direct and inverse impulse responses in the time-wavenumber domain. The 15th International Congress on Sound and Vibration, Daejeon, Korea,2008
[97]Thomas J H, Grulier V, Paillasseur S, et al. Real-Time Nearfield Acoustical Holography for continuously visualizing nonstationary acoustic fields. J. Acoust. Soc. Am.,2010,128(6): 3554-3567
[98]Grulier V, Paillasseur S, Thomas J H, et al. Forward propagation of time evolving acoustic pressure:Formulation and investigation of the impulse response in time-wavenumber domain. J. Acoust. Soc. Am.,2009,126(5),2367-2378
[99]Paillasseur S, Thomas J H, Pascal J C. Regularization method applied to deconvolution problem in Real-Time Acoustic Holography. Acoustics 08 Paris, Paris, France,2008
[100]Paillasseur S, Thomas J H, Pascal J C. Regularization for improving the deconvolution in real-time near-field acoustic holography. J. Acoust. Soc. Am.,2011,129(6):3777-3787
[101]Moulet M H, Le Roux J C, Thomas J H. Characterisation of car equipments by Real-Time Nearfield Acoustic Holography, SIA,2010
[102]Oey A, Ih J G. Visualization of transient response of acoustic source field using the BEM-based NAH. The 15th International Congress on Sound and Vibration, Daejeon, Korea, 2008
[103]Alestra S, Terrasse I, Troclet B. Inverse method for identification of acoustic sources at launch vehicle liftoff. AIAA J.,2003,41(10):1980-1987
[104]Troclet B, Alestra S, Srithammavanh V, et al. A time domain inverse method for identification of random acoustic sources at launch vehicle lift-off. Journal of Vibration and Acoustics, 2011,133:021010-1-021010-11
[105]Wu S F, Lu H, Bajwa M S. Reconstruction of transient acoustic radiation from a sphere. J. Acoust. Soc. Am.,2004,117(4):2065-2077
[106]Bajwa M S. Reconstruction of transient acoustic radiation using Helmholtz Equation Least Squares method. PhD dissertation, Wayne State University, Detroit, Michigan,2008
[107]Hansen T B. Spherical expansions of time-domain acoustic fields:Application to near-field scanning. J. Acoust. Soc. Am.,1995,98(2):1204-1215
[108]Sapozhnikov O A, Ponomarev A E, Smagin M A. Transient Acoustic Holography for Reconstructing the Particle Velocity of the Surface of an Acoustic Transducer. Acoustical Physics,2006,52(3):324-330
[109]Bai M R, Lin J H. Source identification system based on the time-domain nearfield equivalence source imaging:Fundamental theory and implementation. J. Sound. Vib.,2006, 307:202-225
[110]Bai M R, Lin J H, Tseng C W. Implementation issues of the nearfield equivalent source imaging microphone array. J. Sound. Vib.,2011,330:545-558
[111]Schiff J L. The Laplace Transform:Theory and Applications. Springer, New York,1999
[112]Tikhonov A. Solutions of incorrectly formulated problems and the regularization method. Soviet. Math. Dokl.,1963,4:1035-1038
[113]Hansen P C. Rank-deficient and discrete ill-posed problems. SIAM, Philadelphia,1998
[114]Harris G R. Transient field of a baffled planar piston having an arbitrary vibration amplitude distribution. J. Acoust. Soc. Am.,1981,70(1):186-204
[115]Steiner R, Hald J. Near-field acoustical holography without the errors and limitations caused by the use of spatial DFT. Int. J. Acoust. Vib.,2001,6:83-89
[116]Hald J. Patch near-field acoustical holography using a new statistically optimal method. Proceedings of Inter-Noise 2003, Seogwipo, Korea,2003:2203-2210
[117]Cho Y T, Bolton J S, Hald J. Source visualization by using statistically optimized nearfield acoustical holography in cylindrical coordinates. J. Acoust. Soc. Am.,2005,118(4): 2355-2364
