摘要:

A fast, efficient algorithm for computing acoustic fields scattered by inhomogeneous objects in an otherwise homogeneous space is presented. The algorithm, called the Recursive Green’s Function Method (RGFM), constructs the domain Green’s function by recursively combining known Green’s functions from smaller subdomains. The fields on the scatterer surface are then computed using a boundary integral formulation. Proper implementation of the RGFM results in a storage requirement ofO(N)and computational costs ofO(N3/2)andO(N2)for two- and three-dimensional problems, respectively, whereNis the total number of discrete points in the inhomogeneous region. Results are compared with those obtained from exact solutions to show the accuracy of the method.

ISSN:0001-4966    

DOI:10.1121/1.421197

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

The problem of determining the field scattered by a cluster of scatterers when they are insonified by a known acoustical field is addressed. The problem is formulated by using theT-matrix method and the resulting system of linear equations is solved by using the multilevel fast multipole algorithm (MLFMA) and the fast multipole method–fast Fourier transform (FMMFFT) method, and the efficiency of the two methods is compared. It was observed that, in general, the MLFMA performs better than the FMMFFT algorithm. However, when the scatterers are distributed uniformly on a rectangular grid, the FMMFFT algorithm performs as good as the MLFMA. The accuracy of the methods is evaluated by modeling a spherical scatterer as composed of many small spheres.

ISSN:0001-4966    

DOI:10.1121/1.421231

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

The parabolic equation technique is used to solve the Helmholtz equation in the presence of scatterers of arbitrary shape, in two and three dimensions. The scattered field is computed directly, using non-homogeneous boundary conditions on the scattering object to represent the incident field. Effectively this decouples the PE paraxial direction from the direction of incidence. For convex objects the whole range of scattering angles can be covered with a small number of narrow-angle calculations. Finite-difference implementations involve tridiagonal matrices in two dimensions and more general sparse matrices in three dimensions. The resulting codes can be used to solve scattering problems for objects ranging in size from a few wavelengths to hundreds of wavelengths. The method has been tested against analytical solutions for soft and rigid circular cylinders in 2D and soft and rigid spheres in 3D, showing good agreement at all scattering angles.

ISSN:0001-4966    

DOI:10.1121/1.421198

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

High-frequency scattering from convex and non-convex bodies is studied using an iterative algorithm. The key point of the method is a self-adjoint formulation of the Helmholtz integral equation, which ensures the convergence of the iteration process toward the true solution. For all investigated structures with different surface impedances fast convergence could be observed. The number of surface elements of the scatterer varies from about 6000 to 60 000 and the calculations are performed in the high-frequency range with Helmholtz numberskabetween 20 and 63. Even for a scattering structure with nearly 60 000 boundary elements, all computations could be carried out on a regular personal computer.

ISSN:0001-4966    

DOI:10.1121/1.421238

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

This paper presents a probabilistic study of the effects of structural irregularity on wave propagation along an infinite 1-D chain. A general integral equation method based on Markov chain theory is used to determine the phase probability density function (pdf) at the scatterers distributed irregularly along the chain. The scatterers could be atoms in a one-dimensional crystal, or ribs on a flat plate or membrane. The integral equation derived for the phase pdf is simplified considerably when the scatterers are distributed completely randomly or quasi-periodically. In these cases, the integral equations may be asymptotically solved for the phase density functions in the limit of weak or strong scattering; the localization factors are then obtained. The present approach is quite general and is directly applicable to any disordered one-dimensional system consisting of identical scatterers that are arranged according to a probability distribution function. The validity of the present asymptotic solutions is examined and verified by comparing against the existing analytical solutions for simple atomic or mechanical disordered systems.

ISSN:0001-4966    

DOI:10.1121/1.421239

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

The pure shear problem is one of relative mathematical simplicity and includes the essential physics common to more complicated cases, where multiple and coupled deformations occur. In this sense, the analysis of torsional waves serves as a pilot problem for investigating the influence of anisotropy and/or anelasticity on solution behavior. We obtain the kinematic and dynamic properties of torsional axially symmetric harmonic waves propagating in an infinitely long circular cylinder. The medium is transversely isotropic and dissipative, with its symmetry axis coincident with the axial axis of the cylinder. For an elastic cylinder each mode has a cutoff frequency and below that frequency there is no propagation. For tubes made of quartz and aluminum Lucite, we found that the existence of the cutoff frequencies depend on the degree of anisotropic attenuation, i.e., if the axial quality factor is greater than the transverse quality factor, the modes propagate at all frequencies. In contrast to the elastic case, the Poynting vector and the energy velocity have a component along the radial direction, whose values depend on the transverse attenuation. The presence of intrinsic attenuation confines the energy near the (elastic) cutoff frequencies while the radial distribution of the energy is governed by the geometrical features of the cylinder.

