摘要:

A theoretical method for determination of multiple scattering of an acoustical wave by a grating of elastic obstacles is presented. The main advantages of the method are: The same formulation works for finite arbitrary gratings as well as for infinite plane gratings; and the calculation of the properties of the whole grating is decoupled from the calculation of the scattering properties of the individual components set in free field. Some results on compliant tube gratings (plane gratings and a parabolic reflector) are shown and compared to experiments.

ISSN:0001-4966    

DOI:10.1121/1.399310

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

A Schwinger‐type variational principle is presented for the scattered field in the case of scalar wave scattering with an arbitrary field incident on an object of arbitrary shape with homogeneous Dirichlet boundary conditions. The result is variationally invariant at field points ranging from the surface of the scatterer to the farfield and is an important extension of the usual Schwinger variational principle for the scattering amplitude, which is a farfield quantity. Also, a generic procedure, physically motivated by the general principles of boundary conditions and shadowing, is presented for constructing simple trial functions to approximate the fields. The variational principle and the trial function design are tested for the special case of a spherical scatterer and accurate answers are found over the entire frequency range.

ISSN:0001-4966    

DOI:10.1121/1.399311

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

A two‐dimensional mathematical model has been developed to analyze the scattering of plane acoustic waves from an infinite, uniform, plane grating of compliant tubes. It relies upon the finite element method and uses theatilacode [J. N. Decarpignyetal., J. Acoust. Soc. Am.78, 1499 (1985)]. To do this, only the unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, thanks to the Bloch–Floquet theorem, and the effects of the remaining fluid domain are accounted for by matching the pressure field in the finite element mesh with simple plane wave expansions of the ingoing and outgoing waves. This paper describes results obtained for the scattering of a plane wave from different tube gratings, including internal losses, at oblique incidence. Comparing finite element results to analytical or experimental results allows for the validation of the model. Then, various compliant tube gratings are considered to demonstrate the efficiency and versatility of this approach. Finally, the generalization to doubly periodic gratings is emphasized.

ISSN:0001-4966    

DOI:10.1121/1.399312

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

The problem of the scattering of a spherical acoustic wave by an elastic circular cylinder of infinite length is investigated theoretically in this paper. In a cylindrical coordinate system, the mathematical form of a spherical wave is similar to that of a plane wave. Thus it is not necessary to solve the relevant differential equations and boundary conditions. An exact solution to the present problem can be directly formulated by using the already known solution for plane‐wave incidence. This solution is expressed by an integral, which always involves a numerical treatment. The scattered pressure is calculated for an aluminum cylinder in water. A detailed discussion of the results reveals the features of the scattering of a spherical wave.

ISSN:0001-4966    

DOI:10.1121/1.399313

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

Analysis of an echo from a solid elastic cylinder had been limited to the case of a plane incident wave so far. Recently, plane wave theory was modified to the case of a spherically incident wave. In this paper an arbitrary ultrasonic transmitter and receiver are considered as a set of point sources and point receivers, respectively. The analysis is modified to the practical case, that is, the cylinder is placed so that its axis coincides with the central line of curvature of a cylindrical shell transducer. The dependence of the echo from the cylinder on the cylinder material is examined. These results are compared with those experimentally obtained using metal and plastic cylinders and they show very good agreement.

ISSN:0001-4966    

DOI:10.1121/1.399314

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

Earlier forms for the coherent reflection and incoherent scattering by multicomponent mixtures of bosses on rigid or free base planes [V. Twersky, J. Acoust. Soc. Am.29, 209–225 (1957)] are applied to recent high‐frequency results for aligned hemiellipsoidal bosses [R. J. Lucas and V. Twersky, J. Acoust. Soc. Am.83, 2005–2011 (1988)] to investigate continuous distributions in boss size. Approximations for the coherent reflected intensity and incoherent differential scattering cross sections are obtained in terms of integrals of simple functions and a general probability density. To provide illustrations, numerical computations and graphical results are based on truncating the two‐parameter gamma probability density functionP(t;m,v) withtas a dimensionless variable that scales one or more boss dimensions,mas the mean value oft, andvas the normalized variance (ranging from zero to unity). Forvsmall,Pis Gaussian and reduces to a delta function asvapproaches zero (to reproduce one‐component results). More generally, the curve ofPis skewed, and asvapproaches unityPreduces to the exponential for the simplest Poisson case. Graphs are shown for cases where one (e.g., keel depth), two (e.g., base axes), or all three dimensions of the protuberances are randomized. The essentials are indicated by plots versus angle of incidence, withvas the parameter. The coherent intensity and the associated forward and backscattered incoherent differential scattering cross sections per unit area are emphasized.

