潜浮状态下圆柱壳结构的声振特性研究
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摘要
论文的工作是国家自然科学基金资助项目“水下流场－圆柱壳耦合系统的振动能量流特性研究”（项目编号：40976058）的一部分。论文的目标是研究浸没在有限域流场中的圆柱壳结构的声振特性，基于波传播的方法，分别对半浸状态下圆柱壳结构、部分浸没状态下圆柱壳结构以及有限浸没深度下考虑自由液面影响的圆柱壳结构以及考虑刚性壁存在下的圆柱壳结构的远场辐射声压和输入能量流进行了系统的研究。
论文首先对本领域的国内外研究现状进行比较系统的介绍，分别介绍了自由声场下圆柱壳流场耦合系统声振特性研究，概括了结构声辐射的分析方法，回顾了半无限域下结构声振特性的研究以及介绍了镜像原理在声学领域中的应用。
论文的第二部分对半浸状态下的圆柱壳结构为对象进行研究分析，这里的半浸状态是指圆柱壳结构的轴线与自由液面共面，圆柱壳结构的一半表面积浸没在流场中，另外一半表面积所在的环境假设为真空。为了满足自由液面处的边界条件，可以通过级数展开的形式给出流体声压的表达式，进而通过圆柱壳流场交界处的连续条件建立结构和声压间的联系，最终得到流固耦合振动方程。通过稳相法，得到圆柱壳结构远场声压的近似表达式，计算了半浸状态下的远场辐射声压并与无限域中的结果进行了对比分析。
在对半浸状态下圆柱壳结构进行计算，特别是进行能量流的计算时，发现这种半无限域的存在导致了各阶周向模态之间是互相耦合的，这种耦合使得计算效率大为降低，计算时间急剧增加。基于此，针对半浸状态下圆柱壳结构辐射声压的快速计算方法展开了研究。这里借鉴有限长圆柱壳结构的解耦思路，认为半浸圆柱壳结构的耦合振动方程所得阻抗矩阵中非对角元素为零，从而对耦合方程进行解耦，通过对比验证了这种思路的可行性。基于这种解耦方法，计算分析了不同周向模态下半浸状态圆柱壳结构的输入能量流特性。
接下来对部分浸没状态下圆柱壳结构的声振特性展开分析，考虑到部分浸没状态下流体声压的解析表达式不易直接给出，文中采用参考文献中声学边界的近似处理方法，给出了流体声压载荷的近似表达式，最终计算分析了部分浸没状态下圆柱壳结构的远场辐射声压和输入能量流特性。
对于有限浸没深度下考虑自由液面影响的圆柱壳结构，这里利用镜像原理来处理自由液面处的流体声学边界条件，利用汉克尔函数的Graf加法定理，建立了实源和镜像所处的两个坐标系之间的联系，最后利用流体和结构边界处的连续条件，最终建立了这种浸没状态下声固耦合振动方程。计算了圆柱壳结构的远场辐射声压并与无限域中的结果进行对比分析，研究发现，当圆柱壳结构离自由液面距离较近时，圆柱壳结构的辐射声场表现出较大的差异性；而当圆柱壳结构离自由液面距离足够大时，其辐射声场和无限域中的结果基本一致。
实际工程中，也存在诸如海底和码头壁面的情况，文中将海底和码头壁面近似当成刚性壁面来处理，建立了刚性壁面存在时水下圆柱壳结构的声固耦合振动方程，对其远场辐射声压进行计算，并与考虑自由液面影响下的结果进行对比分析。
最后对自由液面和刚性壁面同时存在时的组合边界下水下圆柱壳结构的声辐射特性进行分析，令自由液面和刚性壁面是一种垂直关系，这里假设自由液面和刚性壁面只形成一次反射，也就是说自由液面的反射波不会在刚性壁面处形成二次反射。基于此，得到了计算组合边界下圆柱壳结构远场辐射声压的表达式，并与仅存在自由液面和仅考虑刚性壁面的情景进行对比研究。
论文给出了不同浸没状态下圆柱壳结构远场辐射声压的计算方法，比较系统地对处于各种浸没状态下圆柱壳结构的声振特性展开了分析，为不同浸没状态下圆柱壳结构的声辐射预报建立了理论基础。
The work of the thesis is a part of the research project “Characteristics of VibrationalPower Flow in Submerged Coupled Cylindrical shell”, which is supported by the NationalNatural Science Foundation of China (Contract Number:40976058). Based on the wavepropagation approach, the vibro-acoustic characteristics of the cylindrical shells in thefollowing cases are studied: the semi-submerged cylindrical shell, the partially immersedcylindrical shells, the cylindrical shells which is submerged in the fluid with finite depthfrom the free surface or with finite distance form the rigid wall and the cylindrical shellssubmerged in the fluid with the boundary of the free surface and the rigid wall.
