Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

Characteristics of the vibrational power flow propagation in a submerged periodic ring-stiffened cylindrical shell

By using space-harmonic analysis method, the characteristics of the vibrational power flow propagation in an infinite periodic ring-stiffened cylindrical shell immersed in water are studied. The harmonic motion of the shell and the sound pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively, and four kinds of the rings’ forces and moments are considered. Along the shell axial direction, the propagation of the power flow carried by different internal forces (moments) of the shell wall can be obtained, thus the total power flow in the shell wall and the ratios of the component power flow carried by different shell internal forces (moments) to the total power flow are also studied. It is found that characteristics of the vibrational power flow propagation vary with different circumferential modes order and different frequencies. Moreover, the presence of the stiffeners and structural damping will greatly influence the results.     

Space harmonic analysis of sound radiation from a submerged periodic ring-stiffened cylindrical shell

An analytical method is developed to study radiated sound power characteristics from an infinite submerged periodically stiffened cylindrical shell excited by a radial cosine harmonic line force. The harmonic motion of the shell and the pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively. By using periodic theory of space harmonic analysis, the response of the periodic structure to harmonic excitations has been obtained by expanding it in terms of a series of space harmonics. Radiated sound power on the shell wall along the axial direction and the influence of different parameters on the results are studied, respectively. A conclusion is drawn that the stiffeners have a great influence at low and high frequencies while have a slight influence at intermediate frequencies for low circumferential mode orders. The work will give some guidelines for noise reduction of this kind of shell.     

Active control of sound radiated by a submarine in bending vibration

This paper theoretically investigates the use of inertial actuators to reduce the sound radiated by a submarine hull in bending vibration under harmonic excitation from the propeller. The radial forces from the propeller are tonal at the blade passing frequency and are transmitted to the hull through the stern end cone. The hull is modelled as a fluid loaded cylindrical shell with ring stiffeners and two equally spaced bulkheads. The cylinder is closed by end-plates and conical end caps. The actuators are arranged in circumferential arrays and attached to the prow end cone. Both Active Vibration Control and Active Structural Acoustic Control are analysed. The inertial actuators can provide control forces with a magnitude large enough to reduce the sound radiated by the vibrations of the hull in some frequency ranges.     

Structural and acoustic responses of a fluid-loaded cylindrical hull with structural discontinuities

This paper studies the low frequency vibrational behaviour and radiated sound of a submarine hull under axial excitation. The submarine is modelled as a fluid-loaded cylindrical shell with internal bulkheads and ring-stiffeners and closed at each end by circular plates. A smeared approach is used to model the ring stiffeners. The external pressure acting on the hull due to the fluid loading is calculated using an infinite model and is shown to be a good approximation at low frequencies. The radiated sound pressure is obtained by considering the finite cylindrical hull to be extended by two semi-infinite rigid baffles. The sound pressure is then only due to the radial displacement of the cylindrical shell, without taking into account the scattering at the finite ends. The main aim of this paper is to observe the influence of the various complicating effects such as the bulkheads, ring-stiffeners and fluid loading on the structural and acoustic responses of the finite cylindrical shell. Results from the analytical models presented in this paper are compared to the computational results from finite element and boundary element models.     

准周期加隔板有限长圆柱壳声散射

研究准周期加隔板有限长圆柱壳在水中的声散射特性,隔板位置存在小的随机偏差.首先给出理论推导,通过计算周期加隔板情况验证理论公式的正确性.然后以角度-频率谱形式给出准周期加隔板圆柱壳声散射计算结果.计算表明隔板的准周期性导致Bloch-Floquet弯曲波和散射声场背景出现扩散和增强现象,而近乎平行于横轴的由隔板共振引起的亮条纹被散射声场背景所掩盖.最后讨论了随机因子、隔板个数以及隔板间距对Bragg散射的影响.计算表明随机因子越大Bragg散射条纹的频率范围越宽扩散越明显,隔板个数越多Bragg散射条纹的频率范围越窄能量越集中,隔板间距变大时Bragg散射条纹增多而且越高阶次的Bragg散射条纹扩散越严重.根据Bragg散射的几何特征导出的近似估算公式可以较准确预报Bragg散射在频谱图上的位置,也可以大致预报隔板准周期排列时Bragg散射的扩散现象.     

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.     

