Volume 81, Issue 5, May 1987
Index of content:

Acoustic waves in alternating fluid/solid layers
View Description Hide DescriptionThis article describes the results of ultrasonicexperiments made to investigate several features of wave propagation in parallel fluid/solid layer systems and compares the results to theory. Immersion experiments were made at frequencies from 0.2–2 MHz on systems composed of water/Plexiglas and water/aluminum parallel layers. The one wave normal to the layering, and the two waves that can propagate parallel to the layering were both observed. Key experimental results demonstrating anisotropy, wavenumber and frequency stop bands, and phase velocity dispersion are shown that are in agreement with theory. The exact analytical theory based on first principles and the corresponding model experiments have implications leading to a better understanding of Biot’s theory of long wavelength propagation in a fluid saturated porous elastic medium.

Anomalous polarization of elastic waves in transversely isotropic media
View Description Hide DescriptionThe orientation of the displacement vector U of a plane wave in a homogeneous anisotropicelastic medium is the polarization of that plane wave. For transversely isotropic media, U of the fastest plane wave propagating in a given direction need not be in or near the direction of propagation, i.e., the direction of the slowness vector s. Moreover, with the x _{3} axis the transverse axis of the medium, when c _{1} _{3}+c _{4} _{4}<0, there are directions of propagation for which U can be perpendicular to s which means that the first arrival in that direction is a purely transverse wave. The two plane waves whose displacement vectors lie in the plane of the direction of propagation and the x _{3} axis—the faster usually called ‘‘quasi‐P’’ and the slower usually called ‘‘quasi‐S V’’—have mutually orthogonal displacement vectors. The polarization of these waves as a function of propagation direction depends strongly on the sign of c _{1} _{3}+c _{4} _{4} whereas the magnitudes of the slowness vectors, which give the shape of the slowness surface, do not. In the x _{3} direction and perpendicular to the x _{3} direction the waves are purely longitudinal and purely transverse. When c _{1} _{3}+c _{4} _{4} is positive, which is the usual case, the particle displacement vectors rotate in the same sense as the slowness vector. When c _{1} _{3}+c _{4} _{4} is negative, which is the ‘‘anomalous’’ case, the sense of rotation of the particle displacement vector is opposite to that of the slowness vector and there always exists a direction of propagation in the medium for which U of the fast (or inner or quasi‐P) sheet of the slowness surface is perpendicular to that direction and U of the slow (or outer or quasi‐S V) sheet is parallel to that direction. The stability conditions on the transversely isotropic moduli even admit media that are (almost) kinematically isotropic, i.e., characterized by spherical wave fronts emanating from point sources, but which are characterized by anomalous polarization.
A layered medium can be equivalent, in the long‐wavelength limit, to an anomalous transversely isotropic medium. For a layered medium composed of two alternating constituent substrates, this can occur when the larger volume fraction constituent has a negative Poisson’s ratio, the smaller volume fraction constituent has a positive Poisson’s ratio, and the ratio of the shear modulus of the negative Poisson’s ratio constituent to the shear modulus of the positive Poisson’s ratio constituent is very large.

An extrapolation procedure for transient reflection measurements made on thick acoustical panels composed of lossy, dispersive materials
View Description Hide DescriptionThe underwater acoustic behavior of an elastomeric coating material is frequently evaluated by performing a reflection experiment on a sample, e.g., a rectangular panel, of the coating material. Extrapolation of the transient portion of the reflected wave in such measurements is required when steady‐state conditions do not occur prior to interference from extraneous reflections. This article describes a technique for the extrapolation of measurements made on thick acoustical panels (the interrogating wave is assumed to be normally incident). The technique involves fitting a multiple‐layer model to the experimental data via a least‐squares process. The model assumes homogeneous and isotropic panel layers. The technique can perform the extrapolation using a much shorter leading portion of the reflected wave than is possible with other existing techniques. Experiments on three sample panels were conducted to investigate the usefulness of the technique. The first panel consists of three simple homogeneous layers. The second and third samples are fabricated from viscoelastic layers including macrovoids. The experiment covered the frequency range 2–20 kHz. The measurements on the simple three‐layer panel are in reasonably good agreement with theoretical calculations based on the known acoustical properties of the layers. The acoustical properties of the more complicated panels are unknown. However, the extrapolations based on the measurements obtained from these panels appear to have reasonable behavior.

