Index of content:
Volume 75, Issue 3, March 1984

Transverse stresses in plane and cylindrical Rayleigh waves
View Description Hide DescriptionPlane and cylindrical Rayleigh waves are shown to involve tractions perpendicular to the propagation direction, on planes perpendicular to both the free surface and direction of propagation. Experiments show that backscatter from interruptions of these transverse tractions is sufficiently efficient to allow the observation of planar cracks the planes of which are perpendicular to the free surface and contain the propagation direction.

A unified theory for elastic wave propagation in polycrystalline materials
View Description Hide DescriptionWe have developed a unified approach to solve for the attenuation and phase velocity variations of elastic waves in single‐phase, polycrystalline media due to scattering. Our approach is a perturbation method applicable for any material whose single‐crystal anisotropy is not large, regardless of texture, grain elongation, or multiple scattering. It accurately accounts for the anisotropy of the individual grains. It is valid for time‐harmonic waves with all ratios of grain size to wavelength. It uses an autocorrelation function to characterize the geometry of the grains, and thereby avoids coherent artifacts that occur if the grains are assumed to have symmetrical shapes and suggests new methods for characterizing distributions of grains that are irregularly shaped. We have carried out numerical calculations for materials that are untextured and equiaxed, and have cubic‐symmetry grains and an inverse exponential spatial autocorrelation function. These calculations agree with the previous calculations which are valid in the Rayleigh, stochastic, and geometric regions, and show the transitions between these regions. The complex transition between the Rayleigh and stochastic regions for longitudinal waves, and the severe limitations of the stochastic region for grains with fairly large anisotropy are of particular interest.

Rayleigh waves in a poroelastic half‐space
View Description Hide DescriptionThe propagation of Rayleigh waves in a poroelastic half‐space is investigated for pervious and impervious surfaces. It is seen that the solutions presented by Jones for ‘‘Rayleigh waves in a porous elastic saturated solid’’ [J. Acoust. Soc. Am. 3 3, 959–962 (1961)] are incorrect. A plot of phase velocity versus Poisson’s ratio is presented.

Acoustic scattering by baffled membranes
View Description Hide DescriptionA flexible membrane is set in an infinite plane baffle. The plane separates an acoustic field from a vacuum. A time harmonic wave is incident from the fluid on the membrane. When the frequency of the incident wave is not close to an i n‐v a c u oresonant frequency of the membrane, the reaction of the fluid on the membrane is small. However, near a resonant frequency the fluid–membrane coupling is significant. We use the method of matched asymptotic expansions to obtain an asymptotic expansion of the scattered field. It is uniformly valid in the incident frequency. The expansion parameter ε≪1 is the ratio of the fluid and membrane densities. The outer expansion, valid away from resonance, is O(ε). The inner expansion, valid near resonance, is of order unity. The fluid loading is shown to have the effect of decreasing the resonant frequencies from those of the i n‐v a c u o membrane. Simple and double resonant frequencies are analyzed. However, the method is applicable to higher order resonant frequencies. Finally, the method is applied to normal incidence of a plane wave on a circular membrane.

Nearfield diffraction patterns at a sphere or cylinder
View Description Hide DescriptionA steady train of plane waves impinges normally on a right circular cylinder of infinite extent. The nearfield diffraction patterns for the normalized rms pressure were computed for values of k a from 1.5 to 6, where k is the wavenumber and a is the radius of the cylinder. Charts are given, showing the contours of rms pressure for k a=1.5, 2, 3, 4, 5, and 6, for each of two boundary conditions, pressure reflecting and pressure release. Each chart shows the contour pattern out to a distance of ten radii. The computed expressions are infinite series containing Bessel functions and their gradients. In some cases 75 terms in the series must be evaluated to get convergence to within 1%. The charts show that there are substantial areas where the pressure differs from the undisturbed value by 6 dB or more. Similar charts are given for the diffraction patterns at a sphere.

On the acoustics of a coupled space
View Description Hide DescriptionAn examination of acoustic wave propagation in a coupled space is presented. The analysis presented is limited to the first two longitudinal modes of the cavity. It is shown that the spacial behavior of the modes of vibration in the cavity is affected by the coupling discontinuity. The degree with which the discontinuity influences the pressure variation is parametrized by a single small parameter ε, where ε is the ratio of the typical cavity height, H _{0} to the cavity length L _{0}. An approximate solution for the pressure in the space is obtained using the method of matched asymptotic expansions. Experimental results are also presented as verification of the theoretical results.

