Diffraction Of Acoustic Waves Research Articles

Diffraction of acoustic waves by multiple semi-infinite arraysa).

Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate. However, there are some strict limitations to its use, usually the boundary conditions need to be imposed on parallel lines (after a suitable mapping). Such mappings exist for wedges with continuous boundaries, but for discrete boundaries, they have not yet been constructed. In our previous article, we have overcome this limitation and studied the diffraction of acoustic waves by a wedge consisting of point scatterers. Here, the problem is generalised to an arbitrary number of periodic semi-infinite arrays with arbitrary orientations. This is done by constructing several coupled systems of equations (one for every semi-infinite array) which are treated independently. The derived systems of equations are solved using the discrete Wiener-Hopf technique and the resulting matrix equation is inverted using elementary matrix arithmetic. Of course, numerically this matrix needs to be truncated, but we are able to do so such that thousands of scatterers on every array are included in the numerical results. Comparisons with other numerical methods are considered, and their strengths/weaknesses are highlighted.

The Sommerfeld Integral in Problems of Simulating the Diffraction of Acoustic Waves Using a Triangular Lattice

The Sommerfeld Integral in Problems of Simulating the Diffraction of Acoustic Waves Using a Triangular Lattice

Super-resolution ultrasonic Lamb wave imaging based on sign coherence factor and total focusing method

Improving the resolution of ultrasound array imaging systems for multiple defects in a measured medium is a popular research topic in nondestructive testing technology. However, because of the diffraction of acoustic waves, the resolution of ultrasound array imaging systems must follow Rayleigh's criterion and hence is limited, and defects with a spacing smaller than the resolution limit cannot be identified using conventional ultrasound imaging methods. Ultrasonic Lamb waves have dispersion and mode conversion characteristics, and the scattering acoustic field after the interaction between Lamb waves and defects is usually complex, making it even more difficult to improve the imaging resolution. In this paper, ultrasonic Lamb wave imaging is investigated with the sign coherence factor-total focusing method (SCF-TFM) when the spacing of the detected defects is smaller than the resolution limit, and the imaging resolution limit of SCF-TFM is analyzed. Experiments on a single blind-hole defect show that the lateral resolution of the SCF-TFM imaging is nearly twice as high as that of the total focusing method (TFM), with a higher signal-to-noise ratio. For experiments on multiple blind-hole defects, the resolution of the SCF-TFM improves by 71.32%, which is higher than that of the TFM when the spacing of the detected defects is larger than the resolution limit. The SCF-TFM enables super-resolution imaging and achieves a higher resolution limit than time-domain topological energy when the spacing of the detected defects is smaller than the resolution limit.

Exposure to acoustic waves on viscoelastic cylinder

The problem of the impact of acoustic waves in a homogeneous viscoelastic cylinder is considered. The investigation aims to investigate the diffraction of acoustic harmonic waves in a viscoelastic cylinder. The body is assumed to be in an infinite acoustic space filled with an ideal fluid. Numerical calculations of the angular and frequency characteristics of the scattered field for viscoelastic cylinders under the action of harmonic acoustic waves are carried out. In the case of steady waves, the Helmholtz equation describes the propagation of small disturbances in an acoustic medium. And in a viscoelastic homogeneous isotropic cylinder, scalar and vector Helmholtz equations with complex coefficients, the solution of which is described by Bessel and Neumann functions with complex arguments. A technique and algorithm have been developed for solving the problem of diffraction of acoustic harmonic waves in a viscoelastic cylinder. It has been established that the stress and displacement of a point of a viscoelastic cylinder take on a maximum value in the region of long waves. It was also found that considering the material’s viscous properties reduces the stress components to 10%.

ЗАМЕЧАНИЕ О ВЫЧИСЛЕНИИ СКОРОСТИ ВОЛНЫ РЭЛЕЯ И ПРОИЗВОДНОЙ ОПРЕДЕЛИТЕЛЯ РЭЛЕЯ В УПРУГИХ СРЕДАХ

There are many approximate and exact formulae to calculate surface wave velocity in an elastic medium. An analytical expression for Rayleigh wave velocity in volume wave velocity values has been obtained. A formula which determines the remainder in the excitation and diffraction of surface acoustic waves in a homogeneous isotropic elastic half-space involving solutions for the strain and stress fields in the form of quadratures is worked out. The values of the Rayleigh wave velocity and the derivative of the Rayleigh determinant for different media according to the reference data were obtained. The results can help in obtaining analytic expressions and reducing the calculation time of numerical solutions of the diffraction and excitation of acoustic waves.

Diffraction grating with varying slit width: Quasi-periodic homogenization and its numerical implementation

We study the diffraction of acoustic waves by thin grating with varying slit width. Using quasi-periodic homogenization, we derive an effective model in which the grating is replaced by effective jump conditions with effective parameters varying along the equivalent interface. The numerical implementations of the actual problem and of its homogenized counterpart are achieved using multimodal methods for a periodic grating with a macro-period containing many slits with varying widths. The ability of the effective grating to reproduce the scattering properties of the actual one is inspected and discussed.