[118]李卫兵,陈剑,于飞等.统计最优平面近场声全息理论与声场分离技术.物理学报,2005,54(3)：1253-1260
[119]Hald J. Basic theory and properties of statistically optimized near-field acoustical holography. J. Acoust. Soc. Am.,2009,125(4):2105-2120
[120]Leclere Q. Acoustic imaging using under-determined inverse approaches:Frequency limitations and optimal regularization. J. Sound. Vib.,2009,321:605-619
[121]Lee S. Prediction of acoustic scattering and its applications to rotorcraft noise. PhD dissertation, The Pennsylvania State University, USA,2009
[122]Tamura M. Spatial Fourier-transform method for measuring reflection coefficients at oblique incidence. I:Theory and numerical examples. J. Acoust. Soc. Am.,1990,88(5):2259-2264
[123]Tamura M, Allard J F, Lafarge D. Spatial Fourier-transform method for measuring reflection coefficients at oblique incidence. II. Experimental results. J. Acoust. Soc. Am.,1995,97(4): 2255-2262
[124]Cheng M T, Mann III J A, Pate A. Wave-number domain separation of the incident and scattered sound field in Cartesian and cylindrical coordinates. J. Acoust. Soc. Am.,1995, 97(4):2293-2303
[125]Cheng M T, Mann III J A, Pate A. Sensitivity of the wave-number domain field separation methods for scattering. J. Acoust. Soc. Am.,1996,99(6):3550-3557
[126]于飞,陈剑,李卫兵等.声场分离技术及其在近场声全息中的应用.物理学报,2005, 54(2)：789-797
[127]Pachner J. Investigation of scalar wave fields by means of instantaneous directivity patterns. J. Acoust. Soc. Am.,1956,28(1):90-92
[128]Weinreich G, Arnold E B. Method for measuring acoustic radiation fields. J. Acoust. Soc. Am.,1980,68(2):404-411
[129]Zhao X, Wu S F. Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography. J. Acoust. Soc. Am.,2005,117(2):555-565
[130]Jacobsen F, Jaud V. Statistically optimized near field acoustic holography using an array of pressure-velocity probe. J. Acoust. Soc. Am.,2007,121(3):1550-1558
[131]Zhang Y B, Chen X Z, Jacobsen F. A sound field separation technique based on measurements with pressure-velocity probes. J. Acoust. Soc. Am.,2009,125(6):3518-3521
[132]Langrenne C, Melon M, Garcia A. Boundary element method for the acoustic characterization of a machine in bounded noisy environment. J. Acoust. Soc. Am.,2007, 121(5):2750-2757
[133]Bi C X, Chen X Z, Chen J. Sound field separation technique based on equivalent source method and its application in nearfield acoustic holography. J. Acoust. Soc. Am.,2008, 123(3):1472-1478
[2]Maynard J D, Veronesi W A. Nearfield acoustic holography (NAH) Ⅱ. Holographic reconstruction algorithms and computer implementation. J. Acoust. Soc. Am.,1987,81(5): 1307-1322
[3]Naval Research Laboratory. Generalized nearfield acoustical holography. Report No. NRL/PU1001-99-393, March 2000
[4]Williams E G, Maynard J D. Holographic imaging without the wavelength resolution limit. Phys. Rev. Lett.,1980,45:554-557
[5]Williams E G, Maynard J D. Numerical evaluation of the Rayleigh integral for planar radiators using the FFT. J. Acoust. Soc. Am.,1982,72(6):2020-2030
[6]Williams E G, Dardy H D, Fink R G Nearfield acoustical holography using an underwater, automated scanner. J. Acoust. Soc. Am.,1985,78(2):789-798
[7]Williams E G Fourier Acoustics:Sound Radiation and Nearfield Acoustical Holography. Academic Press, San Diego,1999
[8]Veronesi W A, Maynard J D. Digital holography reconstruction of sources with arbitrarily shaped surfaces. J. Acoust. Soc. Am.,1989,85(2):588-598
[9]Kim G T, Lee B T.3-D sound source reconstruction and field reproduction using Helmholtz integral equation. J. Sound. Vib.,1990,136:245-261
