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Volume 95, Issue 2, February 1994

Elastodynamic wave propagation in a continuously twisted structurally chiral medium along the axis of spirality
View Description Hide DescriptionThe stress tensor in a continuously twisted structurally chiral medium (CTSCM) is symmetric and the stiffness tensor varies helicoidally about the axis of spirality. Exact analytic solutions are found for elastodynamic wave propagation along the axis of spirality in a CTSCM.

Acoustic transient radiation from fluid‐loaded shells of revolution using time‐dependent in vacuo eigenvector expansions
View Description Hide DescriptionA new method is presented to evaluate the acoustic transient radiation from fluid‐loaded shells of revolution which are excited by axisymmetric mechanical or acoustical excitations. This method is based on the use of an in‐vacuo modal vector (eigenvector) expansion with time‐dependent coefficients to describe the velocity field of the fluid‐loaded shell. Modal acoustic impulse responses which account for the coupling between the in‐vacuo modal vectors for the fluid‐loaded shell are introduced in the formulation of the general solution. The time‐dependent modal velocity coefficients are expressed as the solution of a set of coupled convolution integral equations which are readily solved by marching forward in time. The associated time‐dependent surface pressure is subsequently expressed as a modal vector expansion in which the time‐dependent coefficients are readily related to the modal velocity coefficients. Since the surface velocity and pressure are then known, the time‐dependent pressures in the field are simply obtained via quadrature methods from the space‐time Kirchhoff integral solution. The special case of a fluid‐loaded spherical shell is addressed to illustrate the application of the method to determine the general characteristics of the transient velocity response of the shell and the associated pressure field resulting from axisymmetric mechanical force excitations of spherical shells. Numerical results are presented to illustrate the effects on the velocity response and pressure field of time‐dependent fluid coupling between the modal vectors corresponding to the upper and lower branches of the in‐vacuo frequency spectrum of the spherical shell.

Plane‐wave response of an elastic chiral solid slab sandwiched between achiral solid half‐spaces
View Description Hide DescriptionConsidered in this paper are two boundary‐value problems: first, a plane wave incident upon a planar interface separating an achiral elastic half‐space from a chiralelastic half‐space; second, a plane wave incident upon a chiral slab interposed between two achiral elastic solid half‐spaces. The inability of the achiral solid medium to support the microrotation field and the couple‐stress dyadic provides the option of two distinct sets of boundary conditions at achiral/chiral interfaces. It is observed from numerical computations that using either set of boundary conditions in either of the two boundary‐value problems results in the satisfaction of the principle of conservation of energy. Thus, it appears that the physically proper set of boundary conditions for a chiral/achiral interface may have to be decided experimentally.

On the pressure field of a transducer in the form of a curved strip
View Description Hide DescriptionA new analytical expression for the impulse response of a transducer in the form of a curved strip is derived. The radiator is defined as part of a concave spherical shell delimited by two horizontal parallel planes and two vertical parallel planes. The field of the transducer is obtained by means of the impulse response method proposed by F. Oberhettinger [J. Res. Natl. Bur. Stand. 65, 1–6 (1961)] and P. R. Stepanishen [J. Acoust. Soc. Am. 49, 841–849 (1971)] and the formalism developed by M. Arditti et al. [Ultrason. Imag. 3, 37–61 (1981)]. Exact analytical expressions of the impulse response and of the continuous pressure field were obtained in the three planes xOy, xOz, yOz, where Oz is the propagating axis of the ultrasound and O the focal point. The results of numerical modeling were compared with experimental results obtained using a 5‐MHz rectangular spherical strip (7×21 mm) focused at 75 mm. The agreement was excellent.

