Sound radiation from fluid loaded orthogonally stiffened plates

The radiation of sound from infinite fluid loaded plates is examined when the plates are reinforced with two sets of orthogonal line stiffeners. The stiffeners are assumed to be equally spaced and exert only forces on the plate. The response to a convected harmonic pressure is found by using Fourier transforms and is given in terms of the harmonic amplitudes of the stiffener forces. These forces satisfy an infinite set of simultaneous equations to which a numerical solution must be found. An expression for the response to a general excitation is derived and from this the acoustic pressure in the far field is determined with particular reference to point force excitation.     

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.     

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.     

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.     

Calculation of bulkhead vibrations in a supported shell simulating a plane fuselage

Noise from external sources penetrates a plane cabin through the board construction in several ways. They include direct penetration through loose-fiber layers and indirect penetration through the attachment points of interior panels to transverse ribs (bulkheads). The analytical method of calculating vibrations of an orthogonally supported shell (developed by us earlier) makes it possible to correctly calculate bulkhead vibrations. As a result, noise penetration into the cabin through the attachment points of interior panels can be determined analytically. The first part of the solution to this problem is presented (i.e., the relations and examples of calculating bulkhead vibrations upon point excitation of the shell and excitation by pressure fluctuations of the turbulent boundary layer are given).     

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.     

Input power flow in a submerged infinite cylindrical shell with doubly periodic supports

A submerged cylindrical shell reinforced by supports of rings and bulkheads is the primary structure of submarine, torpedo and all kinds of submerged aircrafts, so it is significant to study its characteristics of structure-borne sound. By means of periodic structure theory, the input power flow from a cosine harmonic line force into a submerged infinite cylindrical shell, reinforced by doubly periodic supports of rings and bulkheads, is studied analytically. The harmonic motion of the shell and the sound pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively. Since the fluid radical velocity and the shell radical velocity must be equal at the interface of the outer shell wall and the fluid, the motion equations of this coupled system are obtained. Both four kinds of forces (moments) between rings and shell and four kinds of forces (moments) between bulkheads and shell are considered. The solution is obtained in series form by expanding the system responses in terms of the space harmonics of the spacings of both stiffeners and bulkheads. The input vibrational power flow into the structure is obtained and the influences of different structural parameters on the results are analyzed. The analytic model is close to engineering practice, and it will give some guidelines for noise reduction of this kind of shell.     

Sound pressure in cylindrical shells with regular orthogonal system of stiffeners excited by a random fields of forces

To identify deterministic and random vibrations of a closed cylindrical shell with a regular orthogonal system of stiffeners (stringers and frames) the effective prediction method was worked out. This method is a generalization of the known method of space-harmonic expansion based on the theorem of Bloch-Floquet for a two-dimensional case. The method permits considering correctly the stiffener discreteness and their interaction with the shell through all the components of displacement. On the basis of the method worked out the task of determining the sound field inside the cylindrical volume bounded by the shell excited by the deterministic and random fields of external forces is solved. The high efficiency of the method permits making the prediction of the shell vibrations and of the sound pressure levels inside the volume with account for sound-insulating layers over a wide frequency range. Examples of predicting the strengthened shell vibrations at large aircraft fuselage parameters are given as well as the sound pressure levels inside it under the point force excitation and under excitation by the random field of wall pressure fluctuations of the turbulent boundary layer (within the limits of one of the representation of the space correlation spectrum).     

Elastic response of an orthogonally reinforced plate

This paper develops a three-dimensional fully elastic analytical model of a solid plate that has two sets of embedded, equally spaced stiffeners that are orthogonal to each other. The dynamics of the solid plate are based on the Navier–Cauchy equations of motion of an elastic body. This equation is solved with unknown wave propagation coefficients at two locations, one solution for the volume above the stiffeners and the second solution for the volume below the stiffeners. The forces that the stiffeners exert on the solid body are derived using beam and bar equations of motion. Stress and continuity equations are then written at the boundaries and these include the stiffener forces acting on the solid. A two-dimensional orthognalization procedure is developed and this produces an infinite number of double indexed algebraic equations. These are all written together as a global system matrix. This matrix can be truncated and solved resulting in a solution to the wave propagation coefficients which allows the systems displacements to be determined. The model is verified by comparison to thin plate theory and finite element analysis. An example problem is formulated. Convergence of the series solution is discussed. The frequency limitations of the model are examined.     