Sample boundary effect in acoustic attenuation of fluid‐saturated porous cylinders
View Description Hide DescriptionIt was shown previously, by using Biot theory, that there exists an attenuation in the low‐frequency elastic modulusmeasurement on fluid‐saturated porous rock cylinders caused by the open‐pore boundary condition. This attenuation is associated with the energy dissipation of the viscousflow of the pore fluid in and out of an open‐pore boundary of a fluid‐saturated rock sample. For the extensional mode, the relaxation frequency of this attenuation is directly proportional to the permeability of the rock and inversely proportional to the viscosity of the pore fluid and the square of the sample radius. In this article, experimental studies that support the theoretical prediction of this sample boundary effect are reported. Experiments of varying saturation, sample radius, pore fluid viscosity, and rock permeability were carried out. The results, though consistent with the theoretical prediction, are not satisfactory in a quantitative sense because of the lack of an idealized sample. It was found, however, the procedure of jacketing the sample with an aluminum sleeve and measuring it at ambient pressure condition is not sufficient to remove the attenuation caused by the boundary effect completely.

Asymptotic modal analysis for dynamic stresses of a plate
View Description Hide DescriptionAsymptotic modal analysis has been applied to stress analysis of a uniform thin rectangular plate under point forces that are bandlimited white noise. The asymptotic limits of the temporal averages of the bending stresses and the distortion energy have been determined. It is shown that the dependence on the center frequency of the asymptotic limits of stresses is different from that of deflection. The concentration factors with respect to various locations on the plate are discussed.

Analysis of liquid‐core cylindrical acoustic waveguides
View Description Hide DescriptionTransmission properties of guided modes in liquid‐core cylindrical acoustic waveguides are investigated. It is observed that for each value of the circumferential order n the first mode becomes of Stoneley‐type above a certain frequency. There are two modes without cutoff frequencies, in contrast to only one mode in solid‐core waveguides. They are the first modes with n=0 and 1. The application of liquid‐core waveguides in sensor devices is pointed out and some preliminary experimental results are reported.

Three‐dimensional acoustic analysis of a circular expansion chamber with side inlet and end outlet
View Description Hide DescriptionNoiseattenuationcharacteristics of a simple expansion chamber with a side inlet and an end outlet are studied. A theoretical method is derived to investigate the influences caused by higher‐order modes, using a three‐dimensional analysis in which the chamber is considered as a piston‐driven circular cylinder. Also, quantitative estimation for the transmission loss can be performed, using the derived four‐pole parameters. Accordingly, the characteristics of the chamber, as a result of the interactions between the plane wave and the transverse waves, can be investigated easily with respect to the relative locations of the inlet/outlet and chamber length. Experiments are performed for the verification of the theory. In the case of the chamber with a concentric end outlet, plane‐wave theory agrees with the theoretical and experimental results below the rather high frequency range, but not for the case of the chamber with an offset end outlet. Experimental results are in good agreement with the theoretical results obtained.

An implicit least‐square method for the inverse problem of acoustic radiation
View Description Hide DescriptionA simple and natural method, called the implicit least‐square method, is developed to solve the inverse problem, especially for first‐kind Fredholm integral equations of acoustic radiation. Unlike most previous methods, there are no artificial constraints or parameters to be specified. This method is proven to be equivalent to the pseudoinverse method and is tested in three examples: (i) inversion of Poisson’s formula of harmonic continuation, (ii) inversion of the free‐space turbulent flamenoiseradiation for the heat release rate source, and (iii) inversion of the ducted combustion system noiseradiation for the heat release rate source. Comparisons performed using the results of the present prediction, the exact solution, and the experimental data in these examples are satisfactory.

Surface admittance of highly porous foams with finite stiffness
View Description Hide DescriptionThis work responds to some comments on the surface admittance of highly porous foams with finite stiffness by Allard e t a l. [J. Acoust. Soc. Am. 7 9, 1734–1740 (1986)]. The analysis, based on a more exact theory of sound propagation in flexible foams with finite stiffness, shows that stiffness effects should not be ignored even at frequencies well above the so‐called decoupling frequency, and also that they can contribute significantly to the admittance (conductance and susceptance) at lower frequencies. The conductance is increased somewhat while the susceptance is decreased at low frequencies. The predictions are compared with experimental data available at high frequencies on an open‐cell, fully reticulated foam with finite stiffness, and the agreement is much improved.