Frequency and time domain Bragg‐modulated ray acoustics for truncated periodic arrays
View Description Hide DescriptionMany scenarios in underwater acoustics involve radiation from, or scattering by, configurations with periodic or quasiperiodic features. Depending on the operating conditions, the acoustic field generated by these processes carries the gross imprint of periodicity or quasiperiodicity, without or with effects of truncation, regardless of the detailed structure in each unit cell. To understand and quantify the phenomenology under time harmonic and pulsed excitation, especially in the mid‐ to high‐frequency regime where the width of each cell can cover many wavelengths, it is instructive to explore alternative parametrizations that emphasize, respectively, the nondispersive direct radiation from each cell and the dispersive collective treatment of strict or weakly perturbed periodicity, without and with truncations. The prototype configuration for this two‐dimensional study is a finite periodic array of linearly phased parallel filamentary elements. The formulation makes use of Poisson summation and subsequent asymptotics applied to the finite array, and is parametrized in the configuration‐spectrum phase space; it highlights the connection between local and global phenomena in both the space‐time and wave‐number‐frequency domains, with a view toward phase‐space data processing. Formal aspects and general principles are presented in this paper and are applied to infinite and truncated periodic arrays to illustrate how known results obtained by other methods are recovered with the Poisson‐based algorithm. The outcome is a new frequency and time domain Bragg‐modulated ray acousticmodel that generalizes the nonuniform and uniform ray fields of the geometrical theory of diffraction, so as to include effects of periodic dispersion, with truncations. Under transient conditions, such dispersion gives rise to new time domain Bragg modes.

Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface in water
View Description Hide DescriptionThe transient response of a wave front that forms a transverse cusp caustic is studied. The travel time surface of a simple cuspoid caustic is known to have the general shape of the singular surface of the next higher order cuspoid catastrophe. Though the transverse cusp wave front considered here is curved in two dimensions, it is also shown to have a travel time surface with the general shape of the singular surface of the swallow tail catastrophe. Ultrasonic experiments to image the travel time surface of the transverse cusp caustic were performed. The imaged travel time surface has the shape of the swallow tail singular surface imposed on a slowly varying travel time surface due to the spherical nature of the source. Imaged cuts through the travel time surface compare very well to calculated travel time curves. The calculated curves are a superposition of a smooth background contribution and a contribution due to the shape of the reflecting surface. It is the second contribution that describes the merging and disappearance of rays as the cusp caustic is crossed. There are no adjustable parameters used in the comparison. It is possible to infer at least qualitative information about the reflecting surface from the imaged travel time surface.

Study of phase velocity and energy distribution of Stoneley waves at a solid–liquid interface
View Description Hide DescriptionCharacteristics of surface Stoneley (Scholte) waves propagating along the interface bismuth germanate–water solution of glycerol are investigated both theoretically and experimentally. These waves have been generated and detected using interdigital transducers(IDT). The phase velocity of the Stoneley wave and its energy distribution between the two media are measured at frequencies between 15 and 50 MHz over a wide region of sound speeds in the liquid v _{ L }, including those exceeding the speed of the Rayleigh wave in the solidv _{ R }. It is shown that at v _{ L }≳v _{ R } the speed of the Stoneley wave markedly differs (≳10%) from the speed of the longitudinal wave in the liquid. The former remains limited by v _{ R }, and the major part of wave energy propagates in the solid. The insertion and transducer losses (TL) were measured for the generation of Stoneley waves by the IDT; the minimal value of TL was close to 10 dB per transducer. This suggests that it is feasible to use this method for the generation of Stoneley waves.

Diffraction of acoustic waves by rigid plane baffles
View Description Hide DescriptionThe integral‐equation method is applied to study the diffraction of acoustic waves by rigid plane baffles, such as a circular disk and a ring. A set of six real Fredholm integral equations of the second kind is solved simultaneously to determine the velocity potentials on a circular disk. These equations are transformed into discrete forms by applying the Gauss–Legendre quadrature formula in the radial direction and the best possible numerical integration formula in the angular direction. The discrete equations are solved by the method of successive approximations, which is also called the direct integral‐equation method. A new method is also developed to take care of integrations involving the Cauchy principal values, which occur when the moving point coincides with the fixed point. The accuracy of the present numerical approach has been tested by computing the excess‐pressure ratio ‖p/p _{0}‖ on the surfaces of a circular disk exposed to a plane wave and by comparing it with both analytical and experimental results. Our numerical results coincide with both results quite well, especially on the shadow side, where the diffraction field is not sensitive to the thickness of the circular disk. The effect of different parameters on the diffracted acoustic field about a circular disk due to a monochromatic acoustic source is systematically studied and compared. These parameters include the location of the acoustic source, the wave number, and the disk thickness. Some interesting results are obtained. As the wave number increases, the excess‐pressure ratio approaches two on the ‘‘illuminated’’ side and zero on the ‘‘shadow’’ side of the disk, which indicates that Kirchhoff’s approximation is appropriate at higher wave numbers. As the acoustic source moves away from the symmetric axis toward one side, the bright spot on the shadow side moves toward the opposite side and has the same peak value. Finally, following the same approach as that for a circular disk, the diffraction of acoustic waves by a rigid ring is studied. Instead of six, a set of eight real Fredholm integral equations is solved simultaneously. The effect of different parameters on the diffraction field is also systematically studied and compared.

