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.     

Radiation and vibrational properties of submerged stiffened cylindrical shells

The vibratory response of submerged cylindrical shells is investigated. The shell response is presented in terms of the spatial wave-number spectrum of the normal surface displacement. The power output of the vibrating shell into the fluid and the far-field radiation from the shell are presented as a function of the wave number of the exciting force. The effects of structural damping and stiffeners are also studied.     

Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells

Employing Biot's theory of wave propagation in liquid saturated porous media, axially symmetric vibrations of fluid-filled and empty poroelastic circular cylindrical shells of infinite extent are investigated for different wall-thicknesses. Let the poroelastic cylindrical shells are homogeneous and isotropic. The frequency equation of axially symmetric vibrations each for a pervious and an impervious surface is derived. Particular cases when the fluid is absent are considered both for pervious and impervious surfaces. The frequency equation of axially symmetric vibrations propagating in a fluid-filled and an empty poroelastic bore, each for a pervious and an impervious surface is derived as a limiting case when ratio of thickness to inner radius tends to infinity as the outer radius tends to infinity. Cut-off frequencies when the wavenumber is zero are obtained for fluid-filled and empty poroelastic cylindrical shells both for pervious and impervious surfaces. When the wavenumber is zero, the frequency equation of axially symmetric shear vibrations is independent of nature of surface, i.e., pervious or impervious and also it is independent of presence of fluid in the poroelastic cylindrical shell. Non-dimensional phase velocity for propagating modes is computed as a function of ratio of thickness to wavelength in absence of dissipation. These results are presented graphically for two types of poroelastic materials and then discussed. In general, the phase velocity of an empty poroelastic cylindrical shell is higher than that of a fluid-filled poroelastic cylindrical shell.The phase velocity of a fluid-filled bore is higher than that of an empty poroelastic bore. Previous results are shown as a special case of present investigation. Results of purely elastic solid are obtained.     

Acoustic radiation from a shell-encapsulated baffled cylindrical cap

An exact study of radiation of an acoustic field due to radial/axial vibrations of a baffled cylindrical piston, eccentrically positioned within a fluid-filled thin cylindrical elastic shell, into an external fluid medium is presented. This configuration, which is a realistic idealization of a liquid-filled cylindrical acoustic lens with a focal point inside the lens when used as a sound projector, is of practical importance with a multitude of possible applications in underwater acoustics and ocean engineering. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for cylindrical wave functions to develop a closed-form solution in the form of an infinite series. Numerical results reveal the key effects of excitation frequency, cap angle, radiator position (eccentricity), dynamics of the elastic shell, and cap surface velocity distribution on sound radiation.     

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 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.     

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.     

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.     

Liquid flows and vibration characteristics of straight-tube cylindrical shells

The influence of a moving fluid confined by a solid circular cylindrical shell on the propagation of acoustic waves generated by sources located on the circular cylindrical shell is examined. An expression for the acoustic pressure in a moving fluid is derived including azimuthal asymmetry effects in the general case, where the fluid velocity points along the cylindrical shell axis and can be written as an infinite power series expansion in the radial co-ordinate. Secondly, continuity of pressure and normal velocity at the liquid-shell interface is imposed to (a) derive a set of coupled differential equations governing the possible vibrational modes of the shell and (b) determine dispersion relations, i.e., mode propagation constants β as a function of frequency as well as changes in β values accomodated by flow. In the remaining part of the paper, phase speed changes with flow and transit-time differentials of circular cylindrical shell vibrations are discussed with special emphasis to flow measurement properties.     

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.     

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.     

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shell's natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency.The vibrational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.     

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。     

Modeling of offshore pile driving noise using a semi-analytical variational formulation

Underwater noise radiated from offshore pile driving got much attention in recent years due to its threat to the marine environment. This study develops a three-dimensional semi-analytical method, in which the pile is modeled as an elastic thin cylindrical shell, to predict vibration and underwater acoustic radiation caused by hammer impact. The cylindrical shell, subject to the Reissner–Naghdi’s thin shell theory, is decomposed uniformly into shell segments whose motion is governed by a variational equation. The sound pressures in both exterior and interior fluid fields are expanded as analytical functions in frequency domain. The soil is modeled as uncoupled springs and dashpots distributed in three directions. The sound propagation characteristics are investigated based on the dispersion curves. The case study of a model subject to a non-axisymmetric force demonstrates that the radiated sound pressure has dependence on circumferential angle. The case study including an anvil shows that the presence of the anvil tends to lower the frequencies and the amplitudes of the peaks of sound pressure spectrum. A comparison to the measured data shows that the model is capable of predicting the pile driving noise quantitatively. This mechanical model can be used to predict underwater noise of piling and explore potential noise reduction measures to protect marine animals.     

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping(i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

Sound transmission through layered cylindrical shells with applied damping treatment

Sound transmission through closed circular cylindrical shells with unconstrained damping treatment and sandwich shells with constrained damping treatment is considered in an acoustoelastic formulation in which the full interaction between the structural vibration and the internal cavity pressure field are taken into account. Only the axisymmetric modes of vibration of the shell are considered in an initial formulation. The structural response and the sound transmission characteristics for an external random pressure field are computed through an efficient matrix inversion procedure. Results indicate insensitivity of noise reduction and structural response to variations in core parameters of the sandwich shell. The sandwich shell has better noise transmission characteristics in the higher frequency ranges as compared to an equivalent layered shell with unconstrained damping treatment.     

弯管对末端带弹性障板充液管路辐射声能量的影响

基于声固耦合有限元方法建立了末端带弹性障板的充液管路数值模型,重点分析了不同激励下弯管对管口辐射声能量的影响.结果表明:弯管引入的高阶周向模式耦合使结构振动和流体声传播都发生明显改变,以致系统辐射声能量及主要能量贡献源也发生转移,并随激励方式和频率而不同.对本文管路模型,平面波激励下弯管系统在低频的结构辐射声能量明显增...     

On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.     

A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach

Large-amplitude (geometrically non-linear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh's dissipation function. Four different non-linear thin shell theories, namely Donnell's, Sanders-Koiter, Flügge-Lur’e-Byrne and Novozhilov's theories, which neglect rotary inertia and shear deformation, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four non-linear shell theories are also compared to results obtained by using the Donnell's non-linear shallow-shell equation of motion. A validation of calculations by comparison with experimental results is also performed. Both empty and fluid-filled shells are investigated by using a potential fluid model. The effects of radial pressure and axial load are also studied. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized co-ordinates, associated with natural modes of simply supported shells, are used. The non-linear equations of motion are studied by using a code based on an arclength continuation method allowing bifurcation analysis.