Diffraction grating with space-time modulation

We present a theoretical and numerical analysis of the diffraction of acoustic waves by space-time modulated gratings with rigid-type modulations. This is done by deriving the form of the modes which are exact, uncoupled, solutions of the problem in the unbounded regions, inside and outside the grating. The dispersion of the modes is studied as a function of the ratio of the modulation speed to the speed of sound which shows that each spatial diffraction order is associated with a single temporal diffraction order. For a grating of finite extend, the solution is obtained as a superposition of these modes, which couple at the grating interfaces. This provides a numerical, multimodal, method when considering a truncated version of the solution. We provide analysis of the solutions in the harmonic and in the transient regimes.

Shadow radiation and Fresnel diffraction of acoustic waves.

Fresnel diffraction is a fundamental wave phenomenon. This article explains its physical nature using the examples of the diffraction of acoustic waves at soft and hard half-planes and at large apertures on a black screen. It is shown that the shadow radiation by opaque screens plays a central role in these diffraction phenomena. Fresnel-Kirchhoff diffraction at large apertures is presented as an asymptotic form of the shadow radiation. Fresnel and Grimaldi-type diffraction at the soft and hard half-planes is revealed as interference of the shadow radiation and the incident wave.

Diffraction of Acoustic Waves by a Wedge of Point Scatterers

This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete Wiener--Hopf technique. An effective and accurate iterative numerical procedure is developed to solve the diffraction problem, which allows us to compute the interaction of thousands of scatterers forming the wedge. A crucial aspect of this numerical procedure is the effective truncation of slowly convergent single and double infinite series, which requires careful asymptotic analysis. A convergence criterion is formulated and shown to be satisfied for a large class of physically interesting cases. A comparison to direct numerical simulations is made, highlighting the accuracy of the method.

Symbolic Computation Applied to Cauchy Type Singular Integrals

The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system Mathematica to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article.

Mathematical modeling of monochromatic acoustic wave diffraction on a system of bodies and on flat screens

Some problems of diffraction of a monochromatic acoustic wave on surfaces of complex shapes are considered. To solve such problems, an approach is applied, in which the problem is reduced to a boundary hypersingular integral equation, where the integral is understood in the sense of a finite value according to Hadamard. Such approach allows solving diffraction problems both on solid objects and on thin screens. To solve the integral equation, the method of piecewise constant approximations and collocations, developed in the previous works of the author, is used. In the present study, examples of modeling the diffraction of an acoustic wave by bodies with partial filling are given. It is shown how the filling of bodies influences the acoustic pressure field, and the field direction patterns are given. An example of applying this approach to solving the problem of sound propagation in an urban area is also given: the diffraction of an acoustic wave from a point source on a system of buildings is considered. The presented results demonstrate that this method allows constructing reflected fields and analyze their characteristics on surfaces of complex shapes.

Boundary element methods in diffraction of a point-source acoustic wave by a rigid infinite wedge

The paper presents some boundary element methods (BEM) applied to diffraction of the harmonic acoustic wave generated by a point source. The authors first consider a basic boundary integral equation (BIE). Its analytical analysis permits development of some explicit conclusions. Then, some boundary element methods arise as a result of the dicretization of the BIE by various quadrature formulas. The matrices of the arising systems of linear algebraic equations (SLAE) are studied in the aspect of the structure of their spectrum. It is shown that the spectrum of the matrices is located in the right half-plane, hence the matrices are positive-definite. This predetermines a rapid convergence of the iterative algorithms applied, to solve the SLAEs.

A Nonstationary Problem of Diffraction of Acoustic Waves from a Point Source by an Interface of Two Half-Planes with Positive Effective Curvature

A nonstationary problem of diffraction of acoustic waves excited by a point source by an interface between two acoustic media with positive effective curvature is considered. This is a model problem for wave phenomena arising near the ocean bottom in the approximation of the “liquid bottom”. Using the complex analysis techniques, a method for finding the exact solution to the studied class of problems is proposed. A method for constructing exact solutions in the form of an integral representation of the problem stated is given.

Modeling the recoveryof the optoacoustic image of oxygenated erythrocyte

Optoacousticimaging makes it possible to detect the generated ultrasonic waves in the medium under study, while absorbing pulsed laser radiation based on the optoacoustic effect. This method combines the advantages of spectral optical contrast and scalable acoustic resolution at depths from millimeter to centimeter and is gradually becoming a practical tool for many biomedical applications. Optoacoustic imaging is a hybrid, non-invasive technique.In recent years, much attention has been paid to the restoration of optoacoustic images, in particular, various reconstruction methods are being developed, such as rear projection, frequency do-main reconstruction, time reversal and model-based reconstruction. Although these methods are based on various propagation theories, they have relatively simple implementations for im-age reconstruction in homogeneous environments. However, in the case of heterogeneous lay-ered media, the existing propagation models need to be modified to take into account various acoustic effects at the interface of the layers, which complicates the reconstruction process. To eliminate distortions caused by diffraction of acoustic waves, the method of moving a virtu-al detector is used for image reconstruction. The proposed method can be used to obtain imag-es in layered inhomogeneous media.

