Sound scattering from underwater elastic spherical shell covered with multilayered medium approximated acoustic cloak

The anechoic performance and mechanism of underwater elastic spherical shell covered with coating are studied at low frequencies.The acoustic cloak is anisotropic material,which can be designed with homogeneous isotropic materials on the basis of effective medium approximation theory.The analytic expression of scattering acoustic field from the shell covered with multilayered medium is formulated and the scattering form function,resonance mode,acoustic field distribution are computed,the scattering characteristics and mechanism of transmission are analyzed.The results show that the direction of sound transmission inside the multilayered medium is changed,the acoustic field is deflected gradually,and the acoustic energy flux is guided around the target,which reduces the scattering intensity at low frequencies,the acoustic intensity of target＇s surface is very weak.Excepting the first resonance peak in spectrum produced by the zero order partial wave,the other resonance modes of elastic spherical shell are not excitated and the multilayered medium can suppress the resonance of the spherical shell effectively.     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.     

充水圆柱壳声散射的环绕波分析

研究了内部充水圆柱壳散射声场的构成。采用弹性薄壳理论和Sommerfeld-Watson变换(SWT)方法导出散射声场的解析解。数值搜索环绕波的复波数极点,比较圆柱壳体内部真空和内部充水两种情况下表面环绕波的相速度、衰减等性质。用镜反射波和环绕波的叠加合成反向散射形态函数,与简正级数解符合良好。计算流体附加环绕波的回波时序并与实验数据对照。结果表明,流体附加环绕波的再辐射是内部充水圆柱壳的形态函数出现更加丰富的共振峰和回波结构形成的重要原因。      

Analysis of circumferential waves on a water-filled cylindrical shell

The formation of scattering field from a water-filled cylindrical shell was studied. The analytic solutions of scattering field are derived using elastic thin shell theory and Sommerfeld-Watson Transformation(SWT) method.Complex wave-number poles of circumferential waves are found numerically,the phase speed and attenuation of circumferential waves between the situation of a hollow cylindrical shell and a water-filled cylindrical shell are compared. The synthesis of backscattering form functions which are sum of specular reflection component and circumferential waves is consistent with normal mode result.The calculated echo sequences of additional fluid circumferential waves are compared with experimental results. The results show that richer resonance peaks appeared in the backscattering form functions of a water-filled cylindrical shell and the formation of echo’s structure are due to re-radiation effects of additional fluid circumferential waves.     

近似声斗篷的多层介质覆盖水中弹性球壳的声散射

对水中弹性球壳的低频覆盖层消声效果和消声机理进行研究。声斗篷(Acoustic cloak)是各向异性的超常材料,根据有效介质近似理论(Effective MediumApproximationTheory),采用各向同性多层介质近似各向异性材料的声斗篷,推导出覆盖多层介质水中弹性球壳散射声场的解析表达式,计算了弹性球壳覆盖多层介质前后的散射形态函数、谐振模态以及声场分布,分析了覆盖前后球壳的声散射特性和声传播机理。研究表明,覆盖层内的声波在多层介质之间的声传播方向发生改变,声场形成弯曲变形,声能流绕过目标,这不仅极大的降低了低频散射强度,而且使到达弹性体表面的声场强度非常小,散射频响中除了0阶子波产生的第一个谐振峰外,无法激发弹性球壳的其它谐振模态,有效的抑制弹性球壳的谐振散射。      

Acoustic scattering from a fluid-filled finite cylindrical shell in water:Ⅰ.Theory

Acoustic scattering from a submerged fluid-filled finite cylindrical shell insonified by an incident plane wave was studied.The analytic solutions of the scattering field are derived using the elastic thin shell theory with the boundary conditions.The fluid-filled impedance,due to the effect of internal fluid,must add to the impedance of the system.The results show that in the backscattering field,rigid scattering has a large contribution only on the broadside and elastic scattering play a major role when oblique incidence.The dispersion curves of the phase velocity show that comparing with the internal vacuum condition,except the contribution by longitudinal wave and shear wave near the broadside a series of the additional waves caused by the internal fluid is added which have great contribution to the scattering field.Bowl-shape resonance curves are presented in the frequency-angle spectrum as the contribution of the internal fluid waves.     