The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations
View Description Hide DescriptionThis article is concerned with the problem of obtaining a unique solution for radiation and scattering problems at characteristic wavenumbers when a boundary integral equation formulation is used. It is shown that the combined Helmholtz integral equation formulation (CHIEF) method works even when numerous interior points lie exactly on nodal surfaces of a mode corresponding to an eigenfrequency of the related interior problem, when at least one interior point does not lie on a nodal surface. CHIEF is compared to the Helmholtz gradient formulation (HGF) for circumventing nonuniqueness and is found to yield a more accurate solution. A procedure is used to indicate the solution error when using integral equation methods, with or without a technique to circumvent nonuniqueness. This procedure uses the velocity potential of an interior point as an indicator of solution error. In all cases considered, the interior potential correctly indicated a good or bad solution; whereas the matrix condition number falsely indicated a bad solution in several instances.

Nearfield acoustic holography (NAH) II. Holographic reconstruction algorithms and computer implementation
View Description Hide DescriptionThe basic theory treating steady‐state acoustic radiation problems in the nearfield has been presented in several articles on nearfield acoustic holography. In this article, the approximations and assumptions necessary to reduce the infinite and continuous convolution integrals encountered in these problems to a finite and discrete form, suitable for high‐speed numerical processing, are illuminated theoretically and tested numerically. To evaluate the convolution integrals two assumptions are made: First, the boundary field may be replaced with a patchwise constant field for reasonably small patches; and, second, the field is negligible outside of a finite region. With these two assumptions, the problem reduces to one of representing the Green’s functions. Six methods of sampling or representing the Green’s functions are developed, and these are compared theoretically and numerically.

A criterion for an energy vortex in a sound field
View Description Hide DescriptionMeasurements with intensity meters have shown that energy vortices exist in certain sound fields. In these vortices, sound energy flows around closed paths, in the steady state. Vortices occur in some sound fields (e.g., that of a point source near a reflecting edge), but not in others (e.g., that of a plane rigid piston in a plane rigid baffle). It is shown that in a two‐dimensional or axisymmetric sound field, a necessary and sufficient condition for a vortex to exist is the presence of an isolated maximum or minimum in the stream function. Two examples are given for a vortex in (a) a duct of square cross section, and (b) the field of two monopole sources, one of which just extinguishes the other. Some relations for the interaction between two monopole sources are also given.

Acoustic radiation force on a particle in a temperature gradient
View Description Hide DescriptionA general expression is derived for the acoustic radiation force on a small spherical particle of radius R in a standing wave field in a temperature gradient.The case of a particle inside a long tube chamber with a temperature gradient along the axis of symmetry is examined in more detail. The analysis is considerably simplified by the introduction of the mass flux density potential ψ. Assuming k R≪1, and neglecting convection,acoustic streaming,heat conduction, and viscosityeffects, an expression is obtained for the force that consists of a ‘‘local’’ version of Gor’kov’s result as well as correction terms of order β/k, where β∼(1/T)(d T/d z).

A numerical study of thermal effects on nonlinear bubble oscillations
View Description Hide DescriptionAn integral‐differential system was derived by Miksis and Ting describing the nonlinear oscillations of a gas bubble including thermal and viscous effects. Here, an efficient numerical scheme is presented to solve this system for long times relative to the forcing period. Examples are presented and compared with the Rayleigh–Plesset equation, which has no thermal damping. Numerical results show that the initial free oscillations are damped out much faster when thermal damping is included. Also shown is the fact that it is possible for a bubble to have its mean radius grow slowly with time. In this case for large time the bubble will approach a new constant mean radius, which is larger than the initial equilibrium radius. For the special case of small amplitude forcing, asymptotic periodic solutions for very large time are constructed and a method to systematically derive the higher‐order terms is demonstrated.

Impulse propagation in a neutral atmosphere
View Description Hide DescriptionComputer simulation studies are presented for the propagation of an impulsive sound over a uniform impedance boundary in the presence of a neutral atmosphere. Based on typical explosive and gunfire waveforms, results from two levels of approximation arising from continuous wave propagation theory are compared and the simpler equation, involving just the plane‐wave reflection coefficient and the boundary loss factor, is found to be adequate over a range of source–receiver geometries. The effect of changing the impulse shape and the ground impedance is discussed by considering the frequency dependence of the effective image source and, in particular, on the ground wave contribution to this source. A brief comparison is made between the predictions and measurements using two different duration impulses.

