Scattering of an Acoustic Field by Refraction–Density Inhomogeneities with a Small Wave Size and Solution of the Problem of Direct Scattering in an Inhomogeneous Medium

The paper considers acoustic wave scattering by inhomogeneities with a small wave size using the Green’s function apparatus, which makes it possible universally to take into account both the refraction and density components of an inhomogeneity. Estimates for the multipole components of a field scattered by a nonresonance inhomogeneity are presented. For an inhomogeneity with small dimensions, it suffices to consider only monopole and dipole scattering. These conclusions are confirmed by an analysis of the field scattered by a circular cylinder with a small wave radius. The results are used to numerically simulate a Lippmann–Schwinger equation. The form of the discretized matrix Green’s function for identical values of the spatial arguments is presented. This makes it possible to take into account multiple scattering processes within a discretization element with a small wave size. Its use automatically fulfills the relations between the phase and amplitude of secondary acoustic field sources.     

The matched asymptotic expansion (MAE) technique applied to acoustic radiation from vibrating surfaces

The MAE technique has been used in the field of fluid mechanics for many years. Only recently this technique has been applied to acoustic problems, where it has been found to be an excellent and powerful tool in analyzing either scattering and diffraction or radiation from moving rigid objects (propellers). The purpose of this paper is to very briefly review the MAE technique as applied to low frequency acoustics in general, and then apply the resulting approach to a series of progressively more difficult problems which are of interest to many underwater acousticians. The analysis is first applied to two problems with single degrees of freedom for structural vibrations: (1) a sphere, both velocity and force driven, and (2) a circular piston in infinite rigid baffle. These are classical problems and the solutions as obtained by the MAE technique are then compared to the exact classical solutions. The MAE solutions are then generalized to a more difficult problem, with two degrees of freedom for the surface vibration, where two concentric pistons in an infinite rigid baffle are vibrating and coupled via the fluid. For each of the problems analyzed, the structural wavelength a is assumed to be small compared to the fluid wavelength (i.e., ka ? 1). The inner region close to the vibrating structure, in which the fluid motion is effectively incompressible in nature, is governed by the Laplace equation while the outer solution is governed by the Helmholtz equation. The inner and outer solutions are obtained independently and are then joined together by the MAE matching procedure. A composite solution is then obtained from a combination of the inner and the outer solutions. Agreements with the exact theory for the radiated pressure, surface resistance and reactance are shown to be excellent.     

A novel unsplit perfectly matched layer for the second-order acoustic wave equation

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach.     

Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct

A methodology is presented which allows to determine the coefficients of transmission and reflection of plane acoustic waves at flow discontinuities in piping systems by combining large eddy simulation (LES) of turbulent compressible flows with system identification. The method works as follows. At first, an LES with external, broadband excitation of acoustic waves is carried out. Time series of acoustic data are extracted from the computed flow field and analyzed with system identification techniques in order to determine the acoustic scattering coefficients for a range of frequencies. The combination of broadband excitation with highly parallelized LES makes the overall approach quite efficient, despite the difficulties associated with simulation of low-Mach number compressible flows. The method is very general, here it is applied to study the scattering behavior of acoustic waves at a sudden change in cross-section in a duct system. The complex aero-acoustic interactions between acoustic waves and free shear layers are captured in detail by high resolution compressible LES, such that the scattering coefficients can be determined accurately from first principles. In order to demonstrate the reliability and accuracy of the method, the results for the scattering behavior and the acoustic impedance are presented and physically interpreted in combination with several analytical models and experimental data.     

The use of an orthogonality relation for reducing the size of finite element models for 3D guided waves scattering problems

The scattering of guided waves by complex shaped defects in three-dimensional (3D) waveguides is considered. For such problems, analytical solutions do not exist, and modal decomposition techniques based on the establishment of the displacement and stress fields in the vicinity of the scatterer are quite heavy and complicated to perform. On the other hand, finite elements (FE)-based methods constitute a powerful way to obtain solutions, but they are known to be very memory consuming. This paper proposes a post-processing technique, based on a 3D orthogonality relation, to decompose a complex acoustic field produced by a scatterer and predicted by a 3D FE model, into plane waves, the amplitudes of which are quantified in the far field. This technique allows important reductions in the size of the FE models to be made. Two applications are presented to demonstrate the potential of this method. The first one concerns the scattering of the S₀ Lamb wave incident on a flat bottom circular hole. In this example, the amplitude of each mode is calculated via the orthogonality relation-based method, and compared to that obtained by simply monitoring the displacements at appropriate through-thickness positions. In the second application, the incident S₀ Lamb mode is converted into five modes scattered by a defect of complex geometry.     