The studies which are related to our work are introduced briefly. The main contentsinclude the outlines of the studies about the vibro-acoustic characteristics of cylindricalshell in the free space, the summary of the methods exployed in the sound radiationanalysis, the overview of the studies of the vibro-acoustic characteristics of cylindricalshell in half space and the introduction of the image method applied in acoustics.
The vibro-acoustic characteristic of the semi-submerged cylindrical shell is studied.The domain of the fluid can be seen as semi-infinite. The expression can be expanded intoseries which can satisfy the boundary condition of the free surface in this case. Thestructure-fluid coupling equation can be obtained applying the boundary condition of theinterface of the structure and fluid. Introducing the stationary phase method, theapproximate expression of the far field sound pressure is obtained and the results arecompared with those in infinite fluid field.
The coupling of the circumferential mode of the semi-submerged cylindrical shellmakes the impedance matrix very complicate which leads to the low solution efficiency ofthe coupling equation. A method of diagonal decoupling is employed here to solve theproblem. Using the method, the non-diagonal elements of the impedance matrix areassumed to be zero and the equation can be decoupled. The far field sound pressure can becalculated more efficient and the validity is proved by comparing the results with those inliterature. Based on the method, the input power flow is studied. This method alsofacilitates the study of more complicate cylindrical shells partially immersed.
The characteristics of the sound radiation and vibrational power flow of the partiallysubmerged cylindrical shell under a harmonic excitation are studied. The approximateacoustic boundary of the free surface is used to solve the fluid domain. The structure-fluidcoupling equation is established based on the Flügge and Helmholtz theories. The far-fieldsound pressure is calculated and compared with that in infinite field.
The far-field sound radiation of a submerged cylindrical shell with finite depth fromthe free surface is studied. The image method is applied to satisfy the boundary conditionof the free surface. Based on the Flügge shell theory and the Helmholtz equation, thestructure-acoustic coupling equation is established. The expression of the far-field soundpressure is obtained using the stationary phase method. In order to evaluate the effect ofthe depth from the free surface, the results of the submerged cylindrical shell with finitedepth from the free surface are compared to those of the submerged cylindrical shell in theinfinite fluid. The characteristics of the far-field sound pressure with the change of thedepth are investigated. It is found that the depth has important influence on the far-fieldsound pressure radiated from the submerged cylindrical shell due to the presence of freesurface.
In practice, when the submarine runs near the seabed or the submarine is tested in thepresence of dock, the fluid domain can be seen as semi-infinite and the seabed and thedock can be processed as rigid wall The far-field acoustic radiation of a submergedcylindrical shell which is located at a finite distance from the rigid wall is studied. Basedon the image method, Flügge shell theory and the Helmholtz equation, thestructure-acoustic coupling equation is established and the expression of the far-fieldsound pressure is obtained. In order to evaluate the effect of the rigid wall, the results arecompared to those of the submerged cylindrical shell in presence of free surface.
The far field sound pressure of the cylindrical shells with the boundary of thecombination of free surface and rigid wall is finally studied. The free surface and rigidwall is assumed to be perpendicular. It is assumed that the sound wave is reflected onlyonce by the boundary that is the reflected wave from the rigid wall can not be reflectedagain by the free surface and vice versa. Based on the assumption, the expression of thefarfiled sound pressure radiated by the cylindrical shell is otained.