Absorption of sound in water fog composed of submicron droplets
View Description Hide DescriptionA previous review [J. Acoust. Soc. Am. 7 0, 1213–1219 (1981)] emphasized sound absorption in water fog of droplets within sizes near 10 μ. This supplemental article presents results for the core where droplet size is much smaller, ≂0.01 μ. Theoretical formulation for these small droplets is shown to be basically the same as for the larger droplets. The attenuation coefficient due to mass transfer, which some authors claimed to be two (or three) orders of magnitude larger for small drops than for large ones, is accompanied by an increase in the frequency of maximum absorption by the same orders of magnitude. A correction factor is also introduced for the relaxation times from the viewpoint of modern fog kinetics. The result predicts a counter effect or a drastic decrease in the absorption abnormality due to submicron droplets, but the effect is less, the larger the droplet, which, therefore, may lead to a theoretical generalization of the problem applicable to droplets of all sizes.

Factorization and path integration of the Helmholtz equation: Numerical algorithms
View Description Hide DescriptionThe propagator for the reduced scalar Helmholtz equation plays a significant role in both analytical and computational studies of acoustic direct wave propagation. Path (functional) integrals are taken to provide the principal representation of the propagator and are computed directly. The path integral is the primary tool in extending the classical Fourier methods, so appropriate for wave propagation in homogeneous media, to inhomogeneous media. For transversely inhomogeneous environments, the n‐dimensional Helmholtz equation can be exactly factored into separate forward and backward one‐way wave equations. A parabolic‐based (one‐way) phase space path integral construction provides the generalization of the Tappert/Hardin split‐step FFT algorithm to the full one‐way (factored Helmholtz) wave equation. These extended marching algorithms can readily accommodate density profiles and range updating, and further, in conjunction with imbedding methods, provide the basis for incorporating backscatter effects. In a complementary manner, for general range‐dependent environments, elliptic‐based (two‐way) path integral constructions lead to an approximate representation of the propagator (Feynman/Garrod) and a natural statistical (Monte Carlo) means of evaluation. Taken together, the path integrals provide the basis for a global analysis in addition to providing a unifying framework for dynamical approximations, resolution of the square root operator, and the concept of an underlying stochastic process. The one‐way marching algorithms are applied to ocean acoustic environments, seismological environments, and extreme model environments designed to establish their range of validity and manner of breakdown.

The reflection of radiation from randomly irregular surfaces
View Description Hide DescriptionSurface interactions of radiation propagating in a nonuniform, scattering medium are treated using the strength and diffraction parameters, which currently serve to describe volume scattering in the application of the path‐integral formalism. A procedure for tracing the volume diffraction parameter through specular surface reflections is outlined and illustrated. Subsequently, a phase screen model is used to account for scattering by surface irregularities. The statistics of these irregularities take up the role of the statistics of the refractivity fluctuations, and the Rayleigh roughness parameter replaces the strength parameter. The diffraction parameter is defined using the correlation length of the surface irregularities and an appropriate surface phase curvature. The application is illustrated by the computation of the two‐point, two‐frequency correlation for a surface‐to‐surface multipath in a linear sound‐speed channel.

Numerical modeling of acoustic tomography in the Straits of Florida: Sensitivity to bathymetry
View Description Hide DescriptionAn acoustic model based on the split‐step parabolic equation technique is used to study the effects of irregularities in bathymetry on the transmission loss or equivalently, sound energy distribution for continuous wave (cw) acoustic signals. In particular, contours of transmission loss in the range‐depth plane are predicted for the propagation of a 510‐Hz cw signal across the Straits of Florida between Miami, Florida and Bimini, Bahamas. The predicted intensity contours exhibit recognizable energy bundles that correspond to actual ray bundles. The stability of these bundles is studied as random bottom irregularities are introduced. The distribution of acoustic energy is found to be insensitive to random variations in bottom bathymetry of up to 5 m rms. The same model is used to investigate the feasibility of transport and depth‐averaged temperature measurements of the Florida current by acoustic method. Energy contour plots are predicted for several source–receiver geometries. A system of five transceivers positioned to form two triangles sharing a common vertex in the eastern edge of the Miami terrace is evaluated as a monitoring strategy.

Scintillations of partially coherent signals in nonscattering channels
View Description Hide DescriptionThe quadratic approximation is used to derive a procedure for computing the mean‐square intensity in a channel excited by a partially coherent source, using the characteristics (rays of geometrical acoustics) of the four‐point coherence equation, and their properties. The procedure is employed to obtain exactly the scintillation field of a partially coherent Gaussian beam emerging from a weak phase screen into a quadratic channel. A simple approximate formula for the mean‐square intensity in the farfield of a localized source is derived and tested: It is found to closely reproduce the aforementioned exact result for a quadratic channel, except for the immediate vicinity of focal planes. Various modes of application of the approximate formula are discussed.