[10]Sarkissian A. Reconstruction of the surface acoustic field on radiating structures. J. Acoust. Soc. Am.,1992,92(2):825-830
[11]Kim B K, Ih J G On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method. J. Acoust. Soc. Am.,1996,105(5): 3003-3016
[12]Valdivia N, Williams E G Implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography. J. Acoust. Soc. Am.,2004,116(3): 1559-1572
[13]Zhang Z, Vlahopoulos N, Raveendra S T, et al. A computational acoustic field reconstruction process based on an indirect boundary element formulation. J. Acoust. Soc. Am.,2008, 108(5):2167-2178
[14]Chappell D J, Harris P J. A Burton-Miller inverse boundary element method for near-field acoustic holography. J. Acoust. Soc. Am.,2009,126(1):149-157
[15]毕传兴,陈剑,陈心昭等.分布源边界点在声场全息重建和预测中的应用.机械工程学报,2003,39(8)：81-85
[16]毕传兴,陈剑,陈心昭.基于分布源边界点法的多源声场全息重建和预测技术理论研究.中国科学(E辑),2004,34(1)：111-120
[17]毕传兴,陈剑,陈心昭.半自由场的全息重建和预测实验研究.物理学报,2004,53(12)：4268-4276
[18]李卫兵,陈剑,毕传兴等.基于分布源边界点法的声散射场全息重建和预测理论.2005,23(4)：384-388
[19]毕传兴,袁燕,贺春东等.基于分布源边界点法的局部近场声全息技术.2010,59(12)；8646-8654
[20]Koopmann G H, Song L M, Fahnline J. A method for computing acoustic fields based on the principle of wave superposition. J. Acoust. Soc. Am.,1989,86(6):2433-2438
[21]Song L M, Koopmann G H, Fahnline J. Numerical errors associated with the method of superposition for computing acoustic fields. J. Acoust. Soc. Am.,1991,89(6):2625-2633
[22]Sarkissian A. Extension of measurement surface in near-field acoustic holography. J. Acoust. Soc. Am.,2004,115(4):1593-1596
[23]于飞,陈剑,李卫兵等.腔体内三维声场重构和预测的波叠加方法.自然科学进展,2005,15(1)：90-96
[24]薛玮飞,陈进,李加庆.机械噪声源识别的混合波叠加法.中国机械工程,2006,23；2503-2507
[25]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,2008,57(1)：313-321
[26]毕传兴,陈心昭,陈剑等.基于等效源法的声全息技术.中国科学(E辑),2005,35(5)；535-548
[27]Valdivia N P, Williams E G. Study of the comparison of the methods of equivalent sources and boundary element methods for near-field acoustic holography. J. Acoust. Soc. Am.,2006, 120(6):3694-3705
[28]毕传兴,陈心昭,徐亮等.基于等效源法的Patch近场声全息.中国科学(E辑),2007,37(9)：1205-1213
[29]Wang Z, Wu S F. Helmholtz equation-least-squares method for reconstructing the acoustic pressure field. J. Acoust. Soc. Am.,1997,102(4):2020-2032
[30]Wu S F, Yu J. Reconstructing interior acoustic pressure fields via Helmholtz equation least-squares method. J. Acoust. Soc. Am.,1998,104(4):2054-2060
[31]Rayess N, Wu S F. Experimental validation of the HELS method for reconstructing acoustic radiation from a complex vibrating structure. J. Acoust. Soc. Am.,2000,107(6):2955-2964
[32]Wu S F, Zhao X. Combined Helmholtz equation-least squares method for reconstructing the acoustic radiation from arbitrarily shaped objects. J. Acoust. Soc. Am.,2002,112(1): 179-188
[33]Wu S F. Hybrid near-field acoustic holography. J. Acoust. Soc. Am.,2004,115(1):207-217
[34]Zhao X, Wu S F. Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography. J. Acoust. Soc. Am.,2005,117(2):555-565
[35]Wu S F. Methods for reconstructing acoustic quantities based on acoustic pressure measurements. J. Acoust. Soc. Am.,2008,124(5):2680-2697
[36]Morse P M. Vibration and Sound. McGraw-Hill, New York,1948
[37]Fischer F A. Die Abstrahlung von Impulsen durch ebene Kolbenmembranen in starrer Wand. Acustica,1951,1:35-39
[38]Miles J W. Transient Loading of a Baffled Piston. J. Acoust. Soc. Am.,1953,25:200-203
[39]Oberhettinger F. On Transient Solutions of the 'Baffled Piston' Problem. J. Res. Nat. Bur. Stand.,1961,65B:1-6
[40]Kozina O G, Makarov G I. Transient Processes in the Acoustic Fields Generated by a Piston Membrane of Arbitrary Shape. Sov. Phys. Acoust.,1961,7:39-43
