层合板壳振动和声辐射预测方法
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摘要
复合板壳在航空航天、船舶与海洋工程中有广泛的应用。研究复合板壳的振动和声辐射特性对于设计新型船舶和潜艇至关重要。本文以潜艇的振动与声辐射为背景，给出了五种板壳的结构振动和声辐射预测方法：两组筋加强层合板、环肋加强约束阻尼层合圆柱壳、多周期筋加强层合圆柱壳、层合圆锥壳和轴向矩形板加强圆柱壳。加筋层合板和多周期筋加强层合圆柱壳可以用来研究水下航行器的声辐射。环肋加强约束阻尼层合圆柱壳可以用来研究覆盖有约束阻尼层的潜艇和鱼雷的声辐射。层合圆锥壳的振动与声辐射可以用来研究艇体艉部的振动与声辐射。轴向矩形板加强圆柱壳可以用来研究带龙骨或长基座的艇体的声辐射。本文所做的工作如下：
(1)本文从理论上研究了剪切变形加筋层合板的声辐射，基于一阶剪切变形理论推导了复合层合板的运动方程。两组平行筋仅仅通过法向线力同层合板相互作用。利用波数变换和稳相法，解析描述了远场声压。对比了一阶剪切变形理论和经典层合板理论给出的声压，对于一块各向同性板，在中高频范围表现出声压的差异。本文利用声压和横向位移谱来研究力的位置、筋和角铺设层的影响，同时研究了多种载荷作用下的对称和反对称铺设层合板的声辐射，给出了加筋层合板的声辐射功率。
(2)理论研究了两组环肋加强带约束阻尼层合圆柱壳的声辐射，基于Sanders薄壳理论推导了约束阻尼层圆柱壳的控制方程。两组环肋仅仅通过法向线力同主壳相互作用。在波数域，利用稳相法得到远场声压的解析表达式。分析了粘弹性核心层、约束层和多种载荷对声压的影响。声压和径向位移的螺旋波谱清晰地揭示了加筋约束阻尼层合圆柱壳的振动和声辐射特性，约束阻尼层能有效地抑制径向振动和减少声辐射。
(3)理论研究了多周期筋加强剪切变形层合圆柱壳的声辐射。两组环肋和一组纵桁分别均匀分布在圆柱壳的轴向和周向。这种典型结构广泛地用来建造水下航行器的外壳。两种模型用来研究加筋层合圆柱壳声辐射。一种是简化的模型，仅仅用在低频段，稠密纵桁加强的条件下。另外一个是耦合模型，需要数值求解，在全频段范围内使用。利用径向位移和声压的螺旋波谱本文发现轴向波数转换由环肋引起，周向波数转换由纵桁产生。这可以理解为轴向波和周向波会被加强筋调制，并且多周期加强筋抑制了圆柱壳的径向位移和声压。对于反对称层合圆柱壳，径向位移和表面声压的螺旋波谱揭示出了这些现象，合适设计的多周期加强筋将减少圆柱壳的振动和声辐射。在环频率以上时，大型圆柱壳结构的远场声辐射在波数域上的特性被一个声椭圆节制，只有声椭圆内部的波才具备声辐射能力。周向纵桁能减少圆柱壳的声辐射功率和输入功率，但从输入功率到声辐射功率的能量转化效率会在很大的程度上提升。
(4)本文详细研究了一个正交铺设层合圆锥壳的声辐射模型，基于Reissner-Naghdi薄壳理论，推导了圆锥壳的控制方程。作用在锥壳上的流体载荷通过将层合圆锥壳分割成小圆柱段近似。圆锥壳的位移场通过波传播法和Galerkin法求解，远场声压在波数域内通过两端带有无限长圆柱障板的小圆柱声辐射的迭加得到，研究了层合圆锥壳的振动和声学特性。
(5)以研究带龙骨或长基座面板的潜艇声辐射为背景，本文建立了轴向矩形板加强圆柱壳的声辐射模型。各向同性矩形板的横向运动通过经典的薄板理论描述，平板的面内运动采用二维弹性理论表达，矩形板对圆柱壳的作用力通过圆柱壳的位移表示。由于结构在圆周方向表现出非均匀性，周向方向的波数是耦合的。在波数域内求解耦合系统的控制方程，得到了圆柱壳的位移场。在径向载荷和轴向载荷作用下，研究了矩形板对圆柱壳振动和声辐射特性的影响。
最后，本文对板壳结构声的进一步研究工作进行总结。指出以后工作的研究重点。
Composite plates and shells have wide applications in aeronautic and astronautic,marine engineering. Study on the vibrational and acoustic characteristics is critical todesigning new ships and submarines. The present research contents are in the contextof the vibrational and acoustic behavior of submarine. Structural and acousticcharacteristics of five kinds of plates and shells are analyzed, such as laminatedcomposite plates with two sets of stiffeners, constrained layer damping cylindricalshells with ring stiffeners, laminated composite shells with multiple stiffeners,laminated conical shells and circular cylindrical shells with an axial rectangle plate.Laminated composite plate with stiffeners and laminated composite shells withmultiple stiffeners can be used to investigate acoustic radiation from