Acoustic radiation force analysis using finite difference time domain method

Acoustic radiation force exerted by standing waves on particles is analyzed using a finite difference time domain Lagrangian method. This method allows the acoustic radiation force to be obtained directly from the solution of nonlinear fluid equations, without any assumptions on size or geometry of the particles, boundary conditions, or acoustic field amplitude. The model converges to analytical results in the limit of small particle radii and low field amplitudes, where assumptions within the analytical models apply. Good agreement with analytical and numerical models based on solutions of linear scattering problems is observed for compressible particles, whereas some disagreement is detected when the compressibility of the particles decreases.     

On the modeling of narrow gaps using the standard boundary element method

Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications.     

Scattering of focused ultrasonic beams by cavities in a solid half-space

The ultrasonic field generated by a point focused acoustic lens placed in a fluid medium adjacent to a solid half-space, containing one or more spherical cavities, is modeled. The semi-analytical distributed point source method (DPSM) is followed for the modeling. This technique properly takes into account the interaction effect between the cavities placed in the focused ultrasonic field, fluid-solid interface and the lens surface. The approximate analytical solution that is available in the literature for the single cavity geometry is very restrictive and cannot handle multiple cavity problems. Finite element solutions for such problems are also prohibitively time consuming at high frequencies. Solution of this problem is necessary to predict when two cavities placed in close proximity inside a solid can be distinguished by an acoustic lens placed outside the solid medium and when such distinction is not possible.     

Fast volumetric integral-equation solver for acoustic wave propagation through inhomogeneous media

Elements are described of a volumetric integral-equation-based algorithm applicable to accurate large-scale simulations of scattering and propagation of sound waves through inhomogeneous media. The considered algorithm makes possible simulations involving realistic geometries characterized by highly subwavelength details, large density contrasts, and described in terms of several million unknowns. The algorithm achieves its competitive performance, characterized by O(N log N) solution complexity and O(N) memory requirements, where N is the number of unknowns, through a fast and nonlossy fast Fourier transform based matrix compression technique, the adaptive integral method, previously developed for solving large-scale electromagnetic problems. Because of its ability of handling large problems with complex geometries, the developed solver may constitute an efficient and high fidelity numerical simulation tool for calculating acoustic field distributions in anatomically realistic models, e.g., in investigating acoustic energy transfer to the inner ear via nonairborne pathways in the human head. Examples of calculations of acoustic field distribution in a human head, which require solving linear systems of equations involving several million unknowns, are presented.     

Reflection of sound at area expansions in a flow duct

An analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented. The application we have in mind is large industrial duct systems, where sound attenuation by reactive and absorptive baffle silencers is of great importance. Such devices commonly have a rectangular cross-section, so the model is chosen as two-dimensional. Earlier solutions to this problem are reviewed in the paper. The modelling of the flow conditions downstream of the area expansion, with and without extended edges, and its implications for the resulting acoustic modes are discussed. Here, the scattering problem is solved with the Wiener-Hopf technique, and a Kutta condition is applied at the edge. The solution of the wave equation downstream of the expansion includes hydrodynamic waves, of which one is a growing wave. Theoretical results are compared with experimental data for the reflection coefficient for the plane wave, at frequencies below the cut-on for higher order modes. Influence of the interaction between the sound field and the flow field is discussed. A region where the reflection coefficient is strongly Strouhal number dependent is found.     

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.     

Modeling scattering from azimuthally symmetric bathymetric features using wavefield superposition

In this paper, an approach for modeling the scattering from azimuthally symmetric bathymetric features is described. These features are useful models for small mounds and indentations on the seafloor at high frequencies and seamounts, shoals, and basins at low frequencies. A bathymetric feature can be considered as a compact closed region, with the same sound speed and density as one of the surrounding media. Using this approach, a number of numerical methods appropriate for a partially buried target or facet problem can be applied. This paper considers the use of wavefield superposition and because of the azimuthal symmetry, the three-dimensional solution to the scattering problem can be expressed as a Fourier sum of solutions to a set of two-dimensional scattering problems. In the case where the surrounding two half spaces have only a density contrast, a semianalytic coupled mode solution is derived. This provides a benchmark solution to scattering from a class of penetrable hemispherical bosses or indentations. The details and problems of the numerical implementation of the wavefield superposition method are described. Example computations using the method for a simple scattering feature on a seabed are presented for a wide band of frequencies.     

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.     

Towards the automation of micron-sized particle handling by use of acoustic manipulation assisted by microfluidics