[41]Sherman D, Moran D A. Transient Sound Field of Simple Arrays of Circular Pistons. Scl. Rep. No.1, Parke Math. Labs., Carlisle, MA,1966
[42]Stepanishen P R. An Approach to Computing Time-Dependent Interaction Forces and Mutual Radiation Impedances between Pistons in a Rigid Planar Baffle. J. Acoust. Soc. Am.,1971, 49(1):283-292
[43]Stepanishen P R. The Time-Dependent Force and Radiation Impedance on a Piston in a Rigid Infinite Planar Baffle. J. Acoust. Soc. Am.,1971,49(3):841-849
[44]Stepanishen P R. Transient Radiation from Pistons in an Infinite Planar Baffle. J. Acoust. Soc. Am.,1971,49(5):1629-1638
[45]Lockwood J C, Willette J G High-speed method for computing the exact solution for the pressure variations in the nearfield of a baffled piston. J. Acoust. Soc. Am.,1973,53(3): 735-741
[46]Stepanishen P R. Impulse response and radiation impedance of an annular piston. J. Acoust. Soc. Am.,1974,56(2):283-292
[47]Robinson D E, Lees S, Bess L. Near Field Transient Radiation Patterns for Circular Pistons. IEEE Trans. Acoust Speech Sig. Proc.,1974, ASSP-22:395-403
[48]Auphan M, Dormont H. Pulsed acoustic radiation of plane damped transducers. Ultrasonics, 1977,15:159-168
[49]Stepanishen P R, Fisher G. Experimental verification of the impulse response method to evaluate transient acoustic fields. J. Acoust. Soc. Am.,1981,69(6):1610-1617
[50]Harris G R. Review of transient field theory for a baffled planar piston. J. Acoust. Soc. Am., 1981,70(1):10-20
[51]Stepanishen P R. Acoustic transients from planar axisymmetric vibrators using the impulse response approach. J. Acoust. Soc. Am.,1981,70(4):1176-1181
[52]Harris G R. Transient field of a baffled planar piston having an arbitrary vibration amplitude distribution. J. Acoust. Soc. Am.,1981,70(1):186-204
[53]Naze Tj(?)tta J N, Tjotta S. Nearfield and farfield of pulsed acoustic radiators. J. Acoust. Soc. Am.,1982,71:824-834
[54]Lasota H, Salamon R, Delannoy B. Acoustic diffraction analysis by the impulse response method:A line impulse response approach. J. Acoust. Soc. Am.,1984,76(1):280-290
[55]Piwakowsakli B, Delannoy B. Method for computing spatial pulse response:Time domain approach. J. Acoust. Soc. Am.,1989,86(6):2422-2432
[56]Jensen J A. Ultrasound fields from triangular apertures. J. Acoust. Soc. Am.,1996,100(4): 2049-2056
[57]Jensen J A. A new calculation procedure for spatial impulse responses in ultrasound. J. Acoust. Soc. Am.,1999,105(6):3266-3274
[58]McGough R J, Kelly J F. A fast time-domain method for calculating the nearfield pressure generated by a pulsed circular piston. IEEE Trans. Ultrason. Ferroelectr. Freq. Control,2006, 53:1150-1159
[59]Chen D, McGough R J. A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons. J. Acoust. Soc. Am.,2008,124(3):1526-1537
[60]Miles J W. On Radiation and Scattering from Small Cylinders. J. Acoust. Soc. Am.,1953, 25(6):1087-1089
[61]Barakat R G. Propagation of Acoustic Pulses from a Circular Cylinder, J. Acoust. Soc. Am., 1961,33(12):1759-1764
[62]Ebenezer D D, Stepanishen P R. Wave-vector-time domain and Kirchhoff integral equation methods to determine the transient acoustic radiation loading on circular cylinders. J. Acoust. Soc. Am.,1991,89(1):39-51
[63]Brillouin J. Rayonnement transitoire des sources sonores et problemes connexes. Ann. Telecommun.,1950,5:160-172,179-194
[64]Kozina O G, Makarov G I, Shaposhnikov N N. Transient Processes in the Acoustic Fields Generated by a Vibrating Spherical Segment. Sov. Phys. Acoust.,1962,8:53-57