underwatervehicles. Constrained layer damping cylindrical shell with ring stiffeners can beemployed to study acoustic radiation from submarine and torpedo hulls. Laminatedconical shell can be used to explore sound radiation from the stern of submarine.Circular cylindrical shells with an axial rectangle plate can be employed to examineacoustic radiation from submarine with the rib plate or complicated long base. Thepresent studies are given as follows:
(1) Sound radiation from shear deformable stiffened laminated plates is studiedtheoretically. The equations of motion for the composite laminated plate are derivedon the basis of the first-order shear deformation plate theory. Two sets of parallelstiffeners interact with the laminated plate only through the normal line forces. Byusing the Fourier wavenumber transform and the stationary phase method, thefar-field sound pressure is described analytically. Sound pressure given by thefirst-order shear deformation plate theory and the classical thin plate theory iscompared, and the differences of sound pressure are shown in the high frequencyrange for an isotropic plate. Sound pressure and the transverse displacement spectraare presented to illustrate the effects of force location, stiffeners and angle-ply layers.Sound radiation from symmetric and antisymmetric composite plates with multiple loadings is investigated and the acoustic power of the stiffened laminated cylindricalshell is also presented.
(2) Acoustic radiation from cylindrical shells stiffened by two sets of rings, withconstrained layer damping, is investigated theoretically. The governing equations ofmotion for the cylindrical shell with constrained layer damping are derived on thebasis of Sanders thin shell theory. Two sets of rings interact with the host cylindricalshell only through the normal line forces. The solutions are derived in thewavenumber domain and the stationary phase method is used to find an analyticalexpression of the far-field sound pressure. The effects of the viscoelastic material core,constrained layer and multiple loadings on sound pressure are demonstrated. Thehelical wave spectra of sound pressure and the radial displacement clearly show thevibration and acoustic characteristics of the stiffened cylindrical shell withconstrained layer damping. Constrained layer damping can effectively suppress theradial vibration and reduce acoustic radiation.
