The modeling of the radiation and response green's function of a fluid-loaded cylindrical shell with an external compliant layer

Scattering and radiation of acoustic waves from a fluid-loaded cylindrical shell with an external compliant layer are of interest. The compliant layer can be modeled by a normally reacting impedance layer, which has the advantage that complex compliant layer geometries, such as partial compliant layers, can be considered. A question may, however, arise as to the accuracy of this approach. A more rigorous approach is to model the elastic shell and compliant layer using a multilayer shell theory, which has the disadvantage that it cannot be extended to consider partial layers. In this paper scattering results from the normally reacting compliant layer model are compared to those from the multilayer shell model to show that the two approaches produce similar results, except for thickness resonances of the compliant layer. Having established the consistency between the two approaches, results for the far-field acoustic radiation as a function of frequency and radiation angle for a fluid-loaded shell with an external compliant layer excited by an internal ring force are obtained using the normally reacting impedance layer model. These results clearly show the reduction in the far field radiation due to the presence of the compliant layer.     

Interaction of a spherical acoustic wave with an elastic spherical shell

The interaction of a spherical acoustic wave with an elastic spherical shell is treated analytically. The solution includes the coupling between the acoustic sound field and vibration of the shell with any degree of fluid loading. The formulation for the far-field acoustic pressure is derived in terms of natural spherical wave functions, the properties of the acoustic medium, and the material constants of the shell. The far acoustic field is computed for a thin aluminum shell and several sound source locations over a large range of ka, where k is the wavenumber, and a is the shell radius. It is shown that the acoustic pressure depends significantly on whether the shell is in air or is submerged in water, particularly when the sound source is very near the surface. In air, the sound field of the shell is nearly identical to that of a rigid sphere but, in water, the shell is more compliant, which results in a damped radiation field that is characterized by vibrational resonances throughout the range of frequencies considered. As the sound sources is moved further away from the surface, however, this resonance response decreases very rapidly, and the sound field corresponds more closely to that of the shell in air.     

Influence of circumferential partial coating on the acoustic radiation from a fluid-loaded shell

Acoustic compliant coatings are a common approach to mitigate the radiation and scattering of sound from fluid-loaded submerged structures. An acoustic compliant coating is a coating that decouples an acoustic source from the surrounding acoustic medium; that is, it provides an acoustic impedance mismatch (different density and speed of sound product). Such a coating is distinct from an ordinary compliant coating in that it may not be resilient in the sense of low stiffness, but still provides an acoustic impedance mismatch. Ideally, the acoustic coating is applied uniformly over the entire surface of the fluid-loaded structure to minimize the acoustic radiation and scattering. However, in certain instances, because of appendages, it may not be practically possible to completely cover the surface of a fluid-loaded structure to decouple it from the adjacent acoustic medium. Furthermore, there may be some inherent advantages to optimizing the distribution of the coating around areas from which the acoustic radiation appears to be dominant. This would be analogous to the application of damping treatment to a vibrating structure in areas where the vibration levels are highest. In the case of the acoustic radiation the problem is more complex because of the coupling between the acoustic fluid and the structure. In this paper, the influence of a partial coating on the acoustic radiation from a fluid-loaded, cylindrical shell of infinite extent and excited by either a line force or an incident plane acoustic wave is examined. The solution to the response and scattered pressure is developed following the procedure used by the authors in previous work on the scattering from fluid-loaded plates and shells. The coating is assumed to be normally reacting providing a decoupling layer between the acoustic medium and the structure; that is, it does not add mass or stiffness to the base structure. The influence of added mass or stiffness of the coating can be included as an added inhomogeneity and treated separately in the solution.     

Acoustic radiation force on a multilayered sphere in a Gaussian standing field

We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach. An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid. The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed, with particular emphasis on the shell thickness of every layer, and the width of the Gaussian beam. The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka, as well as the shell thickness of each layer. This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave, which may benefit the improvement and development of acoustic control technology, such as trapping, sorting, and assembling a cell, and drug delivery applications.     

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.     