[65]Junger M C, Thompson W. Oscillatory Acoustic Transients Radiated by Impulsively Accelerated Bodies. J. Acoust. Soc. Am.,1965,38(6):978-986
[66]Wu S F. Transient sound radiation from impulsively accelerated bodies. J. Acoust. Soc. Am., 1993,94(1):542-553
[67]Hamilton J A, Astley R J. Exact solutions for transient spherical radiation. J. Acoust. Soc. Am.,2001,109(5):1848-1858
[68]Faure P, Cathignol D, Chapelon J Y, et al. On the pressure field of a transducer in the form of a curved strip. J. Acoust. Soc. Am.,1994,95(2):628-637
[69]Baek D B, Jensen J A, Willatzen M. Spatial impulse response of a rectangular double curved transducer. J. Acoust. Soc. Am.,2012,131(4):2730-2741
[70]Quaegebeur N, Chaigne A, Lemarquand G. Transient modal radiation of axisymmetric sources:Application to loudspeakers. Applied Acoustics,2010,71:335-350
[71]Ferris H G Computation of Farfield Radiation Patterns by Use of a General Integral Solution to the Time-Dependent Scalar Wave Equation. J. Acoust. Soc. Am.,1967,41(2):394-400
[72]Mitzner K M. Numerical solution for transient scattering from a hard surface of arbitrary shape-Retarded potential technique. J. Acoust. Soc. Am.,1967,42(2):391-397
[73]Farn C L S, Huang H. Transient acoustic fields generated by a body of arbitrary shape. J. Acoust. Soc. Am.,1968,43(2):252-257
[74]Thompson L L, Pinsky P M. A Space-Time Finite Element Method for the Exterior Acoustics Problem. J. Acoust. Soc. Am.,1996,99(6):3297-3311
[75]Wu S F, Hu Q. An alternative formulation for predicting sound radiation from a vibrating object. J. Acoust. Soc. Am.,1998,103(4):1763-1774
[76]Hu Q, Wu S F. An explicit integral formulation for transient acoustic radiation. J. Acoust. Soc. Am.,1998,104(6):3251-3258
[77]Mansur W J. A Time-Stepping technique to solve wave propagation problems using the boundary Element Method. PhD thesis, University of Southampton,1983
[78]Bluck M, Walker S P. Analysis of three-dimensional transient acoustic wave propagation using the boundary integral equation method. Int. J. Numer. Methods Eng.,1996,39(9): 1419-1431
[79]Wu T W. Boundary Element Acoustics Fundamentals and Computer Codes. WIT Press, Billerica,2001
[80]Chappell D J, Harris P J, Henwood D, et al. A stable boundary element method for modeling transient acoustic radiation. J. Acoust. Soc. Am.,2006,120(1):74-80
[81]Kropp W, Svensson U P. Time domain formulation of the method of equivalent sources. Acta Acustica,1995,3:67-73
[82]Kropp W, Svensson U P. Application of the time domain formulation of the method of equivalent sources to radiation and scattering problems. Acustica,1995,81:528-543
[83]孙同晶,李桂娟,王科俊.基于Kirchhoff积分的瞬态声场计算方法.计算机仿真,2007,24(10)：319-321
[84]Hald J. Time domain acoustical holography. Proceedings of Inter-noise 1995, Newport Beach, USA,1995:1349-1354
[85]Saemann E U, Hald J. Transient tyre noise measurements using time domain acoustical holography. Proceedings of SAE,1997:1423-1429
[86]Hald J. Non-stationary STSF. B&K Technical Review,2000
[87]Hald J. Time domain acoustical holography and its applications. Sound and Vibration,2001, 35:16-24
[88]La Rochefoucauld O D, Melon M, Garcia A. Time domain holography:Forward projection of simulated and measured sound pressure fields. J. Acoust. Soc. Am.,2004,116(1):142-153
[89]La Rochefoucauld O D, Melon M, Garcia A. Time domain acoustic holography:Influence of filtering on localisation of non stationary source. Proceedings of the 17 International Congress on Acoustics, Rome, Italy,2001
[90]Blais J F, Ross A. Forward projection of transient sound pressure fields radiated by impacted plates using numerical Laplace transform. J. Acoust. Soc. Am.,2009,125(5):3120-3128
