水下有界空间中弹性结构的声辐射预报方法研究
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摘要
水下结构的声辐射预报是水声领域的一项重要研究内容，是减振降噪、定量声学设计等工作的依据与理论基础。实际上，结构所处的环境往往并非自由空间，这涉及了结构与水的耦合振动、声的多途传播以及多次反射声造成的互散射与结构的耦合等多个问题，使得水下有界空间中结构的声辐射预报成为需要研究的课题。
本文首先从现有的自由场声辐射预报方法入手，简单阐述了这些方法的基本原理，并进行了归类、对比。最后选择了点源波叠加法作为有界空间中声辐射预报的主要方法。然而波叠加法（又称作等效源法）却并不完善，存在等效源和振动测点的优化配置等问题。为此，提出了一种最小二乘意义下的等效源配置方法，该方法通过匹配少量参考点的声压幅值，可搜索得到最优的等效源位置，从而改善波叠加法的声辐射预报精度。并在此基础上，分析了利用该方法预报声场的相关误差因素，指出了一些提高精度的等效源和测点位置选取准则，以期波叠加法能更好地运用于声辐射预报。
选择波叠加法作为有界空间中声辐射预报主要方法的原因之一是它将结构等效成了一系列的简单源，简单源的格林函数能较方便地根据反射面的类型和位置作出调整，而且有望与现有的声传播算法结合，实现波导中结构的声辐射预报。但格林函数究竟如何调整却没有定论。为此先从存在单个反射面的半空间声场环境出发，针对水下结构的声辐射快速预报问题，提出了采用自由场格林函数来获得等效源强度的半自由场波叠加法，并针对水和结构的耦合特性，分析了反射面与结构之间的互散射对声辐射预报的影响，进而提出了结构表面法向振速的两种处理方法：波叠加反射声振速分离法和忽略反射声对结构法向振速影响的快速法。最后结合有限元法和边界元法分析了半空间中弹性结构的振动声辐射。
半自由场波叠加法的提出，避开了结构表面三维空间的格林函数求导问题，使得波叠加法能够与波导中的声传播算法结合。因此提出了波动波叠加法和射线波叠加法，它们分别将波叠加法与声传播理论中的简正波法和射线法结合，用于计算结构在平行平面层波导中的辐射声场。进而对这两种方法各自的优势和适用范围进行了分析，指出波叠加法与传播理论结合时需要针对需求选择适宜的传播算法。然后将半空间中弹性结构分析的有限元模型进一步推广用于波导中有限弹性结构的耦合振动及声辐射分析。通过弹性结构的声辐射预报对有限元法、波动波叠加法和射线波叠加法进行了对比，并分析了这些方法各自的适用条件。并指出只要传播算法能给出点源的辐射声场，提出的波叠加法就可以与之结合，实现波导中结构的声辐射预报，因此可以推广到其他类型波导的弹性结构声辐射预报中。
最后针对前面进行的数值分析进行了实体模型在有界空间中声辐射预报的试验验证。首先在水面未敷设吸声尖劈的消声水池中，对半空间中的带帽圆柱壳进行了声辐射预报研究，进而在水声信道水池中进行了波导中柱壳的声辐射预报试验。
由于研究的结构为缩比模型，因此本文更多地关注了3kHz以上的频段，并尽量地将声辐射预报算法往高频段扩展。尝试通过对相似模型的仿真和实验研究为实际工程运用提供一些有益的参考。
The prediction of sound radiated by underwater structures is one of the most importantresearches in the field of underwater acoustics. It is regarded as the theoretical foundation andthe important criterion for quantitative acoustic design and vibration-noise control. Practically,the structure is not always located in free-space, which brings problems, such as the coupledvibration, multipath propagation and scattering, etc. Thus investigations are needed for theprediction of sound radiated by elastic structure in underwater bounded space.
In this dissertation, the methods of acoustic radiation prediction in free-space areinvestigated primarily. Then the methods are expounded and classified according to theirfundamentals. By comparing these methods, the wave superposition method (WSM) is chosenas the main method for acoustic radiation prediction in bounded space. However, the WSM(also known as equivalent source method: ESM) is not perfect, since the optimalconfiguration of the equivalent source and the measuring point has been considering as aproblem. Therefore, an equivalent source configuration method based on the least meansquare is proposed, in which a few reference points of sound pressure should be measuredahead to search the optimal position of equivalent sources. Moreover, the effects of thenumber, position of measuring points and amplitude distribution of vibration were studiednumerically. The principles of how to configurate the equivalent source and measuring pointappropriately are pointed out, in order to improve the accuracy of the WSM and make theWSM more suitable for acoustic radiation prediction.
