Index of content:
Volume 87, Issue 3, March 1990

Asymptotic solution to the crack‐opening displacement integral equations for the scattering of plane waves by cracks: I. The symmetric problem
View Description Hide DescriptionThe scattering of a symmetric pair of plane waves by a crack in an isotropic, homogeneous, linearly elastic solid is considered. For high frequency, an asymptotic solution to the integral equation for the normal crack‐opening displacement (COD) is found. The elliptical and penny‐shaped cracks are considered in some detail. For the penny‐shaped crack, excellent agreement with numerical results is found as well as agreement with other asymptotic results.

Analysis and synthesis of backscattering from a circular cylindrical shell
View Description Hide DescriptionThe farfield backscattered form function is examined for the problem of plane acoustic pressurewavescattering by an empty elastic circular cylindrical shell. The analysis of the exactly computed total form function has been carried out. The approach of finding the contribution introduced by two peripheral Lamb‐type waves—the zero‐order symmetric S _{0} and the zero‐order antisymmetric A _{0}—is outlined. An approximate description of these contributions is used to synthesize the backscattered form function. The presentation is developed using the case of an Armco iron shell with moderate thickness, immersed in water.

Active control of stationary random sound fields
View Description Hide DescriptionPrevious work on the active control of sound has mostly used frequency domain formulations in order to establish the physical limitations of active methods. While entirely adequate for the prediction of the performance of active control systems designed to deal with deterministic primary fields, these methods cannot necessarily be applied in cases where the primary excitation is stationary random in nature. The application of frequency domain techniques often yields results for the optimal control strategy that require the secondary sources to act noncausally with respect to the primary sources. The work described here illustrates classical time domain methods for determining the performance limits of active noise controlsystems that are constrained to act causally. The first example considered is the minimization of the mean‐squared acoustic pressure at a position in the field of a point monopole primary source by the introduction of a point monopole secondary source. The primary source radiates a stationary random signal and the secondary source is constrained to act causally with respect to the primary source. The active control of low‐frequency random sound in enclosures is then addressed and the classical Wiener theory extended in order to deal with problems involving the minimization of multiple errors. The active control of a one‐dimensional enclosed sound field is presented as a simple example. This theory is also used in presenting a third example that consists of a primary/secondary source pair radiating in a free field. The minimum acoustic power output of the source combination is calculated when the primary source radiates random sound and the secondary source is again constrained to act causally with respect to the primary source.

On effective spectrum‐based ultrasonic deconvolution techniques for hidden flaw characterization
View Description Hide DescriptionFrom the pioneering works of Gericke [O. R. Gericke, J. Acoust. Soc. Am. 3 5, 364–368 (1963)] and some other researchers [L. Adler, K. V. Cook, and W. A. Simpson, ‘‘Ultrasonic frequency analysis,’’ in R e s e a r c h T e c h n i q u e s i n N o n d e s t r u c t i v e T e s t i n g, edited by R. S. Sharpe (Academic, London, 1977), Vol. 3; A. F. Brown, ‘‘Ultrasonic spectroscopy,’’ in U l t r a s o n i c T e s t i n g, edited by J. Szilard (Wiley, New York, 1982)], frequency spectra of ultrasonic returns form hidden flaws carry a rich amount of information usable for flaw characterization. With a proper modeling of these ultrasonic echoes, the effectiveness of such frequency analyses can be further enhanced by a process called deconvolution or inverse filtering. In this paper, the performances of several deconvolution algorithms when applied to ultrasonic pulse echoes from artificial flaws embedded in some aluminum blocks are investigated. The relative computational complexities of these algorithms are also analyzed and compared. Empirical results shall justify the applications of these algorithms for flaw characterization. Furthermore, on comparing the experimental results, simpler implementations and higher efficiencies should favor the use of the spectrum‐based deconvolution techniques over time‐domain techniques.

A hybrid (boundary elements)‐(finite elements)‐ray‐mode method for wave scattering by inhomogeneous scatterers in a waveguide
View Description Hide DescriptionWavescattering by inhomogeneous scatterers in a waveguide is studied using a new method that combines the hybrid ray‐mode, boundary element, and finite element methods systematically in a single framework. This is a generalization of the previous work [I. T. Lu, ‘‘Analysis of acoustic wave scattering by scatterers in layered media using the hybrid ray‐mode‐(boundary integral equation) method,’’ J. Acoust. Soc. Am. 8 6, 1136‐1141 (1989)]. The boundary element method is employed to model the interaction among scatterers and the coupling between interior and exterior of scatterers, the finite element method to formulate the interior responses of the scatterers, and the ray‐mode method to provide Green’s function of the waveguide. This hybrid combination optimizes the advantages of each method and hence, provides physical insights and numerical efficiency and accuracy. To further improve the computational efficiency, the Jacobi’s iteration solution is employed.