(3) Acoustic radiation from shear deformable laminated cylindrical shells withmultiple periodic stiffeners is explored theoretically. Two sets of rings and one set ofcircumferential stringers are uniformly distributed along the inner surface of thelaminated cylindrical shell in the axial and circumferential directions. These structuresare widely used for the construction of the hulls for underwater vehicles. Two kindsof models are proposed to investigate acoustic radiation from stiffened laminatedcylindrical shells in the present work. One is a simplified method and only employedin the low frequency range in a condition of dense stringers. The other used in allfrequency range is a coupled model and needs to be solved numerically. It transpiresthat the axial wavenumber conversion is caused by the rings and the circumferentialwavenumber conversion is produced by the stringers, which is clearly identified bythe helical wave spectra of the radial displacement and sound pressure. Therefore, it isunderstandable that the axial waves and the circumferential waves would bemodulated, and the radial displacement and sound pressure would be suppressed oncethe cylindrical shell is reinforced by two sets of rings and circumferential stringers.The helical wave spectra of the radial displacement and the surface sound pressure for the antisymmetric laminated cylindrical shell just show these phenomena. Theproperly designed cylindrical shell with multiple periodic stiffeners will reduce thevibration and acoustic radiation. Above the ring frequency, the characteristic in thewavenumber domain of far-field acoustic radiation from a large cylindrical shell isconfined by an ellipse and only the waves inside the ellipse can radiate sound into thefar field. The circumferencial sringers can reduce the acoustic power and the inputpower of the laminated cylindrical shell, but the energy transformation efficiencyfrom the input power to the acoustic power is increased to great extent.
(4) A model of acoustic radiation from conical shells is explored in detail and theequations of motion for the conical shell are described on the basis ofReissner-Naghdi thin shell theory. Fluid loadings acting on the conical shell aretackled by the approximation of dividing the laminated conical shell into smallcylindrical segments. The displacement field of conical shell is solved by using thewave propagation approach and Galerkin method. The far-field sound pressure isfound in the wavenumber domain by the superposition of acoustic radiation from eachcylinder with infinite circular cylindrical baffles at the two ends. Vibration andacoustic characteristics of laminated cone are studied.
(5) A model of acoustic radiation from circular cylindrical shell with an axialrectangle plate is presented in the context of studying acoustic radiation fromsubmarine with a rib plate or long base panel. Transverse motion of the isotropicrectangle plate is described by using the classical thin plate theory and the equationsof in-plane motion for the plate are expressed on the basis of the two-dimensinalelastic theory. The reactive forces of the plate acting on the cylindrical shell aredetermined by using the displacements of the cylindrical shell. Due to the structuralnon-uniformity in the circumferential direction, the circumferential waves are coupled.The coupling systematic equations are solved in the wavenumber domain, and thenthe displacement field of the structure is obtained. The effects of the rectangle plate onthe vibrational and acoustic behavior of the cylindrical shell are studied under radialand axial loadings.