Apparent optical properties of spherical particles in absorbing medium

An apparent absorption efficiency for spherical particles in absorbing medium is introduced to take into account the non-exponential absorption of the near-field scattered radiation in the absorbing medium. The apparent extinction, which is the summation of the apparent scattering efficiency following previous studies and the apparent absorption efficiency, is the same as the actual extinction. These apparent optical properties are suited to radiative transfer equations.     

充水有限长圆柱薄壳声散射:Ⅰ.理论

研究水中充水有限长圆柱薄壳的声散射。采用弹性薄壳理论结合边界条件导出了有限长圆柱薄壳倾斜入射时散射声场的解析解,内部充水的作用反映在系统总阻抗中增加了内部流体阻抗。数值计算表明,在反向散射声场中,刚性散射部分仅在正横附近有比较大的贡献,而斜入射时起主要作用的是弹性散射部分。散射波相速度频散曲线的计算表明,与内部真空的情况相比内部充水后除正横附近的纵波和剪切波以外,增加了一组内部流体引起的附加波,其对散射声场贡献非常重要。在计算的频率-角度谱图中,内部流体附加波呈现"碗"形共振曲线。      

Hidden black: coherent enhancement of absorption in strongly scattering media

We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results from random matrix theory imply that the reflectivity of the medium can be suppressed by a factor ～(?(a)/?)N(-2), where N is the number of incident channels and ?, ?(a) are the elastic and absorption mean free paths, respectively. It is thus possible to increase absorption from a few percent to >99%. For a localized weak absorber buried in a nonabsorbing scattering medium, we find a large but bounded enhancement.     

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.     

球形粒子在Bessel波束照射下的轴向辐射力计算和分析

通过声散射理论,将水中粒子的Bessel波束声散射场的分波序列(PWS)表达公式加以推广,进而推导出声辐射力的表达公式,获得了液体球及弹性球在Bessel波束下声辐射力的变化规律。通过观察不同散射角形态函数,可发现声辐射力的产生与粒子背向散射抑制程度有关。对于液体球粒子,球壳厚度及材料介质对粒子声辐射力有着重要的影响,同时Bessel波束波锥角越大,产生负声辐射力的可能性越大。对于弹性球和弹性单层壳粒子,声辐射力的产生与其本身的共振特征存在很大的关系。同时,通过改变球壳内介质及壳层厚度的方法,可增加产生的负声辐射力的频率范围及幅值强度.      

INTERACTION OF A SPHERICAL SHOCK WAVE AND A SUBMERGED FLUID-FILLED CIRCULAR CYLINDRICAL SHELL

The complete three-dimensional interaction between a spherical shock wave and a submerged fluid-filled elastic circular cylindrical shell is considered. A hybrid analytical-numerical solving procedure is established. An exact analytical solution in the form of double Fourier series with time-depending coefficients is obtained for the hydrodynamic pressure. Displacements of a shell are approached analytically to reduce the problem to a set of systems of ordinary differential equations, which are treated numerically. Detailed analysis of the interaction is performed with emphasis given to the stress-strain state. A few important features of the interaction process have been found. In particular, it has been shown that the interior fluid not only substantially affects the magnitude of displacements and stresses, but also dramatically changes the nature of the interaction. It has been found that the absolute maximum of stresses can neither be caused by a direct action of a shock wave nor by a constructive superpose of elastic waves in the shell, but by the pressure wave propagating in the interior fluid. This fact seems to be of essential importance for engineering applications, especially when safety is a primary design concern. Another important result is that the maximum stresses are attained at large times, which makes use of early time asymptotics leading to incorrect results. The proposed semi-analytical approach seems to be computationally attractive and suitable for extensive numerical simulations.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