ISSN:0001-4966    

DOI:10.1121/1.421199

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

The approximate theory of localized elastic waves in immersed solid wedges earlier developed for wedges with small values of the apex angle [V. V. Krylov, Proc. IEEE Ultrason. Symp., Cat. #94, CHO 793–796 (1994)] has predicted that the effect of water loading results in velocity decrease for wedge modes travelling in the subsonic regime of wave propagation. The results of this theory, in particular the absolute values of wedge wave velocity calculated for slender Plexiglas wedges, agree well with the corresponding experiments. The present study demonstrates that for relative values of wedge wave velocity, as compared with those for wedges in vacuum, this theory provides good quantitative agreement with the experiments on Plexiglas samples also for large values of the apex angle. In addition to this, a generalization of the theory is undertaken to describe the effect of heavier wedge material and a supersonic regime of wave propagation. The corresponding results show good agreement with the existing velocity measurements in immersed brass wedges.

ISSN:0001-4966    

DOI:10.1121/1.421240

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

The laser thermoelastic generation of ultrasound is a promising technique with many potential applications, but it is also a complicated process with many physical phenomena involved. Contrary to a conventional piezoelectric transducer generation, which is a surface phenomenon, a laser generation can activate acoustic sources within the material by optical penetration of the excitation wavelength, resulting in asynchronous wave arrivals at a given point. More generally, in the ideal case of a nondispersive isotropic material, the laser-ultrasonics displacement signals result from temporal convolutions between optical penetration, laser pulse duration, and laser spot extension effects. In this paper, a deconvolution technique is presented that extracts the laser pulse duration contribution from the experimental displacement signals. This deconvolution scheme applied to one-dimensional experiments, in which the laser excitation is spread over a sufficiently large area on the front side of the sample, allows the measurement of the optical absorption coefficient of the material at the excitation wavelength and also a precise evaluation of its longitudinal acoustic velocity.

ISSN:0001-4966    

DOI:10.1121/1.421241

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

Impulse response backscattering measurements are presented and interpreted for the scattering of obliquely incident plane waves by air-filled finite cylindrical shells immersed in water. The measurements were carried out to determine the conditions for significant enhancements of the backscattering by thick shells at large tilt angles. The shells investigated are made of stainless steel and are slender and have thickness to radius ratios of 7.6% and 16.3%. A broadband PVDF (polyvinylidene fluoride) sheet source is used to obtain the backscattering spectral magnitude as a function of the tilt angle (measured from broadside incidence) of the cylinder. Results are plotted as a function of frequency and angle. These plots reveal large backscattering enhancements associated with elastic excitations at high tilt angles, which extend to end-on incidence in the coincidence frequency region. Similar features are present in approximate calculations for finite cylindrical shells based on full elasticity theory and the Kirchhoff diffraction integral. One feature is identified as resulting from the axial (meridional ray) propagation of the supersonica0leaky Lamb wave. A simple approximation is used to describe circumferential coupling loci in frequency-angle space for several surface waves. The resulting loci are used to identify enhancements due to the helical propagation of the subsonica0−Lamb wave.

ISSN:0001-4966    

DOI:10.1121/1.421200

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP

摘要:

Sound propagation from a point time-harmonic source in a stratified water layer lying over an elastic solid half-space is investigated. It is assumed that the sound speed in the layer is less than the shear speed in the solid bottom, and that it increases with the depth. Numerical examples are given which show that the dependence of the wave field on the range between the source and the receiver can sharply change the character under rather small variations of the frequency. Namely, for some particular frequencies, the sound amplitude shows a periodical dependence on the range, while for other frequencies there is no periodicity. A theoretical explanation of this phenomenon is given in a mathematical development using the normal modes theory and high-frequency asymptotic approximations. The dispersion phase curves are found to have “quasi-intersections,” i.e., small domains where two adjacent curves almost intersect. The corresponding frequencies are called the “specific” frequencies. For any nonspecific frequency, there isoneinterface Stoneley(=Scholte)mode, whilst for each specific frequency there aretwomodes of the Stoneley type with close phase velocities. The periodicity of the field is a result of interference in the two Stoneley modes.

ISSN:0001-4966    

DOI:10.1121/1.421242

出版商:Acoustical Society of America    

年代:1998

数据来源: AIP