Numerical simulation of interface waves by high‐order spectral modeling techniques
View Description Hide DescriptionFew problems in elastodynamics have a closed‐form analytical solution. The others can be investigated with semianalytical methods, but in general one is not sure whether these methods give reliable solutions. The same happens with numerical techniques: for instance, finite difference methods solve, in principle, any complex problem, including those with arbitrary inhomogeneities and boundary conditions. However, there is no way to verify the quantitative correctness of the solutions. The major problems are stability with respect to material properties, numerical dispersion, and the treatment of boundary conditions. In practice, these problems may produce inaccurate solutions. In this paper, the study of complex problems with two different numerical grid techniques in order to cross‐check the solutions is proposed. Interface waves, in particular, are emphasized, since they pose the major difficulties due to the need to implement boundary conditions. The first method is based on global differential operators where the solution is expanded in terms of the Fourier basis and Chebyshev polynomials, while the second is the spectral element method, an extension of the finite element method that uses Chebyshev polynomials as interpolating functions. Both methods have spectral accuracy up to approximately the Nyquist wave number of the grid. Moreover, both methods implement the boundary conditions in a natural way, particularly the spectral element algorithm. We first solve Lamb’s problem and compare numerical and analytical solutions; then, the problem of dispersed Rayleigh waves, and finally, the two‐quarter space problem. We show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist. The combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics.

Coherent field and specular reflection at grazing incidence on a rough surface
View Description Hide DescriptionThe coherent component of the field scattered at grazing angles from a slightly rough pressure release surface is found. This is valid for multiple scattering and is based upon the parabolic integral equation method. Also examined are the scattering of planes waves under the method and in particular, the effect of truncating the boundary integral. It is shown that the coherent field remains invariant when the source and receiver are displaced vertically by equal and opposite distances, as was found numerically in a previous paper. In general, this can be shown to hold because the coherent field due to any plane wave is specular; however, under the parabolic equation method reflection is not specular, and thus the result is of particular interest. Reflection coefficients are given in closed form for several surface statistics, valid asymptotically at large distances.

Leaky torsional acoustic modes in infinite clad rods
View Description Hide DescriptionDispersion curves, leakage loss, and displacement profiles obtained from the exact analysis of leaky torsional acoustic modes in infinitely thick cladded rods are presented. Two different structures, in which both the longitudinal and the shear velocities of the core are either larger or smaller than those of the cladding, are considered. Similarities are observed between results obtained and dispersion curves which have been reported previously by other workers. Analytic loss relations are also reported for specific modes at either the low‐ or the high‐frequency limit. Applications for this analysis are discussed.

Weakly nonlinear waves and acoustic streaming produced by an oscillating rigid cylinder
View Description Hide DescriptionThe weakly nonlinear propagation of waves radiated from a rigid cylinder executing harmonic translatory oscillations in a direction perpendicular to its axis into an ideal gas is studied theoretically, under the condition that an acoustic Reynolds number is sufficiently large. The entire propagation process, from generation of sound to the stage where the wave amplitude is saturated, is analyzed in the leading order approximation. It is shown that in the near‐field acoustic streaming occurs around the cylinder in the next order. The compressibility in fluid together with the nonlinearity plays an essential role in this acoustic streaming. For the problem up to the shock formation a far‐field equation is exactly solved and the subsequent evolution into the sawtooth wave is examined using the equal‐areas rule. These multidimensional waves have the directional quality proportional to cos θ (θ is the angle measured from the direction of oscillation of the cylinder). At a great distance it appears that the saturation of the wave and the amplitude simultaneously becomes independent of cos θ there.