Acoustic radiation from fluid‐loaded infinite circular cylinders with doubly periodic ring supports
View Description Hide DescriptionAnalytic expressions are derived for the farfield acoustic radiation from a point‐driven, fluid‐loaded circular cylindrical shell reinforced with doubly periodic ring supports. The ring supports interact with the cylindrical shell only through normal forces. The model includes the effects of fluid loading and interactions between supports. Predictions are compared to measured farfield acoustic radiation data taken on a finite circular cylindrical shell with doubly periodic ring supports. Characteristics of the acoustic radiation are examined by example and some physical interpretation of significant features are offered.

Point‐source representation for laser‐generated ultrasound
View Description Hide DescriptionThe stress‐free thermal strain corresponding to the temperature rise induced in a target by an incident laser pulse constitutes a volume source of ultrasound. In the present work, the appropriate point‐source representation is derived by starting from a general representation theorem for volume sources. A formal solution for the double (Hankel–Laplace) transform of the displacement potentials is obtained for axially symmetric configurations, with the point‐source lying within or on the surface of a half‐space or a plate. The Cagniard‐de Hoop technique is used to invert these double transforms. For the source on the surface of a half‐space, detailed results are presented for the wave‐front expansions, the displacement along the axis of symmetry and on the surface, the directivity pattern, and the partition of energy between longitudinal, transverse, and surface waves. For the source within or on the surface of a plate, only the epicentral displacement is considered in detail.

Wave‐front dislocations in the soundfield of a pulsed circular piston radiator
View Description Hide DescriptionWave‐front dislocations are lines in space along which wave fronts end, named by analogy with dislocations in imperfect crystals. Continuous waves and quasimonochromatic pulses (of continuous waves with slowly varying envelopes) are conveniently represented by complex‐valued wavefunctions, the zeros of which correspond to wave‐front dislocations. Pulse dislocations move through the wavefield, and may interact, as the pulse propagates. As examples of realistic model wavefields, the soundfields of a rigid circular piston radiator vibrating in a fixed rigid baffle plane, driven both by a sinusoidal source producing continuous waves and by this source modulated by a Gaussian envelope, are computed exactly and displayed. The birth of dislocations in the nearfield and their propagation with the pulse into the farfield are observed and discussed, and birth and death events in the nearfield are displayed in detail. The behavior of quasimonochromatic pulses and their dislocations may be understood in terms of the carrier wavefield, both qualitatively and, via a perturbation theory, quantitatively.

Distortion and harmonic generation in the nearfield of a finite amplitude sound beam
View Description Hide DescriptionDistortion and harmonic generation in the nearfield of a finite amplitude sound beam are considered, assuming time‐periodic but otherwise arbitrary on‐source conditions. The basic equations of motion for a lossy fluid are simplified by utilizing the parabolic approximation, and the solution is derived by seeking a Fourier series expansion for the sound pressure. The harmonics are governed by an infinite set of coupled differential equations in the amplitudes, which are truncated and solved numerically. Amplitude and phase of the fundamental and the first few harmonics are calculated along the beam axis, and across the beam at various ranges from the source. Two cases for the source are considered and compared: one with a uniformly excited circular piston, and one with a Gaussian distribution. Various source levels are used, and the calculations are carried out into the shock region. The on‐axis results for the fundamental amplitude are compared with results derived using the linearized solution modified with various taper functions. Apart from a nonlinear tapering of the amplitude along and near the axis, the results are found to be very close to the linearized solution for the fundamental, and for the second harmonic close to what is obtained from a quasilinear theory. The wave profile is calculated at various ranges. An energy equation for each harmonic is obtained, and shown to be equivalent within our approximation to the three‐dimensional version of Westervelt’s energy equation. Recent works on one‐dimensional propagation are reviewed and compared.