[91]Blais J F, Ross A. Backward propagation of sound fields radiated by impacted plates using a transient acoustical holography approach. Proceedings of Inter-noise 2009, Ottawa, Canada, 2009
[92]Parka C S, Kim Y H. Time domain visualization using acoustic holography implemented by temporal and spatial complex envelope (L). J. Acoust. Soc. Am.,2009,126(4):1659-1662
[93]Deblauwe F, Leuridan J, Chauray J L, et al. Acoustic holography in transient conditions. Sixth International Congress on Sound and Vibration, Copenagen,1999:899-906
[94]Deblauwe F. Transient holography-what is possible for engines. Proceedings of SPIE-The International Society for Optical Engineering,2000:1052-1055
[95]Thomas J H, Grulier V, Paillasseur S, et al. Real-time nearfield acoustic holography (RT-NAH):A technique for time-continuous reconstruction of a source signal. Proceedings of Novem 2005, Saint-Raphael, France,2005
[96]Thomas J H, Grulier V, Paillasseur S, et al. Real-Time Nearfield Acoustic Holography: Implementation of the direct and inverse impulse responses in the time-wavenumber domain. The 15th International Congress on Sound and Vibration, Daejeon, Korea,2008
[97]Thomas J H, Grulier V, Paillasseur S, et al. Real-Time Nearfield Acoustical Holography for continuously visualizing nonstationary acoustic fields. J. Acoust. Soc. Am.,2010,128(6): 3554-3567
[98]Grulier V, Paillasseur S, Thomas J H, et al. Forward propagation of time evolving acoustic pressure:Formulation and investigation of the impulse response in time-wavenumber domain. J. Acoust. Soc. Am.,2009,126(5),2367-2378
[99]Paillasseur S, Thomas J H, Pascal J C. Regularization method applied to deconvolution problem in Real-Time Acoustic Holography. Acoustics 08 Paris, Paris, France,2008
[100]Paillasseur S, Thomas J H, Pascal J C. Regularization for improving the deconvolution in real-time near-field acoustic holography. J. Acoust. Soc. Am.,2011,129(6):3777-3787
[101]Moulet M H, Le Roux J C, Thomas J H. Characterisation of car equipments by Real-Time Nearfield Acoustic Holography, SIA,2010
[102]Oey A, Ih J G. Visualization of transient response of acoustic source field using the BEM-based NAH. The 15th International Congress on Sound and Vibration, Daejeon, Korea, 2008
[103]Alestra S, Terrasse I, Troclet B. Inverse method for identification of acoustic sources at launch vehicle liftoff. AIAA J.,2003,41(10):1980-1987
[104]Troclet B, Alestra S, Srithammavanh V, et al. A time domain inverse method for identification of random acoustic sources at launch vehicle lift-off. Journal of Vibration and Acoustics, 2011,133:021010-1-021010-11
[105]Wu S F, Lu H, Bajwa M S. Reconstruction of transient acoustic radiation from a sphere. J. Acoust. Soc. Am.,2004,117(4):2065-2077
[106]Bajwa M S. Reconstruction of transient acoustic radiation using Helmholtz Equation Least Squares method. PhD dissertation, Wayne State University, Detroit, Michigan,2008
[107]Hansen T B. Spherical expansions of time-domain acoustic fields:Application to near-field scanning. J. Acoust. Soc. Am.,1995,98(2):1204-1215
[108]Sapozhnikov O A, Ponomarev A E, Smagin M A. Transient Acoustic Holography for Reconstructing the Particle Velocity of the Surface of an Acoustic Transducer. Acoustical Physics,2006,52(3):324-330
[109]Bai M R, Lin J H. Source identification system based on the time-domain nearfield equivalence source imaging:Fundamental theory and implementation. J. Sound. Vib.,2006, 307:202-225