含玻璃微球的黏弹性复合材料覆盖层的水下吸声性能分析

水下吸声覆盖层对潜艇的隐身具有重要的意义, 因此得到了广泛的关注. 本文对含有玻璃微球的黏弹性复合材料覆盖层的水下吸声性能进行了理论分析. 采用等效参数法计算了玻璃微球的体积含量对复合材料的力学和声学性能的影响. 应用声波在多层介质中传播的一维模型, 计算了不同玻璃微球体积含量的单层复合材料覆盖层的吸声性能.结果表明, 增加玻璃微球的体积含量可以提高覆盖层的低频吸声性能, 但是其高频吸声性能降低.采用遗传算法对玻璃微球在覆盖层厚度方向上的体积含量分布进行优化. 优化的多层结构可以在一定的频带内改善覆盖层的表面与水的声阻抗匹配, 在保证覆盖层的高频吸声系数大于某一限值(0.7)的前提下, 提高其低频吸声性能.另外, 多层优化结构覆盖层不含宏观的空腔结构, 不影响覆盖层的耐压性能.其结构简单, 对制备工艺的要求不高.因此, 本文形成的理论方法适用于水下吸声覆盖层的设计. 关键词： 水下吸声 黏弹性复合材料 玻璃微球 遗传算法     

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.     

Radiation from finite cylindrical shell with irregular-shaped acoustic enclosure

In practical situations, large machinery is usually placed in an underwater vessel and changes the acoustic enclosure shape into an irregular one. The existence of machinery causes the difficulties in expressing sound transmission and radiation analytically. In this study, the sound radiation of a cylindrical shell excited by an internal acoustic source is modeled and analyzed. The cylindrical shell contains a machine modeled as a rectangular object, which is attached to a shell with a spring-mass system. The acoustic field of the cavity is computed by the integro-modal approach. The effect of object size on the coupling between acoustic mode and structural mode is investigated. The relationship between object volume and sound radiation is also studied. Numerical results show that the existence of objects inside vessels leads to a more effective coupling between the structure and acoustic enclosure than the existence of no objects in a regular-shaped cavity(i.e. empty vessel).     

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.     

经典局域共振型水声超材料的吸隔声性能研究*

基于水声超材料吸声机理和多层平行介质平面波理论,建立局域共振型水声超材料结构,通过COMSOL进行建模计算,研究该结构的吸声性能机理,此外为了验证钢背衬的隔声性能,在该水声超材料结构基础上添加一层0.005m厚的钢背衬进行仿真对比。研究结果表明,在频段为200Hz-4000Hz时,水声超材料声学性能较好,吸声性能整体较优,且添加钢背衬的水声超材料隔声性能较优,甚至在某频率点达到15dB的隔声差值;此外通过位移场图进一步揭示水声超材料的吸声机理,发现水声超材料结构的位移场和钢背衬都对吸声性能会产生影响,钢背衬通过影响共振吸收来影响吸声性能,而位移场则通过位移幅度大小影响吸声性能。     

Mathematical model for characterizing noise transmission into finite cylindrical structures

This work presents a theoretical study of the sound transmission into a finite cylinder under coupled structural and acoustic vibration. Particular attention of this study is focused on evaluating a dimensionless quantity, "noise reduction," for characterizing noise transmission into a small cylindrical enclosure. An analytical expression of the exterior sound pressure resulting from an oblique plane wave impinging upon the cylindrical shell is first presented, which is approximated from the exterior sound pressure for an infinite cylindrical structure. Next, the analytical solution of the interior sound pressure is computed using modal-interaction theory for the coupled structural acoustic system. These results are then used to derive the analytical formula for the noise reduction. Finally, the model is used to predict and characterize the sound transmission into a ChamberCore cylindrical structure, and the results are compared with experimental data. The effects of incidence angle and internal acoustic damping on the sound transmission into the cylinder are also parametrically studied.     

On the sound field of a shallow spherical shell in an infinite baffle

A method is presented for calculating the far field sound radiation from a shallow spherical shell in an acoustic medium. The shell has a concentrated ring mass boundary condition at its perimeter representing a loudspeaker voice coil and is excited by a concentrated ring force exerted by the end of the voice coil. A Green's function is developed for a shallow spherical shell, which is based upon Reissner's solution to the shell wave equation [Q. Appl. Math. 13, 279-290 (1955)]. The shell is then coupled to the surrounding acoustic medium using an eigenfunction expansion, with unknown coefficients, for its deflection. The resulting surface pressure distribution is solved using the King integral together with the free space Green's function in cylindrical coordinates. In order to eliminate the need for numerical integration, the radiation (coupling) integrals are solved analytically to yield fast converging expansions. Hence, a set of simultaneous equations is obtained which is solved for the coefficients of the eigenfunction expansion. These coefficients are finally used in formulas for the far field sound radiation.     

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.     