The use of acoustic radiation forces for the manipulation and positioning of micrometer sized particles has shown to be a promising approach. Resonant excitation of a system containing a particle laden fluid filled cavity, can (depending on the mode excited) result in positioning of the particles in parallel lines (1-D) or distinct clumps in a grid formation (2-D) due to the high amplitude standing pressure fields that arise in the fluid. In a broader context, the alignment of particles using acoustic forces can be used to assist manipulation processes which utilise an external mechanical tool, for instance a microgripper. In such a system, particles can be removed sequentially from a line formed by acoustic forces within a microfluidic channel, hence allowing a degree of automation. In order to fully automate the gripping process, the particles must be confined to a repeatable and accurate location in two dimensions (assuming that in the third dimension they sit on the lower surface of the channel). Only in this way it is possible to remove subsequent particles by simply bringing the gripper to a known location and activating its fingers. This combined use of acoustic forces and mechanical gripping requires that one extremity of the channel is open. However, the presence of the liquid-air interface which occurs at this opening, causes the standing pressure field to decay to zero towards the opening. In a volume of liquid in proximity to the interface positioning of particles by acoustic forces is therefore no longer possible. In addition, the longitudinal gradient of the field can cause a drift of particles towards the longitudinal center of the channel at some frequencies, undesirably moving them further away from the interface, and so further from the gripper. As a solution the use of microfluidic flow induced drag forces in addition to the acoustic force potential has been investigated.     

Gauss声束对离轴椭圆柱的声辐射力矩

利用部分波展开法求解得到了Gauss声束入射下刚性和非刚性椭圆柱的声散射系数,推导了一般情况下的声辐射力矩表达式.在此基础上,通过一系列数值仿真详细分析了离轴距离、入射角度和束腰半径对声辐射力矩的影响.结果表明:正向与负向声辐射力矩均可以在一定条件下存在;低频情况下刚性椭圆柱比非刚性椭圆柱更容易产生较强的声辐射力矩;特定频率的入射声场可以激发出非刚性椭圆柱不同阶的共振散射模式,因而非刚性椭圆柱的声辐射力矩峰值与频率的关系更密切;增加束腰半径有利于扩大散射截面,进而增加椭圆柱的声辐射力矩.该研究结果预期可以为利用声辐射力矩实现粒子的可控旋转和流体黏度的反演提供一定的理论指导.     

开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法     

Coupling of Acoustical Plane p-Wave to a Cased Borehole

Theoretical and numerical study on the coupling acoustic field of the plane p-wave to a cased borehole is carried out. The medium outside the cased borehole is modeled as the porous medium. The scattering field characteristics in the cased borehole are investigated when a plane fast p-wave is incident in tilt to the cased borehole from the porous medium. The scattering fields inside and outside the cased borehole are analyzed and deduced by Biot＇s theory under the boundary conditions on each interface, and they are numerically studied. It is found that the scattering field has strong resonant characteristics and there exists a series of resonant frequencies and peaks. The effects of the frequency, radii of each interface, incident angle, porosity, and other parameters on the resonant acoustic field have been investigated in detail in the fast and slow formations respectively. The resonant characteristics of the scattering field are also analyzed from the physical sense.     

Mechanisms for subcritical penetration into a sandy bottom: experimental and modeling results

This paper presents preliminary results of a recent study whose overall objectives are to determine the mechanisms contributing significantly to subcritical acoustic penetration into ocean sediments, and to quantify the results for use in sonar performance prediction for the detection of buried objects. In situ acoustic measurements were performed on a sandy bottom whose geoacoustical and geomorphological properties were also measured. A parametric array mounted on a tower moving on a rail was used to insonify hydrophones located above and below the sediment interface. Data covering grazing angles both above and below the nominal critical angle and in the frequency range 2-15 kHz were acquired and processed. The results are compared to two models that account for scattering of sound at the rough water-sediment interface into the sediment. Although all possible mechanisms for subcritical penetration are not modeled, the levels predicted by both models are consistent with the levels observed in the experimental data. For the specific seafloor and experimental conditions examined, the analysis suggests that for frequencies below 5-7 kHz sound penetration into the sediment at subcritical insonification is dominated by the evanescent field, while scattering due to surface roughness is the dominant mechanism at higher frequencies.     

Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods

One method for deducing the strength of an acoustic source distribution from measurement of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution. In practice, the frequency response function matrix to be inverted may very often be ill-conditioned. This ill-conditioning will also often result in an ill-posed problem and thus regularization algorithms are used to produce reasonable solutions. For this purpose, Tikhonov regularization has been applied, and generalized cross-validation (GCV) has been introduced as an effective method for determining the proper amount of regularization without prior knowledge of either the source distribution or the contaminating errors. In the present work, the emphasis is placed on the relationship between the spatial resolution of the reconstructed source distribution and the small singular values of the frequency response function matrix to be inverted. However, the use of Tikhonov regularization often suppresses the effect of small singular values and these are in turn often associated with high spatial frequencies of the source distribution. Thus, the process of regularization produces a useful estimate of the acoustic source strength distribution but with a limited spatial resolution. Furthermore, in the field of Fourier acoustics, the spatial resolution of the reconstructed source distribution is usually limited by the wavelength of the radiation. This paper expresses the relationship between estimation accuracy, spatial resolution, noise-level and source/sensor geometry, when a range of inverse sound radiation problems are regularised using Tikhonov regularization with GCV. The results presented form the basis of guidelines that enable the reconstruction of acoustic source strength with a resolution that is finer than the intrinsic half-wavelength limit.