Acoustic scattering by a cylindrical shell with symmetric line constraints in the heavy fluid-loading limit

A cylindrical shell, modelled using Donnell-Mushtari thin shell theory, is reinforced by two internal rigid plates attached to the shell along lines parallel to the shell axis. A circumferential mode expansion is used to obtain numerical results for the scattered sound field due to the presence of the reaction forces along the attachment lines. In the heavy fluid-loading limit, which is appropriate for low and mid-frequency ranges for practical underwater structures, asymptotic analysis is presented which allows the peak frequencies in the scattered field due to the reaction forces to be expressed (to leading order) in terms of the geometry and the shell and fluid parameters. These predictions agree well with results obtained by numerically evaluating the infinite sums needed to calculate the reaction forces and hence the scattered field.     

Coupled vibrations of cantilever cylindrical shells partially submerged in fluids with continuous, simply connected and non-convex domain

The approach developed in the present paper is applied for the coupled-vibration analysis of a cantilever cylindrical shell partially submerged in a fluid with a continuous, simply connected and non-convex domain. The shell is partially and concentrically submerged in a rigid cylindrical container partially filled by a fluid which is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions using the collocation method. The interaction between the fluid and the structure takes into account by using the compatibility requirement along the wet surface of the shell and the Rayleigh-Ritz method is used to calculate natural frequencies and modes of the coupled system. The validity of the developed theoretical method is verified by comparing the results with those obtained from the finite element analysis. Furthermore, the effects of submergence depth, radial distance between shell and container, and circumferential wavenumbers on the natural frequencies and modes of the coupled system are investigated.     

Free vibration analysis of a hanged clamped-free cylindrical shell partially submerged in fluid: The effect of external wall,internal shaft,and flat bottom

The free flexural vibration of a hanged clamped-free cylindrical shell with various boundary conditions partially submerged in a fluid is investigated. Specifically, the effects of the boundary conditions such as the existence of the external wall, internal shaft, and bottom on the natural vibration characteristics of the partially submerged cylindrical shell are investigated both theoretically and experimentally. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion. The theoretical predictions were in good agreement with the experimental results validating the theoretical approach developed in this study. The effects of the external wall, internal shaft, and bottom on the natural vibration characteristics can be neglected when its boundaries are not very close to the shell structure.     

Scattering model of a cylindrical shell with internal axisymmetric frames by using the Circumferential Admittance Approach

A numerical model is proposed for predicting scattering pressure by a fluid-loaded cylindrical shell stiffened by axisymmetric internal frames and impacted by an acoustic plane wave. The proposed developments are based on the Circumferential Admittance Approach (CAA) which allows us assembling a numerical model of the fluid loaded shell with finite element models of the internal frames. The scattering pressure model deduced with the CAA can then take into account: (a) internal frames having a cross section with a complex geometry and thickness variations (like T-shaped stiffeners, bulkheads, and hemispherical end caps); (b) variations of frame spacings; and (c) frame-shell coupling in the three translational directions and tangential rotation. Comparison with the numerical and experimental results of the literature for a periodic stiffened shell shows that the scattering from Bragg, Bloch–Floquet, and Helical waves is correctly predicted. The effects on the backscattering pressure of axial and tangential coupling forces are highlighted. Finally, an example of a non-periodically stiffened shell is presented to highlight the versatility of the approach proposed.     

双层周期加肋有限长圆柱壳声散射精细特征研究

研究了双层周期性加肋有限长圆柱壳在水中的声散射特性. 壳体振动用薄壳理论的Donnell 方程描述,环肋振动用相互独立的薄板纯弯曲振动和平面应力状态下的振动方程描述,忽略弦间流体对环肋轴向力的作用. 数值计算给出远场收发合置情况下的周向目标强度和角度-频率谱图,并据此进行机理分析. 计算结果表明远场散射声场中除壳体弹性贡献外,弦间流体以及环肋与内外壳的相互作用对散射声场的贡献也是很重要的,并且在角度-频率谱中出现了舷间流体引起的流体附加波以及周期环肋引起的Bragg散射等回波精细特征,其中流体附加波是双层加肋圆柱壳声散射最重要的散射精细特征,是以往单层圆柱壳声散射所不具有的现象. 最后通过实验对理论推导进行了验证,实验与理论基本符合. 关键词： 声散射 圆柱壳 环肋 流体附加波     