环筋对水下平底圆柱壳的声振特性影响

本文建立了计算两端带平底板的有限长圆柱壳水中声辐射的FEM／BEM三维模型，探索了加筋的高度、宽度、数目对平底圆柱壳的辐射功率、辐射效率、法向声强、声场指向性的影响规律。计算方法是在有限元软件ANSYS中做加筋平底圆柱壳建模、模态分析基础上，将有关数据（网格、模态）导入边界元软件SYSNOISE中计算流体结构耦合状态下的辐射声场特性。结果表明：（1）随着环筋高度、宽度增大，激励点声压峰和法向声强峰在0-400Hz频率范围内数目减少且峰向高频方向移动，同时辐射声功率在减小（除个别模态峰值外），而辐射效率随筋高增大而增大。（2）环筋数目的增加使激励点辐射声压和法向声强峰数目明显减少，使辐射声功率明显低于无筋圆柱壳的辐射声功率，辐射效率随环筋数目增大而增大。（3）环筋宽度变化对声场指向性影响不大；圆柱壳声场指向性随环筋高度和数目增加出现较大变化，尤其是在研究的频段内的f=51Hz和f=301Hz上。这对于水下结构辐射噪声预报以及噪声抑制具有重要意义。     

一种分析周期加筋板声辐射的高效方法

为了研究周期加筋板的声辐射特性,建立了一种计算水中周期加筋板在简谐点力作用下的远场辐射声压的高效方法。该方法借助于傅里叶变换法只要先将耦合系统的声振方程,加强筋的弯曲和扭转运动方程,声学波动方程和耦合边界条件转换到波数域中,联合求解得到一组关于平板横向位移的无限大耦合代数方程组,再将该方程组截断成有限大小由数值方法求出波数域中的位移响应,便可结合稳相法得到远场辐射声压。与现有方法给出的结果对比发现二者完全吻合,验证了本文方法的有效性;通过数值方法研究了激励力位置、板厚,加强筋间距和宽度对周期加筋板声辐射特性的影响,得到了具有实际意义的结论。      

Sound radiation from shear deformable stiffened laminated plates

Sound radiation from shear deformable stiffened laminated plates is studied theoretically. The equations of motion for the composite laminated plate are derived on the basis of the first-order shear deformation plate theory. Two sets of parallel stiffeners interact with the laminated plate only through the normal line forces. By using the Fourier wavenumber transform and the stationary phase method, the far-field sound pressure is described analytically. Sound pressure given by the first-order shear deformation plate theory and the classical thin plate theory is compared, and the differences of sound pressure are shown in the high frequency range for an isotropic plate. Sound pressure and the transverse displacement spectra are 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 also investigated.     

Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations

An analytical method based on the modal expansion technique was developed to predict the vibro-acoustic response of both unidirectionally and bidirectionally stiffened flat panel. This paper presents the response to diffuse acoustic field (DAF) and turbulent boundary layer (TBL) excitations in terms of their joint acceptance. Numerical results for the dynamic and acoustic responses are compared with finite element method (FEM) and boundary element (BEM) results for stiffened panel with complex and eccentrically shaped stiffeners subject to point force excitation. A theoretical prediction of the transmission loss (TL) is also compared with laboratory measurements conducted on flat panels representing aircraft models as well as with hybrid statistical energy analysis (SEA)-FEM periodic model. The results confirm that the stiffened panel has the same acoustic response as the skin without stiffeners at frequencies where the structural wavelengths are equal to the spacing between the stiffeners. In addition, the transmission loss is lowered by the presence of the stiffeners at some particular region of frequencies below the critical frequency with respect to the unstiffened panel.     

Coupled flexural-longitudinal wave motion in a periodic beam

Periodic structure theory is used to study the interactions between flexural and longitudinal wave motion in a beam (representing a plate) to which offset spring-mounted masses (representing stiffeners) are attached at regular intervals. An equation for the propagation constants of the coupled waves is derived. The response of a semi-infinite periodic beam to a harmonic force or moment at the finite end is analyzed in terms of the characteristic free waves corresponding to these propagation constants. Computer results are presented which show how the propagation constants are affected by the coupling, and how the forced response varies with distance from the excitation point. The spring-mounted masses can provide very high attenuation of both longitudinal and flexural waves when no coupling is present, but when coupling is introduced the two waves combine to give very low (or zero) attenuation of the longitudinal wave. The influence of different damping levels on spatial attenuation is also studied.     

基于波数域直接求解法的正交加筋板声辐射研究

为了研究正交加筋板的声辐射问题,基于波数域直接求解法,建立了研究正交加筋板声辐射特性的理论模型。先利用傅里叶变换法求解周期结构的声振理论模型,得到波数域中关于结构响应的无限大耦合代数方程组,采用数值方法将其截断成有限项求解,结合稳相法便可快速获得远场辐射声压。该方法对单向和正交加筋板的预测结果与现有文献中的理论结果取得了良好的吻合,验证了理论模型的准确性和可靠性;并进一步通过数值算例研究了作用点位置,加强筋间距及平板厚度对结构声辐射特性的影响。      

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.     

Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm

In this paper, the genetic algorithm (GA) method is used for the multi-objective optimization of ring stiffened cylindrical shells. The objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. The optimization process contains six design variables including the shell thickness, the number of stiffeners, the width and height of stiffeners, the stiffeners eccentricity distribution order, and the stiffeners spacing distribution order. The real coding scheme is used for representing the solution string, while the generation number-based adaptive penalty function is applied for penalizing infeasible solutions. In analytical solution, the Ritz method is applied and the stiffeners are treated as discrete elements. Some examples of simply supported cylindrical shells with nonuniform eccentricity distribution and nonuniform rings spacing distribution are provided to demonstrate the optimality of the solution obtained by the GA technique. The effects of objective weighting coefficients and bounding values of the design variables on the optimum solution are studied for various cases. The results show that the optimal solution can vary with the weighting coefficients significantly. It is also found that extreme reduction and augmentation in turn in the structural weight and fundamental frequency can be simultaneously achieved by selecting suitable stiffeners’ geometrical parameters and distributions. Furthermore, the bounding values of the design variables have great effects on the optimum results.     