The expressions of the far field sound pressure are obtained while the cylindricalshells are located in the fluid with various boundary conditions. The vibro-acousitccharacteristics of the cylindrical shell in different immersion states are studied in our workwhich can serve as the theoretical basis for the establishment of the sound radiationprediction of the cylindrical shells in different immersion states.
论文首先对本领域的国内外研究现状进行比较系统的介绍，分别介绍了自由声场下圆柱壳流场耦合系统声振特性研究，概括了结构声辐射的分析方法，回顾了半无限域下结构声振特性的研究以及介绍了镜像原理在声学领域中的应用。
论文的第二部分对半浸状态下的圆柱壳结构为对象进行研究分析，这里的半浸状态是指圆柱壳结构的轴线与自由液面共面，圆柱壳结构的一半表面积浸没在流场中，另外一半表面积所在的环境假设为真空。为了满足自由液面处的边界条件，可以通过级数展开的形式给出流体声压的表达式，进而通过圆柱壳流场交界处的连续条件建立结构和声压间的联系，最终得到流固耦合振动方程。通过稳相法，得到圆柱壳结构远场声压的近似表达式，计算了半浸状态下的远场辐射声压并与无限域中的结果进行了对比分析。
在对半浸状态下圆柱壳结构进行计算，特别是进行能量流的计算时，发现这种半无限域的存在导致了各阶周向模态之间是互相耦合的，这种耦合使得计算效率大为降低，计算时间急剧增加。基于此，针对半浸状态下圆柱壳结构辐射声压的快速计算方法展开了研究。这里借鉴有限长圆柱壳结构的解耦思路，认为半浸圆柱壳结构的耦合振动方程所得阻抗矩阵中非对角元素为零，从而对耦合方程进行解耦，通过对比验证了这种思路的可行性。基于这种解耦方法，计算分析了不同周向模态下半浸状态圆柱壳结构的输入能量流特性。
接下来对部分浸没状态下圆柱壳结构的声振特性展开分析，考虑到部分浸没状态下流体声压的解析表达式不易直接给出，文中采用参考文献中声学边界的近似处理方法，给出了流体声压载荷的近似表达式，最终计算分析了部分浸没状态下圆柱壳结构的远场辐射声压和输入能量流特性。
对于有限浸没深度下考虑自由液面影响的圆柱壳结构，这里利用镜像原理来处理自由液面处的流体声学边界条件，利用汉克尔函数的Graf加法定理，建立了实源和镜像所处的两个坐标系之间的联系，最后利用流体和结构边界处的连续条件，最终建立了这种浸没状态下声固耦合振动方程。计算了圆柱壳结构的远场辐射声压并与无限域中的结果进行对比分析，研究发现，当圆柱壳结构离自由液面距离较近时，圆柱壳结构的辐射声场表现出较大的差异性；而当圆柱壳结构离自由液面距离足够大时，其辐射声场和无限域中的结果基本一致。
实际工程中，也存在诸如海底和码头壁面的情况，文中将海底和码头壁面近似当成刚性壁面来处理，建立了刚性壁面存在时水下圆柱壳结构的声固耦合振动方程，对其远场辐射声压进行计算，并与考虑自由液面影响下的结果进行对比分析。
最后对自由液面和刚性壁面同时存在时的组合边界下水下圆柱壳结构的声辐射特性进行分析，令自由液面和刚性壁面是一种垂直关系，这里假设自由液面和刚性壁面只形成一次反射，也就是说自由液面的反射波不会在刚性壁面处形成二次反射。基于此，得到了计算组合边界下圆柱壳结构远场辐射声压的表达式，并与仅存在自由液面和仅考虑刚性壁面的情景进行对比研究。
论文给出了不同浸没状态下圆柱壳结构远场辐射声压的计算方法，比较系统地对处于各种浸没状态下圆柱壳结构的声振特性展开了分析，为不同浸没状态下圆柱壳结构的声辐射预报建立了理论基础。
The work of the thesis is a part of the research project “Characteristics of VibrationalPower Flow in Submerged Coupled Cylindrical shell”, which is supported by the NationalNatural Science Foundation of China (Contract Number:40976058). Based on the wavepropagation approach, the vibro-acoustic characteristics of the cylindrical shells in thefollowing cases are studied: the semi-submerged cylindrical shell, the partially immersedcylindrical shells, the cylindrical shells which is submerged in the fluid with finite depthfrom the free surface or with finite distance form the rigid wall and the cylindrical shellssubmerged in the fluid with the boundary of the free surface and the rigid wall.
