Index of content:
Volume 87, Issue 2, February 1990

Monte Carlo studies of multiple scattering of waves in one‐dimensional random media
View Description Hide DescriptionA numerical study was undertaken for the ensemble average, or coherent, wave in a one‐dimensional random medium composed of uncorrelated point scatterers. Average responses as constructed from numerical solutions of the wave equation were compared to the predictions of the quasicrystalline (QCA) and self‐consistent theories. As anticipated, the QCA was found to fail whenever the Waterman and Truell criterion was not satisfied, and also in the case of high scatterer density and low scatterer strength where the attenuation was badly predicted by the QCA. The self‐consistent coherent potential approximation failed only under extreme conditions of scatterer strength or density. Nonlocality in the self‐energy had a recognizable effect on the average response only in the limiting case of infinite scatterer strength.

A fast exact numerical solution for the acoustic response of concentric cylinders with penetrable interfaces
View Description Hide DescriptionA fast exact numerical algorithm is presented that computes the line source acoustic response of concentric cylinders filled with acoustic material of contrasting impedances. The fast exact numerical method solves a cylinder scattering problem by a boundary integralequation method. By azimuthal symmetry, the discrete approximation of these integral equations are discrete periodic convolutions with respect to the angular variable. Application of a discrete Fourier transform reduces the boundary integral equations to a system of linear algebraic equations. The response is economically computed by algebraic division and an inverse fast Fourier transform. The dominant cost per temporal frequency is O(N log_{2} N) algebraic operations, where N is the maximum number of discretization points along the circumference of the cylinder.

Shear horizontal surface waves on an isotropic elastic cylinder
View Description Hide DescriptionThis paper comprises theoretical and practical results concerning the problem of propagation of surface shear horizontal (S H) waves on monolithic, elastic cylinders. It was proved that S Hsurface waves have a multimode structure and their pulses propagate with a velocity that tends asymptotically to the velocity v _{0} of the shear bulk waves for increasing frequency. On the other hand, the phase velocity v _{ p } of surface S Hwaves decreases asymptotically to the velocity v _{0}, as a function of frequency. For the obtained theoretical formulas, numerical calculations were performed and are valid for homogeneous elastic cylinders. The experiment was carried out for glass cylinders. Satisfactory agreement between theoretical and experimental results was stated.

Scholte wave characterization and its decay for various materials
View Description Hide DescriptionThe Scholte wave propagating at a liquid/solid interface is studied. A device associating an interdigital transducer and a thin piezoelectric film generates such a wave on dielectric substrates; appropriate sticking allows propagation on conducting mediums. The location of the Scholte wave was experimentally checked, its velocity was measured, its weak attenuation was verified, how it decays was widely examined in the liquid medium perpendicular to the interface.

Experimental investigation of the wave propagation on a point‐driven, submerged capped cylinder using K‐space analysis
View Description Hide DescriptionClassically, sparse accelerometer measurements are made on vibrating structures to help in deducing the physics of the vibration. However, the experimenter now has at his command more sophisticated measurement tools, such as nearfield acoustical holography or laser Doppler velocimetry, which provide much more data. Often complete mapping of the acceleration or displacements on the surface of these structures can be acquired. As a result, more sophisticated analysis tools must be developed. Such a tool useful for vibrating structures which are basically cylindrical or planar, is presented herein. The measured spatial velocity is decomposed at fixed temporal frequencies into its helical‐wave spectrum, also known as the K‐space spectrum. This decomposition contains a great deal of information about the physics of the vibrator. For example, it provides the dominant wavenumbers (the dispersion diagram) of free waves that exist on the shell. These free waves reach maximum amplitudes when close to a resonance frequency. The decomposition also provides an indication of the modal density of the shell. This technique is applied to experimental measurements on a shaker‐driven, fluid‐loaded, capped cylinder. The resulting helical wavenumber diagrams, plotted at a single frequency of excitation, show strong ‘‘figure 8’’ patterns. By comparison with helical‐wave spectra computed from infinite‐shell theory, it is shown that these patterns represent the wavenumber loci of the free waves that exist on the experimental shell. Excellent agreement between the measured helical‐wave spectrum and predictions from infinite‐shell theory are reported. The helical‐wave spectra of the acoustic pressure, mapped on a cylindrical contour in the extreme nearfield of the capped cylinder, is also presented. From this spectra, the free waves on the structure can be identified and, in particular, how they participate in acoustic radiation. The frequency region was k a=0.5–2.0.