One reason of choosing WSM as the main method for acoustic radiation prediction inbounded space is that WSM simulates structure by an array of simple sources. The simplesources’ Green function can be adjusted conveniently according to the types and positions ofboundary. Furthermore, the existing algorithms of sound propagation in waveguide canhopefully combined with WSM to predict the sound radiated by elastic structure in waveguide.Unfortunately, there are no guildlines about how to reform the Green function in WSM forcombination. Therefore, the environment of half-spaces with a single boundary is investigatedfirstly, and a half-space wave superposition method is proposed for the fast prediction ofacoustic radiation from a complex structure, in which the free-space Green’s function is usedto match the strength of equivalent sources. As the submerged structure is coupled with water,the scattering between reflector and structure is considered. Moreover, two treatments fornormal velocity of a structure are proposed. One is called separation method which separates normal velocity by wave superposition method and the other is called fast method whichneglects the effect of reflection to the structural vibration, which makes the acoustic radiationprediction more efficiency. The finite element method (FEM) and boundary element method(BEM) are also combined with the proposed method to analyze the vibration and acousticradiation of the elastic structure in half-space.
The proposed half-space wave superposition method avoids the three-dimensionalderivation of Green function on the surface of structure, which makes the possibility ofcombining WSM with the sound propagation algorithms in waveguide. In the dissertation, theWSM is combined with the normal-mode method and the ray method to predict the soundradiated by underwater structures in the plane-parallel waveguide. By analyzing theadvantages and applicability of the two proposed combination methods, it concludes that thecombined propagation algorithm should be chosen appropriately for specific cases. Then theFEM model in half-space is extended to analyze the coupled vibration and acoustic radiationof the elastic structure in waveguide. The applicability of the FEM model is also analyzed andcompared with two proposed combination methods. Actually, the proposed WSM cancombined with any sound propagation algorithm which calculates the sound radiated by amonopole effectively, thus it can combines with more sound propagation algorithms to predictthe sound radiated by elastic structure for cases where more complicated waveguides are to betreated.
In order to prove the efficiency of the proposed methods and the numerical analysises, anexperiment for predicting sound radiated from a cylindrical shell with hemi-caps has beendone successfully in the half-space anechoic tank, and the experiment in the pool ofunderwater acoustic channel was accomplished afterwards.
Since the analyzed structure in this dissertation is the scale model, more attentions havebeen paid to the frequency band above3kHz, and the proposed algorithms of the acousticradiation prediction has been extend to higher frequencies as far as possible. The simulationsand experiments on the scale model are greatly expected to provide useful working guidelinesto practical engineering.
本文首先从现有的自由场声辐射预报方法入手，简单阐述了这些方法的基本原理，并进行了归类、对比。最后选择了点源波叠加法作为有界空间中声辐射预报的主要方法。然而波叠加法（又称作等效源法）却并不完善，存在等效源和振动测点的优化配置等问题。为此，提出了一种最小二乘意义下的等效源配置方法，该方法通过匹配少量参考点的声压幅值，可搜索得到最优的等效源位置，从而改善波叠加法的声辐射预报精度。并在此基础上，分析了利用该方法预报声场的相关误差因素，指出了一些提高精度的等效源和测点位置选取准则，以期波叠加法能更好地运用于声辐射预报。
选择波叠加法作为有界空间中声辐射预报主要方法的原因之一是它将结构等效成了一系列的简单源，简单源的格林函数能较方便地根据反射面的类型和位置作出调整，而且有望与现有的声传播算法结合，实现波导中结构的声辐射预报。但格林函数究竟如何调整却没有定论。为此先从存在单个反射面的半空间声场环境出发，针对水下结构的声辐射快速预报问题，提出了采用自由场格林函数来获得等效源强度的半自由场波叠加法，并针对水和结构的耦合特性，分析了反射面与结构之间的互散射对声辐射预报的影响，进而提出了结构表面法向振速的两种处理方法：波叠加反射声振速分离法和忽略反射声对结构法向振速影响的快速法。最后结合有限元法和边界元法分析了半空间中弹性结构的振动声辐射。
半自由场波叠加法的提出，避开了结构表面三维空间的格林函数求导问题，使得波叠加法能够与波导中的声传播算法结合。因此提出了波动波叠加法和射线波叠加法，它们分别将波叠加法与声传播理论中的简正波法和射线法结合，用于计算结构在平行平面层波导中的辐射声场。进而对这两种方法各自的优势和适用范围进行了分析，指出波叠加法与传播理论结合时需要针对需求选择适宜的传播算法。然后将半空间中弹性结构分析的有限元模型进一步推广用于波导中有限弹性结构的耦合振动及声辐射分析。通过弹性结构的声辐射预报对有限元法、波动波叠加法和射线波叠加法进行了对比，并分析了这些方法各自的适用条件。并指出只要传播算法能给出点源的辐射声场，提出的波叠加法就可以与之结合，实现波导中结构的声辐射预报，因此可以推广到其他类型波导的弹性结构声辐射预报中。
最后针对前面进行的数值分析进行了实体模型在有界空间中声辐射预报的试验验证。首先在水面未敷设吸声尖劈的消声水池中，对半空间中的带帽圆柱壳进行了声辐射预报研究，进而在水声信道水池中进行了波导中柱壳的声辐射预报试验。
由于研究的结构为缩比模型，因此本文更多地关注了3kHz以上的频段，并尽量地将声辐射预报算法往高频段扩展。尝试通过对相似模型的仿真和实验研究为实际工程运用提供一些有益的参考。
The prediction of sound radiated by underwater structures is one of the most importantresearches in the field of underwater acoustics. It is regarded as the theoretical foundation andthe important criterion for quantitative acoustic design and vibration-noise control. Practically,the structure is not always located in free-space, which brings problems, such as the coupledvibration, multipath propagation and scattering, etc. Thus investigations are needed for theprediction of sound radiated by elastic structure in underwater bounded space.