In the end, the further studies of the structural acoustics for the plates and shellsare summarized and the future key points of the researches are pointed out.
(1)本文从理论上研究了剪切变形加筋层合板的声辐射，基于一阶剪切变形理论推导了复合层合板的运动方程。两组平行筋仅仅通过法向线力同层合板相互作用。利用波数变换和稳相法，解析描述了远场声压。对比了一阶剪切变形理论和经典层合板理论给出的声压，对于一块各向同性板，在中高频范围表现出声压的差异。本文利用声压和横向位移谱来研究力的位置、筋和角铺设层的影响，同时研究了多种载荷作用下的对称和反对称铺设层合板的声辐射，给出了加筋层合板的声辐射功率。
(2)理论研究了两组环肋加强带约束阻尼层合圆柱壳的声辐射，基于Sanders薄壳理论推导了约束阻尼层圆柱壳的控制方程。两组环肋仅仅通过法向线力同主壳相互作用。在波数域，利用稳相法得到远场声压的解析表达式。分析了粘弹性核心层、约束层和多种载荷对声压的影响。声压和径向位移的螺旋波谱清晰地揭示了加筋约束阻尼层合圆柱壳的振动和声辐射特性，约束阻尼层能有效地抑制径向振动和减少声辐射。
(3)理论研究了多周期筋加强剪切变形层合圆柱壳的声辐射。两组环肋和一组纵桁分别均匀分布在圆柱壳的轴向和周向。这种典型结构广泛地用来建造水下航行器的外壳。两种模型用来研究加筋层合圆柱壳声辐射。一种是简化的模型，仅仅用在低频段，稠密纵桁加强的条件下。另外一个是耦合模型，需要数值求解，在全频段范围内使用。利用径向位移和声压的螺旋波谱本文发现轴向波数转换由环肋引起，周向波数转换由纵桁产生。这可以理解为轴向波和周向波会被加强筋调制，并且多周期加强筋抑制了圆柱壳的径向位移和声压。对于反对称层合圆柱壳，径向位移和表面声压的螺旋波谱揭示出了这些现象，合适设计的多周期加强筋将减少圆柱壳的振动和声辐射。在环频率以上时，大型圆柱壳结构的远场声辐射在波数域上的特性被一个声椭圆节制，只有声椭圆内部的波才具备声辐射能力。周向纵桁能减少圆柱壳的声辐射功率和输入功率，但从输入功率到声辐射功率的能量转化效率会在很大的程度上提升。
(4)本文详细研究了一个正交铺设层合圆锥壳的声辐射模型，基于Reissner-Naghdi薄壳理论，推导了圆锥壳的控制方程。作用在锥壳上的流体载荷通过将层合圆锥壳分割成小圆柱段近似。圆锥壳的位移场通过波传播法和Galerkin法求解，远场声压在波数域内通过两端带有无限长圆柱障板的小圆柱声辐射的迭加得到，研究了层合圆锥壳的振动和声学特性。
(5)以研究带龙骨或长基座面板的潜艇声辐射为背景，本文建立了轴向矩形板加强圆柱壳的声辐射模型。各向同性矩形板的横向运动通过经典的薄板理论描述，平板的面内运动采用二维弹性理论表达，矩形板对圆柱壳的作用力通过圆柱壳的位移表示。由于结构在圆周方向表现出非均匀性，周向方向的波数是耦合的。在波数域内求解耦合系统的控制方程，得到了圆柱壳的位移场。在径向载荷和轴向载荷作用下，研究了矩形板对圆柱壳振动和声辐射特性的影响。
最后，本文对板壳结构声的进一步研究工作进行总结。指出以后工作的研究重点。
Composite plates and shells have wide applications in aeronautic and astronautic,marine engineering. Study on the vibrational and acoustic characteristics is critical todesigning new ships and submarines. The present research contents are in the contextof the vibrational and acoustic behavior of submarine. Structural and acousticcharacteristics of five kinds of plates and shells are analyzed, such as laminatedcomposite plates with two sets of stiffeners, constrained layer damping cylindricalshells with ring stiffeners, laminated composite shells with multiple stiffeners,laminated conical shells and circular cylindrical shells with an axial rectangle plate.Laminated composite plate with stiffeners and laminated composite shells withmultiple stiffeners can be used to investigate acoustic radiation from underwatervehicles. Constrained layer damping cylindrical shell with ring stiffeners can beemployed to study acoustic radiation from submarine and torpedo hulls. Laminatedconical shell can be used to explore sound radiation from the stern of submarine.Circular cylindrical shells with an axial rectangle plate can be employed to examineacoustic radiation from submarine with the rib plate or complicated long base. Thepresent studies are given as follows:
(1) Sound radiation from shear deformable stiffened laminated plates is studiedtheoretically. The equations of motion for the composite laminated plate are derivedon the basis of the first-order shear deformation plate theory. Two sets of parallelstiffeners interact with the laminated plate only through the normal line forces. Byusing the Fourier wavenumber transform and the stationary phase method, thefar-field sound pressure is described analytically. Sound pressure given by thefirst-order shear deformation plate theory and the classical thin plate theory iscompared, and the differences of sound pressure are shown in the high frequencyrange for an isotropic plate. Sound pressure and the transverse displacement spectraare presented to illustrate the effects of force location, stiffeners and angle-ply layers.Sound radiation from symmetric and antisymmetric composite plates with multiple loadings is investigated and the acoustic power of the stiffened laminated cylindricalshell is also presented.
