摘要:

Reflection, transmission, and scattering of Rayleigh waves that are obliquely incident on a surface‐breaking crack are investigated. The formulation of the problem has been reduced to two systems of singular integral equations of the first kind for the dislocation densities across the crack faces. The systems of integral equations are solved numerically. Substitution of the dislocation densities into appropriate representation integrals yields the reflected and transmitted surface waves. Reflection and transmission coefficients are plotted versus the angle of incidence for various values of the frequency and versus the frequency for various values of the angle of incidence. A critical angle of incidence, which depends on the material properties of the solid, has been observed. Beyond this angle no mechanical energy is radiated into the solid by body waves.

ISSN:0001-4966    

DOI:10.1121/1.390473

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The known exact analytic solutions to the problem of (acoustic and electromagnetic) scattering by a two‐dimensional infinite right circular cylinder are not in closed form, but consist of infinite series, each term of which contains Hankel and Bessel functions of increasing order, and the convergence rate of which decreases rapidly with increasing (ka) numbers. For a given numerical solution, it is thus necessary to compute many Hankel and Bessel functions in high order for each spatial datum point for which the scattered field need be calculated. Presented is an exact numerical method of solution, which is in closed form, and requires the computation of only one Hankel function of order unity per spatial datum point for which the fields need be calculated. The method consists of a closed form numerical deconvolution solution of the scattering integral equation, executed efficiently with the aid of the fast Fourier transform algorithm, thus requiring only ( (3)/(2)  N log2 N) complex arithmetic multiply–add operations, and the computation of onlyNHankel functions of order unity, whereNis the number of spatial datum points for which a solution is required. Because of the extreme simplicity of the method of solution, a computer program listing for the algorithm is presented. Numerico‐experimental results verifying the speed and accuracy of the method are also presented.

ISSN:0001-4966    

DOI:10.1121/1.390474

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

Elements of a geoacoustic model of the geologically young (<10 million years) upper crust, the top few hundred meters of the basalt subbottom, are described. The model is based on analysis of low‐frequency reflectivity versus angle data at a 1 million‐year‐old sediment‐free site, as well as limited Deep Sea Drilling Project downhole logging results, and extrapolated seismic refraction measurements. The upper crust at this site, which is in close proximity to the crest of the East Pacific Rise, may be characterized by low interfacial velocities (Vp∼2800 m/s andVs∼800 m/s), large gradients (3–5 s−1), and substantial rms roughness (∼5 m). The low‐inferred shear speed implies no shear critical angle. Hence, low‐frequency energy incident on the bottom at small grazing angles is in large part transmitted into the rock, refracted by the gradient, and reradiated into the water. Scattering loss occurs at both the initial incidence and the interaction of the refracted energy at the boundary. Low interfacial shear speeds lead to large grazing angles at the boundary for the transmitted shear waves, large wavenumbers and, hence, large boundary‐scattering losses; small changes in interfacial shear speed produce large changes in subsurface boundary‐scattering loss, and hence in the reflection coefficient. A summary of logging and extrapolated seismic refraction measurements in the young crust, below 10 million years, suggests that the range of interfacial shear speeds is between about 800 and 2400 m/s. In older crust, the range of shear speeds is projected to be significantly different. Ramifications of the site dependence of upper crustal properties, particularly shear speed, on sound propagation are discussed.

ISSN:0001-4966    

DOI:10.1121/1.390475

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

Acoustic wave propagation through a dense suspension of solid elastic particles in water is studied. The particles in suspension have a size distribution and their relative positions are described by a pair‐correlation function. Twersky’s multiple scattering formalism is employed to obtain new analytical expressions for the phase velocity and coherent attenuation of a wide range of concentrations. Numerical results presented are of interest in the study of marine sediments.

ISSN:0001-4966    

DOI:10.1121/1.390476

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The problem of scattering of a plane sonic wave from hard and soft eggcrate surfaces, composed of tridimensional protuberances distributed periodically on a plane along two orthogonal directions, is examined by means of the Rayleigh plane wave expansion method, numerically implemented by Fourier base projection of the boundary conditions. The Kirchhoff approximation solution, which predicts that the intensity specularly reflected from a surface of the formx3=f(x1)+f(x2) is the square of the intensity specularly reflected from a simple periodic surface of the formx3=f(x1), is shown, by means of the Rayleigh solutions, to be well‐verified for surfaces with small‐amplitude irregularities.