FREE VIBRATION OF A PARTIALLY LIQUID-FILLED AND SUBMERGED, HORIZONTAL CYLINDRICAL SHELL

The dynamic characteristics (i.e., natural frequencies and mode shapes) of a partially filled and/or submerged, horizontal cylindrical shell are examined. In this investigation, it is assumed that the fluid is ideal, and fluid forces are associated with inertial effects only: namely, the fluid pressure on the wetted surface of the structure is in phase with the structural acceleration. The in vacuo dynamic characteristics of the cylindrical shell are obtained using standard finite element software. In the “wet” part of the analysis, it is assumed that the shell structure preserves its in vacuo mode shapes when in contact with the contained and/or surrounding fluid and that each mode shape gives rise to a corresponding surface pressure distribution of the shell. The fluid-structure interaction effects are calculated in terms of generalized added masses, using a boundary integral equation method together with the method of images in order to impose an appropriate boundary condition on the free surface. To assess the influence of the contained and/or surrounding fluid on the dynamic behaviour of the shell structure, the wet natural frequencies and associated mode shapes were calculated and compared with available experimental measurements.     

径向声子晶体隔声特性*

该文构造了由两种匀质材料交替分布的径向声子晶体柱壳模型。首先,针对声波在其中的轴对称传播情况进行了理论分析,建立了声波由内向外传播的传递矩阵,进而导出了声压透射系数和隔声量表达式。采用数值分析的方法系统地讨论了径向声子晶体柱壳的隔声特性,并与单一材质柱壳的传播规律进行对比分析,其次,借助有限元仿真分析的手段对数值结果进行了验证。最后,详细分析了内外流体的特性阻抗对径向声子晶体柱壳隔声特性的影响,得到了相应的参数影响规律。研究表明,径向声子晶体柱壳存在声波带隙,导致其在带隙范围内的隔声效果远远优于单材质柱壳,并且该结构的固有特性突破了质量定律的限制;声波带隙内表面局域态现象出现与否由内外声场和结构场共同决定。     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

通过周期环板和附连流体的两同心圆柱壳体间的振动耦合效应

理论研究了两个同心圆柱壳体间通过周期环饭和附连流体的耦合效应。在环板内只有准纵波存在的假定下,给出环板的反作用力的表达式,并建立外壳体的声辐射解析表达式。无限长双层壳体的数值分析结果和舱段模型的实验结果一致。通过数值结果同时分析了声学流体和周期环板的载荷特征,以及它们对外壳体远场声辐射的影响。      

Acoustic scattering characteristics of a thick-walled orthotropic cylindrical shell at oblique incidence

The method of wave function expansion is adopted to study the scattering of a plane harmonic acoustic wave incident at an arbitrary angle upon an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the three-dimensional exact equations of anisotropic elasticity. The solution is used to correlate the perturbation in the material elastic constants of an air-filled and water-submerged aluminium cylindrical shell to the sensitivity of resonances associated with various modes of wave propagation appearing in the backscattered amplitude spectrum (i.e., axially guided, Lamb, Rayleigh and Whispering Gallery waves). The effects of shell wall thickness as well as inner fluid loading on the frequency response of the shell are also examined. A limiting case is considered and good agreement with the solution available in the literature is obtained.     

The input mobility of an infinite circular cylindrical elastic shell filled with fluid

The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness $\text{h}\text{a}\text{= 0·05}$ filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.     

Double-layer structural-acoustic coupling for cylindrical shell by using a combination of WDA and BIE

This work formulates the double-layer structural-acoustic coupling problem for cylindrical shell by using a combination of the wave-number domain approach (WDA) and the boundary integral equation (BIE). Expressions for the spectral radial velocity of the outer surface of a finite fluid-filled/submerged (FFS) cylindrical thin shell are formulated by means of the transfer matrix equation in wave-number domain. It is shown that the spectral variables on the inner surface of the shell are related to those on the outer surface of the shell. The far field sound radiation from this kind of shell is numerically evaluated for various fluid cases. An experimental verification is performed, and a good correlation between the theoretical results and the experimental results shows that the theoretical study work in this paper is correct.     

Dynamic behavior and sound transmission analysis of a fluid-structure coupled system using the direct-BEM/FEM

A direct-BEM/Fem method was proposed to analyze the vibration and acoustic radiation characteristics of a submerged structure. Model parameters of the structure and the fluid-structure interaction due to surrounding water were analyzed by using FEM and direct BEM. Vibration velocity of the outer hull surface and underwater sound pressure were computed through modal superposition technique. The direct-BEM/FEM method was first validated by analyzing a submerged cylindrical shell, then was used to analyze the vibro-acoustic behavior of a submarine stern structure. The results have demonstrated the direct-BEM/FEM method is more effective than FEM in computing the underwater sound radiation of the stern structure.