Nearfield of a large acoustic transducer. Part III: General results
View Description Hide DescriptionThe theory presented in two previous papers [Part I, J. Acoust. Soc. Am. 7 2, 1056–1061 (1982) and Part II, J. Acoust. Soc. Am. 7 4, 1013–1020 (1983)] is further developed and generalized to the case of no axisymmetry. Emphasis is given to a study of the parametric generatedsound. Asymptotic formulas are presented, showing the development of the difference frequency sound from the source (transducer) into the farfield. New numerical results for the axisymmetric case are given for the linear and the parametric field of a source which is not radiating uniformly. New experimental results are reported and compared with the theory.

Oscillation modes in single‐step Hartmann–Sprenger tubes
View Description Hide DescriptionWhen a high velocity jet is directed toward the mouth of a tube closed at the downstream end, large, nonlinear flow oscillations may occur within the tube. Shock waves propagate up and down the tube and generate strong heating of the tube walls. The device is called a Hartmann–Sprenger tube (in short, H–S tube). It has been proposed by several investigators to strengthen the shock waves and consequently the heatingeffects by tapering the tube. Conical and multistepped configurations have been investigated, but also tubes having a sudden area contraction (single step). This latter geometry produces remarkable pressure and thermal heating amplification compared to a constant area tube. The paper presents theoretical and experimental results obtained for the single‐step H–S tube. It is shown that several oscillation modes can exist. These are separated by intervals of instability. The influence of geometrical parameters (upstream to downstream cavity diameter and length ratios) and of jet Mach number on oscillation mode is investigated.

The Mid‐Ocean Acoustic Transmission Experiment, MATE
View Description Hide DescriptionAn experiment to measure phase (travel time) and intensity fluctuations in sound pulses transmitted at 2, 4, 8, and 13 kHz over an 18.1 km wholly refracted Fermat path is discussed. Simultaneously with the acoustic monitoring the index of refraction fluctuations were measured in space and time with sufficient resolution to determine the correlation function of the medium. The site was the Cobb Seamount in the northeast Pacific (46°46′N, 130°47′ W), and the time period was 30 days in June–July, 1977. In terms of both the quality and quantity of acoustic and oceanographicmeasurements, this experiment represents a significant improvement over an earlier experiment in the same location [J. Acoust. Soc. Am. 6 0, 46–59 (1976)]. The acoustic measurements cover a wider range of acoustic frequencies and more closely represent measurements from a single Fermat path. Approximately 25% of the acoustic data are discussed here; the representations of the correlation function of the index of refraction are based on all of the oceanographic data. The physical processes responsible for the fluctuations in the index of refraction are those due to the tides, internal waves, and finestructure. The effects of internal waves are treated in detail. The moments of the observed intensity fluctuations are discussed, as are the spectral distributions of the second moments of phase and intensity. The observations are compared with theoretical predictions based on the Rytov approximation and on a multiple scatter formulation (approximate solution to the fourth moment equation).

Ray directions, wave normals, and rigorous ray tracing
View Description Hide DescriptionHerein some exact effective sound velocity profiles for rigorous ray tracing are developed numerically. The equations of motion for rigorous ray tracing are developed and it is shown that in general a ray is not normal to the wave surfaces of constant phase.

Sonar estimates of seafloor microroughness
View Description Hide DescriptionThis paper presents an analysis of the effects of microroughness of the ocean bottom on a sonar signal. The results best apply to features where the roughness amplitude is less than one‐quarter of an acoustic wavelength such as with ripples, beds of rocks, and nodules. The shape of the probability density function (PDF) of the echo envelope is examined in terms of the rms roughness and a new parameter, the correlation area of the bottom. The area is equal to the product of the x and y correlation distances along the floor. The PDF is shown to be extremely sensitive to small changes in the roughness. Furthermore by determining the rms roughness from standard coherent reflection measurements, the correlation area may be extracted directly from the PDF. Thus both vertical as well as lateral information is obtainable from sonar data. The technique can be used to discriminate between different types of bottoms that may have the same roughness but different correlation areas, for example a floor with ripples versus one with rocks or nodules. The analysis combines (1) a general statistical model employing the Rice PDF [S. O. Rice, in S e l e c t e d P a p e r s o n N o i s e a n d S t o c h a s t i c P r o c e s s e s, edited by N. Wax (Dover, New York, 1954), pp. 133–294], and (2) a theory originated by Eckart [C. Eckart, J. Acoust. Soc. Am. 2 5, 566–570 (1953)]. The analysis is applied to sonar data collected from the continental shelf near Cape Hatteras, North Carolina. The results are consistent with the known characteristics of the area.