The identification of sound generating mechanisms of tyres

Tyre noise is generated by several mechanisms. With a modern tyre, wall vibration, air pumping and air resonant radiation are all considered to be important. But tyre noise generating mechanisms are still not clear due to the complication of tyre vibration behaviour. Vibrations of the tyre shell are the combination of several different wave types which appear at different frequencies. In a low frequency range, where the tyre behaves like an elastically supported beam, the circular ring model is used to analyze the dispersion relations. Above 300 Hz, which is the transition point from one-dimensional to two-dimensional waveguide properties of the passenger car tyre, a cylindrical shell model is used to analyze flexural waves propagation. Two important features on the wave propagation, wave-guide behaviour and the curvature effect of the tyre wall are analyzed. In consideration of noise radiation from tyre waves, most of the tyre waves observed in this study are inefficient sound radiators since their wavenumbers are larger than the acoustic wave number. As a result, It is observed that one of the most important features in sound radiation of a tyre shell is acoustically excited wave motion of the tyre wall.     

Radiation impedance loading of a spherical source in a two-dimensional perfect acoustic waveguide

We employ the classical method of separation of variables in combination with the method of images and the translational addition theorems for spherical wave functions to investigate the acoustic radiation load on a finite-sized spherical source which is submerged at an arbitrary point within a plane-parallel sound channel with absolutely reflecting boundaries. To simulate an idealized situation, it is supposed that the fluid layer is homogeneous and is bounded below by an acoustically hard surface and above by a rigid/compliant boundary. Subsequently, the resistive and the reactive components of the modal acoustic radiation impedance load as a function of source position for a pulsating (n = 0) and an oscillating (n = 1) sphere at selected nondimensional frequencies are calculated and discussed. The presented benchmark solution can lead to a better understanding of the acoustics of waveguide sources (transducers) that are of practical interest in underwater acoustics and ocean engineering. It could eventually be used to validate those found by numerical approximation techniques. The text was submitted by the authors in English.     

高频聚焦超声声场和温度场的仿真研究*

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

柱面波对多层球的轴向声辐射力

在理论和数值上研究柱面波对多层球的声辐射力.基于声波的散射理论,得到声辐射力的解析解,并给出数值仿真.结果表明：在特定的ka和kr₀处,柱面行波的辐射力可以是负值（k是波数,a是多层球的半径,r₀是多层球到声源的距离）.随着kr₀增加到无穷大,仿真结果退化为平面波的情形.对双层球而言,每层的相对厚度影响曲线共振峰的大小和位置,但对三层球而言没有显著影响.当最内层的介质换成空气时,由于声阻抗差异较大,共振峰更加明显.该研究可以为研发新一代单行波声束声学镊子提供理论指导,该技术在生物医学超声和材料科学领域有广泛的应用.     

水下复杂壳体结构在多源激励下的振动及声辐射特性研究

为了综合评估水下复杂壳体结构在多源激励下的振动与声辐射特性,专门设计了一个多舱段复杂壳体模型,分别进行了单台设备激励、多台设备激励的壳体振动与声辐射试验。试验结果表明,多源激励下的结构响应和辐射声场可以近似为单源激励下结构响应和辐射声场的非相干叠加。通过对激励源与结构响应、辐射声场之间传递关系的理论分析,讨论了以单源激励响应非相干叠加合成得到多源激励响应的合理性和误差。研究结果对复杂壳体结构在实际激励下的振动与噪声预报具有重要价值。      

Acoustic radiation force due to incident plane-progressive waves on coated spheres immersed in ideal fluids

In this study, the acoustic radiation force resulting from the interaction of a plane progressive wave with a coated sphere was examined. The linear acoustic scattering problem was obtained first by solving the classical boundary conditions to obtain the required coefficients. The radiation force was then determined by averaging the momentum flux tensor expressed in terms of the total scattering pressure or velocity potential in an ideal fluid. Numerical calculations of the radiation force function Yp , which is the radiation force per unit energy density and unit cross-section, were displayed versus the dimensionless size parameter x=k1 b (k1 is the wave number in the exterior fluid and b the radius of the uncoated sphere) over a large range of frequencies. Particular emphasis has been focused on the coating thickness and the absorption of sound inside the outer covering layer. The fluid-loading effect on the radiation force function curves was also analysed.     

有限振幅声波间的非线性相互作用对声源远场指向性的影响

根据Fenlon理论推导得到了多频声源的辐射声压.基于单频声源谐波指向性的求解方法,得到了二阶近似下的双频声源辐射出的声波相互作用时的远场指向性.分别研究和讨论了在初始辐射声压和频率不同情况下,两列波的相互作用对其中一列波的一阶波和二阶波远场指向性的影响.结果表明,声波间的相互作用对声源远场指向性的影响根据各波之间的相对初始辐射声压和相对频率的不同而有所变化. 关键词： 有限振幅声波 非线性相互作用 远场指向性