In this dissertation, the methods of acoustic radiation prediction in free-space areinvestigated primarily. Then the methods are expounded and classified according to theirfundamentals. By comparing these methods, the wave superposition method (WSM) is chosenas the main method for acoustic radiation prediction in bounded space. However, the WSM(also known as equivalent source method: ESM) is not perfect, since the optimalconfiguration of the equivalent source and the measuring point has been considering as aproblem. Therefore, an equivalent source configuration method based on the least meansquare is proposed, in which a few reference points of sound pressure should be measuredahead to search the optimal position of equivalent sources. Moreover, the effects of thenumber, position of measuring points and amplitude distribution of vibration were studiednumerically. The principles of how to configurate the equivalent source and measuring pointappropriately are pointed out, in order to improve the accuracy of the WSM and make theWSM more suitable for acoustic radiation prediction.
One reason of choosing WSM as the main method for acoustic radiation prediction inbounded space is that WSM simulates structure by an array of simple sources. The simplesources’ Green function can be adjusted conveniently according to the types and positions ofboundary. Furthermore, the existing algorithms of sound propagation in waveguide canhopefully combined with WSM to predict the sound radiated by elastic structure in waveguide.Unfortunately, there are no guildlines about how to reform the Green function in WSM forcombination. Therefore, the environment of half-spaces with a single boundary is investigatedfirstly, and a half-space wave superposition method is proposed for the fast prediction ofacoustic radiation from a complex structure, in which the free-space Green’s function is usedto match the strength of equivalent sources. As the submerged structure is coupled with water,the scattering between reflector and structure is considered. Moreover, two treatments fornormal velocity of a structure are proposed. One is called separation method which separates normal velocity by wave superposition method and the other is called fast method whichneglects the effect of reflection to the structural vibration, which makes the acoustic radiationprediction more efficiency. The finite element method (FEM) and boundary element method(BEM) are also combined with the proposed method to analyze the vibration and acousticradiation of the elastic structure in half-space.
The proposed half-space wave superposition method avoids the three-dimensionalderivation of Green function on the surface of structure, which makes the possibility ofcombining WSM with the sound propagation algorithms in waveguide. In the dissertation, theWSM is combined with the normal-mode method and the ray method to predict the soundradiated by underwater structures in the plane-parallel waveguide. By analyzing theadvantages and applicability of the two proposed combination methods, it concludes that thecombined propagation algorithm should be chosen appropriately for specific cases. Then theFEM model in half-space is extended to analyze the coupled vibration and acoustic radiationof the elastic structure in waveguide. The applicability of the FEM model is also analyzed andcompared with two proposed combination methods. Actually, the proposed WSM cancombined with any sound propagation algorithm which calculates the sound radiated by amonopole effectively, thus it can combines with more sound propagation algorithms to predictthe sound radiated by elastic structure for cases where more complicated waveguides are to betreated.
In order to prove the efficiency of the proposed methods and the numerical analysises, anexperiment for predicting sound radiated from a cylindrical shell with hemi-caps has beendone successfully in the half-space anechoic tank, and the experiment in the pool ofunderwater acoustic channel was accomplished afterwards.
Since the analyzed structure in this dissertation is the scale model, more attentions havebeen paid to the frequency band above3kHz, and the proposed algorithms of the acousticradiation prediction has been extend to higher frequencies as far as possible. The simulationsand experiments on the scale model are greatly expected to provide useful working guidelinesto practical engineering.
引文
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