New fast field programs for anisotropic sound propagation through an atmosphere with a wind velocity profile
View Description Hide DescriptionTwo new fast field programs (FFP) have been developed for numerical computation of anisotropicsound propagation through an atmosphere with a wind velocity profile. The first new FFP can be used to compute the near‐field and far‐field sound pressure. The numerical implementation of the FFP is based on an integration algorithm using a two‐dimensional fast Fourier transform with iterative refinement. For studying problems of long‐range propagation, a novel far‐field expression for sound pressure is derived. The second new FFP is based on this far‐field approximation. If the magnitude of wind speed is not very large; this new far‐field expression shows that the component of wind perpendicular to the direction of propagation has no effect on long‐range propagation. Numerical results from both new fast field programs demonstrate that the effective sound‐speed model used in the conventional FFP’s is still valid for propagation within a certain range. However, the agreement between methods becomes worse at longer horizontal distance. These numerical results also show that the effective sound‐speed model will produce phase errors for higher angle modes, which is most apparent when a single mode dominates the solution. When many modes are present, the envelopes of the curves match, but the details do not.

Validity of spectral theories for weakly range‐dependent ocean environments—Numerical results
View Description Hide DescriptionTraditionally, the wave‐number integration approach is limited to horizontally stratified environments. However, due to its interpretational advantages, some recent efforts have been aimed at developing a wave‐number integration approach to range‐dependent problems. In this paper, solutions are presented of the ASA benchmark problems [F. B. Felsen and C. M. Ferla, J. Acoust. Soc. Am. 87, 1499–1510 (1990)] generated with the spectral integral form derived by Lu and Felsen [J. Acoust. Soc. Am. 81, 897–911 (1987)]. The results show that the adiabatic transform method produces good results in the water column but only for situations where the field in the waveguide is dominated by discrete modes. For situations where the sound field is dominated by the continuous spectrum, the adiabatic transform solution deteriorates rapidly. It is discussed how this behavior is consistent with the waveguide physics and it is concluded that the spectral invariant mapping is correct only for discrete modalwave numbers, i.e., those corresponding to an evanescent field in the bottom. The mapping is also approximately valid at the edge of the continuous spectrum and this accounts for its better performance over the conventional adiabatic mode approach. This also implies that the standard adiabatic approach is invalid for virtual modes.

An optimal absorbing boundary condition for finite difference modeling of acoustic and elastic wave propagation
View Description Hide DescriptionThis paper presents an optimal absorbing boundary condition designed to model acoustic and elastic wave propagation in two‐dimensional and three‐dimensional media using the finite difference method. In this condition, extrapolation on the artificial boundaries of a finite difference domain is expressed as a linear combination of wave fields at previous time steps and/or interior grids. The acoustic and elasticreflection coefficients from the artificial boundaries are derived. They are found to be identical to the transfer functions of two cascaded systems—the inverse of a causal system and an anticausal system. The method makes use of the zeros and poles of reflection coefficients in a complex plane. The optimal absorbing boundary condition described in this paper yields, on the average, reflection coefficients about 10‐dB smaller than Higdon’s absorbing boundary condition, and about 20‐dB smaller than Reynolds’ absorbing boundary condition.

Surface scattering measurements using broadband explosive charges in the Critical Sea Test experiments
View Description Hide DescriptionExtensive measurements of low‐frequency (70–1000 Hz) sea surfacebackscattering strengths have been made as part of the Critical Sea Test (CST) experiments. These measurements were made during CST‐1 through CST‐5 for a variety of wind speeds from 1.5 to 13.5 m/s and for mean grazing angles from about 5 to 30 deg. These measurements have revealed several regimes in a frequency versus wind speed domain that probably correspond to at least two distinct scattering mechanisms. For relatively calm seas at high frequencies and for all wind speeds at lower frequencies, perturbation theory is found to give an adequate description of surface scattering. For rougher seas and higher frequencies, the Chapman–Harris empirical curves are adequate predictors of the levels of surface scattering. In between these two regimes is a transition region where the scattering strengths are more difficult to predict, as they depend on the details of the surface and wind characteristics. These observations lead to the idea that there are two mechanisms that dominate the scattering of sound from the surface. In the perturbation theory regime, air–water interface scattering is the dominant mechanism; in the Chapman–Harris regime, another mechanism such as scattering from subsurface bubble clouds must dominate the scattering process. The transition region is then the part of the frequency and wind speed domain where the two effects are competing.