The studies which are related to our work are introduced briefly. The main contentsinclude the outlines of the studies about the vibro-acoustic characteristics of cylindricalshell in the free space, the summary of the methods exployed in the sound radiationanalysis, the overview of the studies of the vibro-acoustic characteristics of cylindricalshell in half space and the introduction of the image method applied in acoustics.
The vibro-acoustic characteristic of the semi-submerged cylindrical shell is studied.The domain of the fluid can be seen as semi-infinite. The expression can be expanded intoseries which can satisfy the boundary condition of the free surface in this case. Thestructure-fluid coupling equation can be obtained applying the boundary condition of theinterface of the structure and fluid. Introducing the stationary phase method, theapproximate expression of the far field sound pressure is obtained and the results arecompared with those in infinite fluid field.
The coupling of the circumferential mode of the semi-submerged cylindrical shellmakes the impedance matrix very complicate which leads to the low solution efficiency ofthe coupling equation. A method of diagonal decoupling is employed here to solve theproblem. Using the method, the non-diagonal elements of the impedance matrix areassumed to be zero and the equation can be decoupled. The far field sound pressure can becalculated more efficient and the validity is proved by comparing the results with those inliterature. Based on the method, the input power flow is studied. This method alsofacilitates the study of more complicate cylindrical shells partially immersed.
The characteristics of the sound radiation and vibrational power flow of the partiallysubmerged cylindrical shell under a harmonic excitation are studied. The approximateacoustic boundary of the free surface is used to solve the fluid domain. The structure-fluidcoupling equation is established based on the Flügge and Helmholtz theories. The far-fieldsound pressure is calculated and compared with that in infinite field.
The far-field sound radiation of a submerged cylindrical shell with finite depth fromthe free surface is studied. The image method is applied to satisfy the boundary conditionof the free surface. Based on the Flügge shell theory and the Helmholtz equation, thestructure-acoustic coupling equation is established. The expression of the far-field soundpressure is obtained using the stationary phase method. In order to evaluate the effect ofthe depth from the free surface, the results of the submerged cylindrical shell with finitedepth from the free surface are compared to those of the submerged cylindrical shell in theinfinite fluid. The characteristics of the far-field sound pressure with the change of thedepth are investigated. It is found that the depth has important influence on the far-fieldsound pressure radiated from the submerged cylindrical shell due to the presence of freesurface.
In practice, when the submarine runs near the seabed or the submarine is tested in thepresence of dock, the fluid domain can be seen as semi-infinite and the seabed and thedock can be processed as rigid wall The far-field acoustic radiation of a submergedcylindrical shell which is located at a finite distance from the rigid wall is studied. Basedon the image method, Flügge shell theory and the Helmholtz equation, thestructure-acoustic coupling equation is established and the expression of the far-fieldsound pressure is obtained. In order to evaluate the effect of the rigid wall, the results arecompared to those of the submerged cylindrical shell in presence of free surface.
The far field sound pressure of the cylindrical shells with the boundary of thecombination of free surface and rigid wall is finally studied. The free surface and rigidwall is assumed to be perpendicular. It is assumed that the sound wave is reflected onlyonce by the boundary that is the reflected wave from the rigid wall can not be reflectedagain by the free surface and vice versa. Based on the assumption, the expression of thefarfiled sound pressure radiated by the cylindrical shell is otained.
The expressions of the far field sound pressure are obtained while the cylindricalshells are located in the fluid with various boundary conditions. The vibro-acousitccharacteristics of the cylindrical shell in different immersion states are studied in our workwhich can serve as the theoretical basis for the establishment of the sound radiationprediction of the cylindrical shells in different immersion states.
引文
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