Extreme acoustic anisotropy in crystals visualized by diffraction tensor

Anisotropic acoustic wave propagation in single crystals is a fundamental phenomenon enabling operation of various acoustic, acousto-electronic and acousto-optic devices. It provides a variety of device performances and application fields, but its role in pre-estimation of achievable device characteristics and location of crystal orientations with desired properties is often underestimated. A geometrical image of acoustic anisotropy can be an important tool in design of devices based on wave propagation in single crystals or combinations of anisotropic materials. We propose a fast and robust method for survey and visualization of acoustic anisotropy based on calculation of the eigenvalues of bulk acoustic wave (BAW) diffraction tensor (curvature of the slowness surface). The stereographic projection of these eigenvalues clearly reveals singular directions of BAW propagation (conical acoustic axes) in anisotropic media and areas with large and small BAW beam divergence. The method is illustrated by application to three crystals of different symmetry used in different types of acoustic devices: paratellurite, lithium niobate and potassium gadolinium tungstate. The specific features of acoustic anisotropy are discussed for each crystal in terms of their potential application in devices. In addition, we demonstrate that visualization of acoustic anisotropy of lithium niobate helps to find orientations supporting propagation of high-velocity surface acoustic waves.

Assessment on the use of additive manufacturing technologies for acoustic applications

Additive manufacturing technologies have demonstrated great potential for reproducing complex geometries, free patterns and meticulous details. These characteristics are present in the design of solutions in the acoustic field with different requirements and functionalities. This paper reviews several articles dealing with different acoustic phenomena (absorption, filtration, modulation, diffraction or propagation of acoustic waves). The work demonstrates the high potential of these technologies in various applications. Solutions were found in the acoustic conditioning of absorbent panels sector, ranging from design to manufacture. Other design and manufacturing examples were evaluated, including hearing protection devices, musical instruments, silencers, hearing aids as well as electroacoustic sensors. It have been evaluated many references of the use of additive manufacturing in the generation and handling of acoustic waves used in advanced medical imaging and therapeutic ultrasound applications, among others. This study aims to obtain an updated overview of the use of additive manufacturing in the acoustic applications. It also summarizes the range and areas of application of these technologies in those environments where they could offer the best benefits.

Behavior of solutions of an acoustic wave diffraction problem on a set of small obstacles

The article discusses the problem of diffraction of an acoustic wave by a multitude of obstacles (or cavities) enclosed in a finite subdomain of a homogeneous material domain. It is assumed that the distance between obstacles (cavities) is much greater than the size of each obstacle (cavity). Conditions are indicated under which the total influence of obstacles on the transmitted wave is expressed as an additional term of the potential type in the wave equation. Conditions at the boundary of the cavities are accepted as boundary conditions of the third kind. The results of the work can be used in the development of non-destructive testing procedures.

A Fast UTD-Based Method for the Analysis of Multiple Acoustic Diffraction over a Series of Obstacles with Arbitrary Modeling, Height and Spacing

A uniform theory of diffraction (UTD)-based method for analysis of the multiple diffraction of acoustic waves when considering a series of symmetric obstacles with arbitrary modeling, height and spacing is hereby presented. The method, which makes use of graph theory, funicular polygons and Fresnel ellipsoids, proposes a novel approach by which only the relevant obstacles and paths of the scenario under study are considered, therefore simultaneously providing fast and accurate prediction of sound attenuation. The obstacles can be modeled either as knife edges, wedges, wide barriers or cylinders, with some other polygonal diffracting elements, such as doubly inclined, T- or Y-shaped barriers, also considered. In view of the obtained results, this method shows good agreement with previously published formulations and measurements whilst offering better computational efficiency, thus allowing for the consideration of a large number of obstacles.

Diffraction of Acoustic Waves on a Half-Plane in the Case of Impedance Boundary Conditions. Applications to Sound Barriers

A method is proposed and the simple analytical solutions are obtained for the diffraction problems of acoustic waves on a half-plane with the impedance boundary condition on its one side and the Neumann or Dirichlet condition on the opposite side. It is shown that the properties of these solutions are essential for the optimal design of sound barriers with sound-absorbing walls.

Scattering of acoustic waves from a point source over an impedance wedge

In this work we study diffraction of a spherical acoustic wave due to a point source, by an impedance wedge In the exterior of the wedge the acoustic pressure satisfies the stationary wave (Helmholtz) equation and classical impedance boundary conditions on two faces of the wedge, as well as Meixner’s condition at the edge and the radiation conditions at infinity. Solution of the boundary value problem is represented by a Weyl type integral and its asymptotic behavior is discussed. On this way, we derive various components in the far field interpreting them accordingly and discussing their physical meaning.