ISSN:0001-4966    

DOI:10.1121/1.390477

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

An examination of wave propagation in waveguides of rectangular cross section having a single boundary discontinuity is presented. Special attention is paid to waveguides with heights that are small compared to an acoustic wavelength. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the value of a single small parameter ε, where ε is the ratio of the typical duct heightH0to the wall wavelengthL0. The influence of planar discontinuities of zero and small but finite thickness on wave propagation is determined using the method of matched asymptotic expansions. Junction conditions, impedance across the junction, and uniformly valid composite expansions for the pressure in the duct are presented.

ISSN:0001-4966    

DOI:10.1121/1.390478

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The method of match asymptotic expansions MMAE, is used to analyze wave propagation in two problem geometries. The acoustic pressure is evaluated for a waveguide having a single discontinuity in wall slope and a waveguide having a right‐angle bend. A two‐port representation of the fluid motion across the discontinuity for each problem is tabulated. A uniformly valid expression for the pressure for each problem is given.

ISSN:0001-4966    

DOI:10.1121/1.390479

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

The application of boundary integral methods to the problem of acoustic radiation suffers from nonexistence or nonuniqueness problems at the characteristic frequencies of the associated interior Dirichlet problem. To overcome this difficulty, an iterative overdetermination scheme is developed. First, the surface integral Helmholtz equation is discretized, and at noncharacteristic frequencies, the resulting system of linear algebraic equations can be solved directly, yielding the values of the acoustic pressure at the boundary nodal points. At characteristic frequencies, the system matrix becomes ill‐conditioned and the direct solution is not possible. An approximate surface impedance function is then assumed to serve as a basis for the computation of approximate farfield pressures. These are then utilized to form an overdetermined system, which is solved with the least‐squares procedure. This solution can be used to compute the next‐order approximation, and the process is continued. The method is applied to the cylindrical transducer problem and proves to yield good results at characteristic frequencies. It is also used to solve a structural radiation problem, for which no characteristic frequencies are found. Nonexistence of such frequencies for problems of this type is conjectured, although no general proof is given.

ISSN:0001-4966    

DOI:10.1121/1.390480

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

Fourier analysis method has been applied to model the diffraction integral of the second harmonic field nonlinearly generated by a surface acoustic wave beam. Cross‐section profiles of the second harmonic field have been calculated at different longitudinal positions along an acoustic beam propagating on a yz‐LINbO3crystal. Theoretical curves are reported together with experimental results relative to the case of a fundamental wave emitted by a 24‐wavelengths‐wide transducer at the frequency of 35 MHz. A theoretical determination of the energy loss produced by diffraction effects in second harmonic generation is performed by evaluating the acoustic energy of the second harmonic wave over cross sections of the acoustic beam and by normalizing these quantities to the ones relative to plane wave propagation. Diffraction loss in isotropic and anisotropic materials has been calculated as a function of the longitudinal position along the beam axis for different directivities of the source. A generalized diffraction loss curve is reported, which takes different beam directivities and different anisotropy parameters into account for the case of isotropic media and of anisotropic media with parabolic velocity surfaces.

ISSN:0001-4966    

DOI:10.1121/1.390481

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP

摘要:

An impulse technique has been developed which allows investigation of the reflection of acoustic transients at different angles from an impedance boundary. From measurements of the direct and reflected impulses, the complex surface impedance has been calculated from the ratio of the corresponding Fourier components. The surfaces were modeled as a locally reacting boundary between homogeneous media; this representation was found to be adequate for grassland and a carpet layer but unsatisfactory for a thick fiberglass layer. There was no need to include a ground wave term when reconstituting pulse shapes at different angles over grass or carpet for the range of frequencies and angles investigated in this paper.

ISSN:0001-4966    

DOI:10.1121/1.390482

出版商:Acoustical Society of America    

年代:1984

数据来源: AIP