Wavenumber space and physical space responses of a periodically ribbed plate to a point drive: A discrete approach

An efficient technique to estimate the vibration of and sound radiation from a stiffened fluid-loaded plate excited by a mechanical point force is presented. The process is based on the formulation in the wavenumber domain of the transversal displacement of the plate and of the acoustic pressure in the fluid domain. Analytical expressions can be easily obtained for these fields in the case of an infinite plate with stiffeners uniformly spaced. The approach consists then on using the discrete Fourier Transform to deduce the associated fields in the physical space. This transform necessitates truncation of the wavenumber domain and sampling of these wavenumber fields with adequate criterions to avoid loss of information and aliasing. These criterions are discussed in this paper concerning displacement point results on the plate and pressure point results in a part of the fluid domain “close to” the plate. This technique requires relatively small computing time and provides an efficient tool to analyse the vibro-acoustic behaviour of the stiffened plate, both, in the physical and the wavenumber spaces. A comparison between a case discussed in the literature and some examples are presented to illustrate the validity and interests of this approach.     

Transmission loss prediction of reactive silencers using 3-D time-domain CFD approach and plane wave decomposition technique

A predictive method is proposed to determine the transmission loss of reactive silencers using the three-dimensional (3-D) time-domain computational fluid dynamics (CFD) approach and the plane wave decomposition technique. Firstly, a steady flow computation is performed with a mass-flow-inlet boundary condition, which provides an initial condition for the following two unsteady flow computations. The first unsteady flow computation is conducted by imposing an impulse (acoustic excitation) superimposed on the constant mass flow at the inlet of the model and then adding the non-reflecting boundary condition (NRBC) when the impulse completely propagates into the silencer. The second unsteady flow computation is conducted for the case without acoustic excitation at the inlet. The time histories of pressure and velocity at the upstream monitoring point as well as history of pressure at the downstream monitoring point are recorded during the two transient computations. The differences between the two unsteady flow computational results are the corresponding acoustic quantities. Therefore, the incident sound pressure signal is obtained by using plane wave decomposition at upstream, while the transmitted sound pressure signal is just the sound pressure at downstream. Finally, those two sound pressure signals in the time-domain are transformed into the frequency-domain by Fast Fourier Transform (FFT) and then the transmission loss (TL) of silencer is determined. For the straight-through perforated tube silencers with and without flow, the numerical results agree well with the published measurements.     

Multiple support excitations of open-plane frames by a filtered white noise and soil-structure interaction

Seismic structural design is essentially the estimation of structural response to a forced motion, which may be deterministic or stochastic, imposed on the ground. The assumption that the same ground motion acts at every point of the base of the structure (or at every support) is not always justifiable; particularly in case of very large structures when considerable spatial variability in ground motion can exist over significant distances—example long span bridges. This variability is partly due to the delay in arrival of the excitation at different supports (which is called the wave passage effect) and due to heterogeneity in the ground medium which results in incoherency and local effects. The current study examines the influence of the wave passage effect (in terms of delay in arrival of horizontal ground excitation at different supports and neglecting transmission through the structure) on the response of a few open-plane frame building structures with soil-structure interaction. The ground acceleration has been modeled by a suitably filtered white noise. As a special case, the ground excitation at different supports has also been treated as statistically independent to model the extreme case of incoherence due to local effects and due to modifications to the ground motion resulting from wave reflections and refractions in heterogeneous soil media. The results indicate that, even for relatively short spanned building frames, wave passage effect can be significant. In the absence of soil-structure interaction, it can significantly increase the root mean square (rms) value of the shear in extreme end columns for the stiffer frames but has negligible effect on the flexible frames when total displacements are considered. It is seen that pseudo-static displacements increasingly contribute to the rms value of column shear as the time delay increases both for the stiffer and for the more flexible frames. When soil-structure interaction is considered, wave passage effect (in terms of total displacements) is significant only for low soil shear modulus, G_s, values (where soil-structure interaction significantly lowers the fundamental frequency) and for stiff frames. The contribution of pseudo-static displacement to these rms values is found to decrease with increase in G_s. In general, wave passage effect for most interactive frames is insignificant compared to the attenuating effect a decrease in G_s has on the response of the interactive structure to uniform support excitation. When the excitations at different supports are statistically independent, it is seen that for both the stiff and flexible frames, the rms value of the column shear in extreme end columns is several times larger (more for the stiffer frames) than the value corresponding to uniform base excitation with the pseudo-static displacements contributing over 99% of the rms value of column shear. Soil-structure interaction has an attenuating effect on the rms value of the column shear, the effect decreasing with increase in G_s. Here too, the pseudo-static displacements contribute very largely to the column shear. The influence of the wave passage effect on the response of three 2-bay frames with and without soil-structure interaction to a recorded horizontal accelerogram is also examined.