[110]Bai M R, Lin J H, Tseng C W. Implementation issues of the nearfield equivalent source imaging microphone array. J. Sound. Vib.,2011,330:545-558
[111]Schiff J L. The Laplace Transform:Theory and Applications. Springer, New York,1999
[112]Tikhonov A. Solutions of incorrectly formulated problems and the regularization method. Soviet. Math. Dokl.,1963,4:1035-1038
[113]Hansen P C. Rank-deficient and discrete ill-posed problems. SIAM, Philadelphia,1998
[114]Harris G R. Transient field of a baffled planar piston having an arbitrary vibration amplitude distribution. J. Acoust. Soc. Am.,1981,70(1):186-204
[115]Steiner R, Hald J. Near-field acoustical holography without the errors and limitations caused by the use of spatial DFT. Int. J. Acoust. Vib.,2001,6:83-89
[116]Hald J. Patch near-field acoustical holography using a new statistically optimal method. Proceedings of Inter-Noise 2003, Seogwipo, Korea,2003:2203-2210
[117]Cho Y T, Bolton J S, Hald J. Source visualization by using statistically optimized nearfield acoustical holography in cylindrical coordinates. J. Acoust. Soc. Am.,2005,118(4): 2355-2364
[118]李卫兵,陈剑,于飞等.统计最优平面近场声全息理论与声场分离技术.物理学报,2005,54(3)：1253-1260
[119]Hald J. Basic theory and properties of statistically optimized near-field acoustical holography. J. Acoust. Soc. Am.,2009,125(4):2105-2120
[120]Leclere Q. Acoustic imaging using under-determined inverse approaches:Frequency limitations and optimal regularization. J. Sound. Vib.,2009,321:605-619
[121]Lee S. Prediction of acoustic scattering and its applications to rotorcraft noise. PhD dissertation, The Pennsylvania State University, USA,2009
[122]Tamura M. Spatial Fourier-transform method for measuring reflection coefficients at oblique incidence. I:Theory and numerical examples. J. Acoust. Soc. Am.,1990,88(5):2259-2264
[123]Tamura M, Allard J F, Lafarge D. Spatial Fourier-transform method for measuring reflection coefficients at oblique incidence. II. Experimental results. J. Acoust. Soc. Am.,1995,97(4): 2255-2262
[124]Cheng M T, Mann III J A, Pate A. Wave-number domain separation of the incident and scattered sound field in Cartesian and cylindrical coordinates. J. Acoust. Soc. Am.,1995, 97(4):2293-2303
[125]Cheng M T, Mann III J A, Pate A. Sensitivity of the wave-number domain field separation methods for scattering. J. Acoust. Soc. Am.,1996,99(6):3550-3557
[126]于飞,陈剑,李卫兵等.声场分离技术及其在近场声全息中的应用.物理学报,2005, 54(2)：789-797
[127]Pachner J. Investigation of scalar wave fields by means of instantaneous directivity patterns. J. Acoust. Soc. Am.,1956,28(1):90-92
[128]Weinreich G, Arnold E B. Method for measuring acoustic radiation fields. J. Acoust. Soc. Am.,1980,68(2):404-411
[129]Zhao X, Wu S F. Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography. J. Acoust. Soc. Am.,2005,117(2):555-565
[130]Jacobsen F, Jaud V. Statistically optimized near field acoustic holography using an array of pressure-velocity probe. J. Acoust. Soc. Am.,2007,121(3):1550-1558
[131]Zhang Y B, Chen X Z, Jacobsen F. A sound field separation technique based on measurements with pressure-velocity probes. J. Acoust. Soc. Am.,2009,125(6):3518-3521
[132]Langrenne C, Melon M, Garcia A. Boundary element method for the acoustic characterization of a machine in bounded noisy environment. J. Acoust. Soc. Am.,2007, 121(5):2750-2757
[133]Bi C X, Chen X Z, Chen J. Sound field separation technique based on equivalent source method and its application in nearfield acoustic holography. J. Acoust. Soc. Am.,2008, 123(3):1472-1478
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