Acoustics of shells

We discuss the physical phenomena that arise in the scattering of acoustic waves from fluid-immersed elastic (metal) shells which may be either evacuated or filled with the same or with a different fluid. The phenomena occurring here include the formation of circumferential (peripheral, or “surface”) waves that circumnavigate the shells, propagating either as elastic waves in the shell material or as fluid-borne waves of the Scholte-Stoneley type in the external or the internal fluid. By phase matching along a closed circuit, these waves may lead to prominent resonances in the acoustic scattering amplitude, and we demonstrate how the set of observed resonance frequencies is related to the dispersive phase velocities of the surface waves, so that one can be determined from the other. In addition, we discuss how the dispersion curves (phase velocity plotted vs. frequency) of the various types of surface waves show repulsion phenomena due to their coupling through the boundary conditions. The cases of spherical and cylindrical shells are investigated here as typical examples, and as an introductory topic we additionally mention surface waves on plates where related phenomena also occur. Both the theoretical and the experimental aspects of the present subject will be considered, including the experimental visualization of the surface waves.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

Acoustical scattering by multilayer spherical elastic scatterer containing electrorheological layer

A computational procedure for analyzing acoustical scattering by multilayer concentric spherical scatterers having an arbitrary mixture of acoustic and elastic materials is proposed. The procedure is then used to analyze the scattering by a spherical scatterer consisting of a solid shell and a solid core encasing an electrorheological (ER) fluid layer, and the tunability in the scattering characteristics afforded by the ER layer is explored numerically. Tunable scatterers with two different ER fluids are analyzed. One, corn starch in peanut oil, shows that a significant increase in scattering cross-section is possible in moderate frequencies. Another, fine poly-methyl methacrylate (PMMA) beads in dodecane, shows only slight change in scattering cross-sections overall. But, when the shell is thin, a noticeable local resonance peak can appear near ka=1, and this resonance can be turned on or off by the external electric field.     

Diffraction of sound pulses on an elastic spherical shell submerged in an oceanic waveguide

The paper is devoted to simulating an acoustic field scattered by an elastic spherical shell placed in a waveguide with a fluid attenuating bottom. The emitted signal is a wideband pulse with a Gaussian envelope. The normal wave method is used in the frequency domain for calculating the field of a point source in a free waveguide and the shell scattering coefficients. Movement of the receiver along a vertical straight line located behind the shell makes it possible to obtain a “three-dimensional” image of the field scattered by the shell. In this representation, the horizontal axis is time; the vertical axis is the submersion depth of the receiver; the intensity shows the amplitude of the received signal. Such three-dimensional structures make it possible to analyze the dependence of the complex diffraction structure of the acoustic field on receiver depth. In the considered numerical example, a thin, elastic, spherical shell is located near the attenuating fluid bottom.     

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.     

Acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials

Using the multilayered cylinder model, we study acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials, which exhibit locally negative effective mass densities. A spring model is introduced to replace the traditional transfer matrix, which may be singular in the negative mass region. The backscattering form function and the scattering cross section are calculated to discuss the acoustic properties of the coated submerged cylindrical shell.     

Helmholtz水声换能器弹性壁液腔谐振频率研究

针对传统Helmholtz水声换能器设计中刚性壁假设的局限性,将Helmholtz腔体的弹性计入到液腔谐振频率计算中,实现低频弹性Helmholtz水声换能器液腔谐振频率精确设计.基于细长圆柱壳腔体的低频集中参数模型,导出了腔体弹性引入的附加声阻抗表达式,得到了弹性壁条件下Helmholtz水声换能器等效电路图,给出了考虑了末端修正的弹性壁Helmholtz共振腔液腔谐振频率计算公式.利用ANSYS软件建立了算例模型,仿真分析了不同材质、半径、长度时的Helmholtz共振腔液腔谐振频率.结果对比表明弹性理论值与仿真值符合得很好,相比起传统的刚性壁理论计算结果,本文的弹性壁理论得出的液腔谐振频率值有所降低,与真实情况更加接近.本文的结论可以为精确设计低频弹性Helmholtz水声换能器提供理论支持.