Acoustic radiation force on a small compressible sphere in a focused beam
View Description Hide DescriptionA general expression for the acoustic radiation force on a small compressible sphere has been derived and expressed in terms of the time‐averaged densities T _{ i } and V _{ i } of kinetic and potential energies, respectively, in the incident sound field. The results have been applied to two focused beams: Gaussian beams and piston beams. For both cases, the analytical expressions of the radiation forces on a small compressible sphere placed on the axis of the beams are calculated. The pertinent applications in acoustic levitation and bubble dynamics are discussed.

Optical analysis of finite‐amplitude ultrasonic pulses
View Description Hide DescriptionFinite‐amplitude pulses are examined acousto‐optically using a newly developed light‐diffraction apparatus. Based on an optical analysis of ultrasonic transducer response to continuous‐wave excitation at and near the fundamental frequency, pulse Fourier spectra are derived for input to a light‐diffraction model, providing quantitative agreement between experiment and theory. The diffraction theory predicts that a light‐diffraction pattern produced by a harmonically distorted acoustic pulse train will exhibit asymmetry in the intensity distribution with respect to the zero order. To simulate harmonic distortion, pulse frequency spectra are used for input to a computational model that is based on the Burgers’ equation for propagation of finite‐amplitude acoustic waves in a nonlinear medium. The spectrum, propagation, and light‐diffraction models give a complete description of light diffraction by finite‐amplitude pulses and provide good agreement with experimentally obtained diffraction patterns.

Surface waves at an interface between air and an air‐filled poroelastic ground
View Description Hide DescriptionUsing a modified Biot theory, employing open pore boundary conditions at the interfaces, and by seeking plane‐wave solutions, dispersion equations are derived for a rigid porous half‐space, for a poroelastic half‐space, and for a layered poroelastic half‐space. That for the rigid porous boundary has a single solution. Numerical search shows that, for parameter values characteristic of a dry soil, the dispersion equation for the interface between air and an air‐filled poroelastic half‐space has three possible solutions corresponding, respectively, to that for the rigid porous case, an air‐coupled pseudo‐Rayleigh wave, and a new fast surface wave with a speed slightly less than the bulk P‐wave speed. The sensitivities of these three surface waves to porosity and elastic parameters are investigated. Of the solutions to the dispersion equation for a system consisting of a single poroelastic layer above a poroelastic half‐space, with parameters typical of a dry soil, one is identifiable as an air‐coupled pseudo‐Rayleigh wave with a phase velocity near to the speed of sound in air. Slower and faster surface waves are predicted also on the layered system when the input parameters for the upper layer are relevant to either a soil or thick snow.

Comparison of ray and wave approaches to acoustic impulse propagation prior to a shadow boundary
View Description Hide DescriptionThe presence of wind and temperature gradients causes sound to follow curved ray paths, changing the relative delay between direct and reflected components. The way this changes the excess attenuation of propagating acoustic impulses and their waveforms is considered by using ray‐bending theory, including intensities, for an atmosphere supporting either a linear or a nonlinear sound‐speed gradient. These predictions are contrasted with those from creeping‐wave theory, assuming a linear gradient, and both are compared with experimental results for impulses propagating close to the ground. Although the measured gradients are nonlinear, impulse behavior is found to be best predicted by assuming an effective linear gradient. A technique involving impulse rise times is used to determine shadow‐boundary distances and hence the profile of the boundary.

Acoustic tracking from closest point of approach time, amplitude, and frequency at spatially distributed sensors
View Description Hide DescriptionThis paper addresses the problem of passive acoustic tracking from closest point of approach (CPA) time, amplitude, and frequency data at spatially distributed sensors in the case of finite sound‐propagation delay. A novel method is presented for the computation of source velocity (speed and direction) from the CPA times at three noncollinear sensors that lie on the same side of the source path. The method reduces the problem to the solution of a linear trigonometric equation. The method is used as the basis for determining the qualitative location of a straight source path with respect to a square grid of calibrated sensors, assuming that the amplitude of the sensor signal at CPA varies monotonically with the distance between source and sensor. In the case of a maneuvering source, qualitative relations are stated between the local shape of the source path, its relative position with respect to an acoustic sensor, and whether amplitude and frequency increase or decrease monotonically with (source) time at that sensor. These qualitative relations from multiple sensors are then used to segment the source path into straight and maneuvering segments (under negligible propagation delay). Experimental results with real data are presented for the source‐velocity computation, together with a sensitivity analysis.