(2) Acoustic radiation from cylindrical shells stiffened by two sets of rings, withconstrained layer damping, is investigated theoretically. The governing equations ofmotion for the cylindrical shell with constrained layer damping are derived on thebasis of Sanders thin shell theory. Two sets of rings interact with the host cylindricalshell only through the normal line forces. The solutions are derived in thewavenumber domain and the stationary phase method is used to find an analyticalexpression of the far-field sound pressure. The effects of the viscoelastic material core,constrained layer and multiple loadings on sound pressure are demonstrated. Thehelical wave spectra of sound pressure and the radial displacement clearly show thevibration and acoustic characteristics of the stiffened cylindrical shell withconstrained layer damping. Constrained layer damping can effectively suppress theradial vibration and reduce acoustic radiation.
(3) Acoustic radiation from shear deformable laminated cylindrical shells withmultiple periodic stiffeners is explored theoretically. Two sets of rings and one set ofcircumferential stringers are uniformly distributed along the inner surface of thelaminated cylindrical shell in the axial and circumferential directions. These structuresare widely used for the construction of the hulls for underwater vehicles. Two kindsof models are proposed to investigate acoustic radiation from stiffened laminatedcylindrical shells in the present work. One is a simplified method and only employedin the low frequency range in a condition of dense stringers. The other used in allfrequency range is a coupled model and needs to be solved numerically. It transpiresthat the axial wavenumber conversion is caused by the rings and the circumferentialwavenumber conversion is produced by the stringers, which is clearly identified bythe helical wave spectra of the radial displacement and sound pressure. Therefore, it isunderstandable that the axial waves and the circumferential waves would bemodulated, and the radial displacement and sound pressure would be suppressed oncethe cylindrical shell is reinforced by two sets of rings and circumferential stringers.The helical wave spectra of the radial displacement and the surface sound pressure for the antisymmetric laminated cylindrical shell just show these phenomena. Theproperly designed cylindrical shell with multiple periodic stiffeners will reduce thevibration and acoustic radiation. Above the ring frequency, the characteristic in thewavenumber domain of far-field acoustic radiation from a large cylindrical shell isconfined by an ellipse and only the waves inside the ellipse can radiate sound into thefar field. The circumferencial sringers can reduce the acoustic power and the inputpower of the laminated cylindrical shell, but the energy transformation efficiencyfrom the input power to the acoustic power is increased to great extent.
(4) A model of acoustic radiation from conical shells is explored in detail and theequations of motion for the conical shell are described on the basis ofReissner-Naghdi thin shell theory. Fluid loadings acting on the conical shell aretackled by the approximation of dividing the laminated conical shell into smallcylindrical segments. The displacement field of conical shell is solved by using thewave propagation approach and Galerkin method. The far-field sound pressure isfound in the wavenumber domain by the superposition of acoustic radiation from eachcylinder with infinite circular cylindrical baffles at the two ends. Vibration andacoustic characteristics of laminated cone are studied.
(5) A model of acoustic radiation from circular cylindrical shell with an axialrectangle plate is presented in the context of studying acoustic radiation fromsubmarine with a rib plate or long base panel. Transverse motion of the isotropicrectangle plate is described by using the classical thin plate theory and the equationsof in-plane motion for the plate are expressed on the basis of the two-dimensinalelastic theory. The reactive forces of the plate acting on the cylindrical shell aredetermined by using the displacements of the cylindrical shell. Due to the structuralnon-uniformity in the circumferential direction, the circumferential waves are coupled.The coupling systematic equations are solved in the wavenumber domain, and thenthe displacement field of the structure is obtained. The effects of the rectangle plate onthe vibrational and acoustic behavior of the cylindrical shell are studied under radialand axial loadings.
In the end, the further studies of the structural acoustics for the plates and shellsare summarized and the future key points of the researches are pointed out.
引文
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