ISSN:0001-4966    

DOI:10.1121/1.399315

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

The radiation of an elastic field from a plane piston source is formulated using the representation theorem, in which the Green’s function for an elastic half‐space is employed. On the basis of this formulation, the radiated elastic wave field for both compressional and shear cylindrical wave sources is derived. The diffraction of elastic waves incident on a receiver that has the same geometry as that of the source and is coaxially aligned with it is studied. The authors present a procedure in which both numerical and asymptotic techniques are employed to allow them to evaluate the diffraction effects in any frequency range of interest. The elastic diffraction is compared with the acoustic diffraction and it is discovered that they differ only in the nearfield of the piston source because of the coupling between shear and compressional components in the elastic case. In the farfield, however, the elastic diffraction approaches the acoustic diffraction. With the help of ultrasonic laboratory measurements, the authors test the theoretical results and find that the theory and experiments agree well for the elastic solution. An important application of the results of this study is in attenuation measurements using pulse propagation techniques, where spectral ratio of a sample relative to a standard sample, or ratio of samples of the same material but different length is used. In the former case, the attenuation can be overestimated. While in the latter case, the attenuation can be significantly underestimated, if corrections for diffraction effects are not made.

ISSN:0001-4966    

DOI:10.1121/1.399316

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

Analysis of an echo from a solid elastic sphere has been limited to the case of a plane incident wave so far. Plane‐wave theory is modified to the case of spherical incident wave first, and then it is modified to the case of an arbitrary ultrasonic transmitter and receiver by considering them as a set of point sources and point receivers, respectively. Using this relation, the general properties of the echo scattered from the sphere are analyzed first, and then the analysis is carried out in full for important practical cases; that is, the sphere is placed on the focal point of a circular concave transducer and in the focal plane of the transducer. It is applied to study the material dependence of the echo from the sphere placed at the focal point of the transducer as well as that of the sidelobe structure of the echo. These results are compared with those experimentally obtained using metal and plastic spheres of 3 mm in diameter, which show very good agreement.

ISSN:0001-4966    

DOI:10.1121/1.399317

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

Dispersion curves are developed for elastic wave propagation in an anisotropic plate of monoclinic or higher symmetry. Emphasis is placed on analytic expressions for various features. Generalization of the isotropic Rayleigh–Lamb dispersion relations are derived for the cases of (a) propagation along a material symmetry axis and (b) propagation in a general direction. Examination of the high‐frequency limit of the lowest symmetric and antisymmetric mode dispersion curves yields expressions for the half‐space surface or Rayleigh wave velocity. It is shown that the dispersion curves for these modes can exhibit multiple crossings in approaching this limit, and an analytic solution is presented for the constant crossing interval that occurs for propagation along symmetry directions. The analytic results are illustrated by extensive numerical calculations for a variety of degrees of anisotropy with emphasis placed on the relationship between the slowness curves governing partial wave propagation and various features of the dispersion curves.

ISSN:0001-4966    

DOI:10.1121/1.399318

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP

摘要:

The time Laplace‐transform domain convolution‐type reciprocity relation for acoustic waves in a fluid/solid configuration is derived. Arbitrary inhomogeneity, anisotropy, and loss mechanisms are taken into account. Reciprocity between transmitting and receiving transducers located in either the fluid or the solid parts of the configuration is established. It is shown how the reciprocity relation leads to the source‐type wave field integral representations for direct source problems and to the integral‐equation formulation of inverse source, and direct and inverse scattering problems through the associated contrast source representations. Since neither a fluid inclusion in a solid nor a solid inclusion in a fluid leads to a regular perturbation problem in the integral‐equation formulation, the embedding must be adapted to the location of the contrast sources as far as the type of medium (fluid or solid) is concerned. Applications to acoustic emission and to acoustic imaging and profile inversion are briefly indicated.

ISSN:0001-4966    

DOI:10.1121/1.399319

出版商:Acoustical Society of America    

年代:1990

数据来源: AIP