The rotated parabolic equation and sloping ocean bottoms
View Description Hide DescriptionA new approach for solving problems involving sloping ocean bottoms with the parabolic equation (PE) method is presented. In most implementations of the PE, range‐dependent environments have been approximated as a sequence of range‐independent regions. The PE, which has one range derivative, does not conserve both pressure and the normal component of particle velocity across boundaries between regions. For problems involving sloping ocean bottoms, this can lead to large errors for slopes of only a few degrees. The rotated PE, which marches parallel to the ocean bottom and has two normal derivatives, handles sloping interfaces properly. A benchmark solution for an upslope problem is presented to demonstrate the accuracy of the rotated PE.

Line and plane arrays of resonant monopole scatterers
View Description Hide DescriptionArrays of n identical resonators (bubbles, gas‐filled balloons, and thin shells) in periodic arrays of spacing l and insonified by a plane wave at frequencies near the monopole resonance (b u b b l e) frequency ω_{0} display strong resonances due to multiple scatter interaction. One‐dimensional systems (linear arrays) in full spaces exhibit pronounced partial resonances (q u a s i r e s o n a n c e s or QRs), for both finite and infinite n, with absolute magnification of the free‐field amplitude (i.e., in the absence of the system) of up to 7×10^{2} inside or on the surface of each resonator. These QR effects have strong directionality: The amplitude response of each scatterer may vary by a factor of about 200, depending upon the direction of arrival of the insonifying plane wave. Of some general interest are the infinite line and plane arrays of the kind discussed by Weston [D. E. Weston, J. Acoust. Soc. Am. 3 9, 316–322 (1967)], for which we provide an improved treatment using exact estimates of multiple scatter interaction, as a result of which strong new resonances (QRs) are predicted under some conditions.

Modeled time variability of acoustic propagation through a Gulf Stream meander and eddies
View Description Hide DescriptionA numerical modeling study of the time variability of acoustic propagation through a Gulf Stream meander and eddies is presented. Both a cold‐core (cyclonic) eddy and a warm‐core (anticyclonic) eddy are included. Time periods of 2, 4, and 7 days; a frequency of 25 Hz; source and receiver depths of 150 m; and propagation out to 180 km are considered. Propagation conditions assumed an absorbing bottom and no azimuthal coupling of energy. Results indicate that variations in the locations and propagation loss levels of convergence zones (CZ) in 2 days can be significant. In the first CZ, the losses can change by more than 5 dB and shift in their pattern range location by as much as 10 km. Changes in the environment over a 2‐day period can be such that perturbations to the acoustic field caused by the environment within the first CZ can be nullified by the environment between the first and second CZs. The differences between propagation with the eddies present and not present were also observed for ranges out to the first CZ. For a source located in the center of a cold‐core eddy, the propagation loss in the CZ increased by 3 dB and the range decreased by about 5 km. With the source located within the eddy but off center, the loss showed little change in level but the range again decreased by about 5 km. For a source located in the center of a warm eddy, the propagation loss in the CZ increased by about 3 dB and the range increased by 7–10 km. With the source located off center, the loss showed little change in level and range location.

Effect of the compliance on the scattering of an elastic object immersed in fluid: A general formulation
View Description Hide DescriptionThe scattering of a linear elastic object can be represented by the product of three linear operators. The first and the third of them represent the coupling of the source of the incident field to the scatterer and the scatterer to the observation point, respectively, and depend only on the boundary geometry and on the fluid acoustic properties. The object physical properties are summarized by the middle operator, expressing the deviation of the relevant elastodynamic properties of the actual object from those of a perfectly transparent object, having the same size and shape. This formalism leads also to a natural rigorous decomposition of the scattering into the sum of a rigid and an elastic component, the latter being possibly substantially higher than the first, as shown by some numerical examples.

Resonance scattering in waveguides: Acoustic scatterers
View Description Hide DescriptionIn this paper, acoustic scattering in shallow and deep inhomogeneous waveguides is analyzed. The full acoustic waveequation that describes the scattered and reflected wave fields, as well as all multipathing within the scatterer and the waveguide, is employed. The explicit finite difference time integration and the k–w transform in the space domain (pseudospectral method) were utilized. Properly chosen boundary conditions enabled the authors to model both shallow and deep oceans. The pseudospectral method was compared with the explicit finite difference technique (see Appendix). The pseudospectral method can be valuable for modeling different underwater wave phenomena: It is characterized by much smaller numerical dispersion than the conventional finite difference method. The results show that in shallow ocean, strong resonance coupling between the underwater scatterer and the waveguide may occur. An important conclusion of this paper is that in a limited aperture experiment when the acoustic reflections are beyond the recording aperture (due to the finite length of the recording cable), the measured data are mainly represented by the primary diffraction arrivals and ‘‘diffraction resonances.’’ In this paper, a detailed discussion will be given on the acoustic scattering in an inhomogeneous waveguide. (For the sake of simplicity, an acoustic scatterer of the rectangular shape was considered.) Different complexities (elastic scatterers, more complicated structures of the index of refraction in the water, etc.) will be compounded in the original model and reported elsewhere.