Noise from Arctic Ocean earthquakes
View Description Hide DescriptionEarthquakes along the mid‐Arctic ridge radiate earthborne compressional and shear waves, which in turn excite the Arctic acoustic channel. These waterborne arrivals, called Twaves, have been observed about 300 km from the source and apparently enter the acoustic channel by scattering of vertical rays into nearly horizontal ones by the Arctic ice canopy above the source. The Twaves are acoustically energetic (up to 400 kJ), are of surprisingly long duration (up to 72 s at its 8‐dB down levels), have low‐frequency content (peaks in the 5–15‐Hz region), and have haystack spectra (4th power positive and negative dependence below and above the peak frequency, respectively). Characteristics of these sporadic noises are displayed for one event in a sonogram, in short time frequency spectra, in a time series, and in directional spectra. Directional analysis was accomplished with use of a large (∼1 km) two‐dimensional horizontal array. Speculations on duration of the observed events suggest that source depth, water‐column reverberation above the source, and source magnitude, including ‘‘rapid‐fire’’ multiple source excitations, could be the primary causes.

Using eigenvalue analysis to identify interference in ambient sea noise vertical directionality measurements
View Description Hide DescriptionAmbient noise vertical directionality measurements at low frequencies have shown that noise arrives from long distances at near horizontal angles, from moderate distances at larger angles, and from local sources at high angles. Therefore levels of noise from different sources can be measured by examining vertical linear array beam powers at the appropriate angles. However, when measurements are made, it is important to be able to distinguish between acoustic signals, ambient noise, and data contamination. Some experimental results are examined, using conventional and adaptive beamforming and eigenvalue–eigenvector decomposition, and used to establish criteria useful in deciding whether the measurements are ambient noise or otherwise.

Wave propagation in an infinite long bar of arbitrary cross section and with a circular cylindrical cavity
View Description Hide DescriptionThis paper presents a method for solving wave propagation problems of an infinite bar of arbitrary cross section with a circular cylindrical cavity. In the analysis the exact solution of the wave equations based on the three‐dimensional theory of elasticity which satisfies the boundary conditions of the inner circular cylindrical cavity has been utilized. The boundary conditions of the outer arbitrarily shaped surface of the bar are satisfied by use of the Fourier expansion collocation method. The analysis derives the frequency equation for determining the phase velocities of the bar of arbitrary cross section with the cavity. As an example numerical calculations have been carried out for an elliptical cross‐section bar with a circular cylindrical cavity.

Vibration and stability of orthotropic circular cylindrical shells subjected to axial load
View Description Hide DescriptionAn analysis is presented for the vibration and stability of an orthotropic circular cylindrical shell subjected to an axial static load by use of the transfer matrix approach. The applicability of the thin‐shell theory is assumed, and the governing equations of free vibration of the shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the matrix has been determined by a solution to the equation, the natural frequencies and the critical loads are calculated numerically in terms of the elements of the matrix for a given set of boundary conditions at the edges. This method is applied to orthotropic circular cylindrical shells simply supported at the edges, and the effects of the length ratio, orthotropy, and axial load on the vibration and stability are studied.

Thresholds of perception of vibration in recumbent men
View Description Hide DescriptionThe thresholds of perception of vibration by recumbent men are a significant index for the governmental agency concerned with regulation of vibration exposure. The thresholds of perception of continuous sinusoidal vibrations and single and multiple bursts of sinusoidal vibrations in the horizontal and vertical directions were investigated in recumbent men. We found that the threshold curves, as a function of the frequency, had different characteristics for vertical vibrations than for horizontal vibrations in the recumbent position. The threshold values for pulsed vibrations became smaller (easier to perceive) as the bursts were elongated until saturation occurred at 4 s duration. Threshold values for pulse durations longer than 4 s were the same as those for continuous vibration. This suggests the existence of temporal integration of sensation of vibrations as in psychoacoustics.