Acoustic scattering from an air‐filled cylindrical shell with welded flat plate endcaps: Experimental and theoretical study
View Description Hide DescriptionMany authors have already studied the acoustic scattering from infinite cylinders or cylindrical shells both theoretically and experimentally. When the shells are insonified in a direction perpendicular to its axis, some circumferential waves propagate. When the insonification is not perpendicular to the axis of the shell, some helical waves propagate. In this paper, the influence of the length limitation of the shell on the different waves which propagate around the shell is studied. In the frequency range used in this work with a normal insonification, there was no difference between an infinite and a finite length shell. With an oblique incidence (10°), there were several resonances with the same vibration mode n but with different frequencies that were close to each other. A calculation, described in this paper, explains these phenomena.

Inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions
View Description Hide DescriptionThe goal of many underwater acousticmodeling problems is to find the physical parameters of the environment. With the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion. The inversion is posed as an optimization problem, which is solved by a directed Monte Carlo search using genetic algorithms. The genetic algorithm presented in this paper is formulated by steady‐state reproduction without duplicates. For the selection of ‘‘parents’’ the object function is scaled according to a Boltzmann distribution with a ‘‘temperature’’ equal to the fitness of one of the members in the population. The inversion would be incomplete if not followed by an analysis of the uncertainties of the result. When using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution. The many samples of the models are used to estimate the a posteriori probabilities of the model parameters. Thus the uniqueness and uncertainty of the model parameters are assessed. Inversion methods are generally formulated independently of forward modeling routines. Here they are applied to the inversion of geoacoustic parameters (P and S velocities and layer thickness) in the bottom using a horizontally stratified environment. The examples show that for synthetic data it is feasible to carry out an inversion for bottom parameters using genetic algorithms.

Spatial and source level distributions of ice cracking in the Arctic Ocean
View Description Hide DescriptionThis paper reports measurements of the spatial and source intensity level distributions of icecracking events occurring in the rough, central Arctic pack ice. These distributions are computed from a total of 916 detected events covering approximately 2 h of data distributed over several days during April 1988. Measurements of individual events were obtained over the frequency band 16–200 Hz on a 22‐element vertical array and a 7‐element horizontal array deployed below the Arctic pack ice in 420 m of water. The observed spatial distribution of detected events is consistent with a uniform distribution. Source levels from 110 to 180 dB//μPa^{2}/Hz at 1 m were measured. The calculated source level distribution for all events approximates a linearly decreasing function on a log‐dB scale of the number of events versus source level. The median occurrence of events having source levels within a 1 dB band centered at 110 dB//μPa^{2}/Hz at 1 m was 4 events per square kilometer per minute. This falls to 10^{−2} events per square kilometer per minute at 140 dB//μPa^{2}/Hz at 1 m. The mean and maximum numbers of events are two and ten times greater, respectively.

Pressure ridging spectrum level and a proposed origin of the infrasonic peak in arctic ambient noise spectra
View Description Hide DescriptionEvidence is presented that the infrasonic peak observed in the 10‐ to 20‐Hz region in Arctic ambient noise spectra may result from a combination of the source spectrum of pressure ridging and the effects of propagation loss on this spectrum. This peak has been attributed to a hypothetical source spectrum but may also be explained by a minimum in the propagation loss. The received spectral level of a nearby active pressure ridge was measured to be monotonously decreasing (from 2–200 Hz), while both measurements and modeling studies indicate a minimum in propagation loss versus frequency near 30 Hz. When the propagation loss effects are included, the resulting spectra of either a single event at a range of tens of kilometers or a distribution of events separated by tens of kilometers resembles the broad infrasonic peak found in the ambient noise.