Comments on the calculation of cross sections for elastic‐wave scattering using the T matrix
View Description Hide DescriptionThe basic formulas for the calculation of cross sections for elastic‐wave scattering from elastic and viscoelastic bodies are reviewed from a simpler perspective than normally encountered, with an emphasis toward casting them into a form suitable for calculation with the T‐matrix formalism. The original formulas of Gubernatis e t a l. [J. E. Gubernatis, E. Domany, and J. A. Krumhansl, J. Appl. Phys. 4 8, 2804–2811 (1977); J. E. Gubernatis, E. Domany, J. A. Krumhansl, and M. Huberman, J. Appl. Phys. 4 8, 2812–2819 (1977)] are obtained and the asymmetric dependence of their optical theorem on the mode of the incident plane‐wave field is resolved by incorporating an average over a phase error. Corrected forms for the T matrix in scattering from a single sphere in an elastic medium are presented.

A parametric analysis of attenuation mechanisms in composites designed for echo reduction
View Description Hide DescriptionThe fundamental attenuation mechanisms operating in a particular class of composites are investigated for their viability as underwater anechoic materials. The type of composites of interest consists of dense (visco‐) elastic inclusions in rigid, low‐density, water impedance‐matched, elastic hosts. Composites similar to this have been studied by Kinra^{2} and shown to attenuate transmitted elastic waves in a resonant regime of the imbedded inclusions. Our calculations indicate that the processes giving rise to the attenuation would also be appropriate for echo reduction. As a reference material, a composite of lead‐loaded silicone rubber spheres in a rigid epoxy is studied. The processes operating at both the water–epoxy and epoxy–rubber interfaces are studied theoretically. Using the spherical elasticT matrix, effects due to resonant scattering are analyzed by reference to the scattered and absorption cross sections calculated for both a single rubber sphere and two rubber spheres imbedded in an infinite epoxy matrix. The dynamics at the water–epoxy interface is analyzed via classical elastictheory at a plane interface. The results of our analysis indicate that resonant compressional to shear mode conversion at the inclusions could be an effective way of producing the desired effects. Consequences of the mode conversion leading to attenuation include the trapping of backscattered shear waves and the enhancement of dissipation processes within the inclusions.

A three‐dimensional parabolic equation model that includes the effects of rough boundaries
View Description Hide DescriptionA three‐dimensional parabolic equation (3DPE) model that handles wide propagation angles in depth, narrow propagation angles in azimuth, and rough boundaries is derived and solved numerically with the method of alternating directions. A homogeneous boundary condition, which is easily incorporated into the numerical solution of the 3DPE, is applied at the ocean surface to approximate the effects of rough boundaries in terms of a reflection coefficient that depends on grazing angle. Calculations are presented to demonstrate the accuracy of the 3DPE and to demonstrate that horizontal coupling, the effects due to the term involving azimuth derivatives, can be important in shallow water (previous work has focused on deep‐water applications). The model is applied to problems involving rough boundaries and range dependence.

A boundary integral equation method for acoustic scattering in a waveguide with nonplanar surfaces
View Description Hide DescriptionA boundary integralequation method (BIEM) is formulated to compute the scattering of underwater sound from compact deformations of an oceanic waveguide’s surfaces. The method involves only integrations over the finite area of the waveguidesurface deformations. Numerical computations are given for specific deformations of the ocean floor.

A sediment time‐angle spreading model
View Description Hide DescriptionTo model time‐angle spreading from rough sediment layers, a large‐scale forward‐scattering approximation is applied to the correlation of the characteristic function in the expected value of the intensity. A composite distribution is derived for the transmitted and reflected portions of the acoustic wave through multiple closely spaced layers. Time spread data comparisons are used to set these composite variances at 20° on the consolidated layers and 2°–4° on unconsolidated surficial layers. These values are tested against some independent measurements of angle spreading and found to give good agreement. The model validation at low grazing angles implies that only a small number of layers are apparently participating in the scattering process at the surface of many sediments.