A boundary integral formulation for thin‐walled shapes of revolution
View Description Hide DescriptionMuch of the recent literature on boundary elements has addressed the practical limitations of the method. One issue under current scrutiny appears to be the inapplicability of formulations based on the Helmholtz integral to free‐flooded shapes characterized by k h≪1, where k and h are the acoustic wavenumber and the object’s cross‐sectional thickness dimension. The present article develops and applies a modal boundary integral technique especially tailored to thin geometries of revolution. The problems chosen for its demonstration are cases of acoustic diffraction by an open‐ended cylindrical duct containing a sound source, where the scattering wall’s outer and inner surfaces are an infinitesimal distance apart, and are respectively rigid and either rigid or compliant. The study concludes that general shapes with k h≪1 or k h=0 should be treatable by at least one established numerical approach, after some analytical reinterpretation.

The angular and frequency characteristics of reflectivity from a solid layer embedded between two solids with imperfect boundary conditions
View Description Hide DescriptionIn this paper, a comprehensive model of an isotropic, homogeneous, solid layer embedded in between two half‐space solids with imperfect interfacial conditions is presented. The Thomson’s matrix technique for transfer of boundary conditions across a thin layer, based on recurrence formulas, coupled with separate normal and tangential rigidity representation for each interface was used. The reflection and transmission coefficients for oblique incidence of both longitudinal as well as transverse waves as a function of angle of incidence, incident frequency, interface condition, and material properties can be numerically computed through this model. Several studies of the reflection factors for a three‐medium case is used to provide insight on the adhesively bonded structures. The ultrasonic quality evaluation of the commonly used aluminum–epoxy‐resin–aluminum bond situation is dealt with here in detail.

Three‐dimensional Green’s function for fluid‐loaded thin elastic cylindrical shell: Formulation and solution
View Description Hide DescriptionThis paper treatssound radiation from a time‐harmonic point pressure source located either inside or outside a thin, homogeneous, infinitely long circular cylindrical elastic shell, which is immersed in different interior and exterior fluid media. This Green’s function problem is attacked by a combination of the method of separation of variables and the method of images applied to an infinitely extended azimuthal (φ) domain. The reduced one‐dimensional problems in the cylindrical (r,φ,z) coordinates are solved by general spectral techniques in terms of one‐dimensional characteristicGreen’s functionsg _{ r }, g _{φ}, g _{ z }, which depend on one or both of the two complex spectral separation parameters (spatial wavenumbers) λ_{1} and λ_{2}. While the one‐dimensional problems in the φ and z domains are straightforward, the presence of the shell in the radial domain introduces substantial complexity. The solution is obtained by defining the discontinuities in the pressure and normal displacement across the shell via recourse to the dynamical equations of motion inside the shell. The synthesis problem is made unique through a complete analysis of the spectral singularities of g _{ r,φ,z } in their respective complex planes, which permits selection of appropriate integration contours. A host of alternative representations, whose choice (concerning utility) is motivated by the parameter range of interest, can be derived from the fundamental spectral form. This is addressed in a companion paper [Felsen e t a l., J. Acoust. Soc. Am. 8 7, xxx–xxx (1990)], which also treats asymptotic reductions that lead to a variety of ray acoustic and other fundamental wave processes.

Three‐dimensional Green’s function for fluid‐loaded thin elastic cylindrical shell: Alternative representations and ray acoustic forms
View Description Hide DescriptionIn this paper, the general spectral integral form of the three‐dimensional pressureGreen’s function for a fluid‐loaded thin elastic cylindrical shell [Felsen e t a l., J. Acoust. Soc. Am. 8 7, xxx–xxx (1990)] is reduced to furnish two alternative representations that emphasize propagation phenomena associated essentially with the radial–azimuthal (r,φ) and the radial–longitudinal (r,z) coordinates, respectively. For the former, a decomposition of the point source field into a continuum of linearly phased z‐directed line sources defines the problem parametrization, whereas for the latter, the decomposition is into a discrete infinity of ring sources with azimuthally periodic (angular harmonic) linear phasing. The reduced forms obtained in this manner are then examined in appropriate parameter regimes. For external phenomena in the (r,φ)‐favored formulation, asymptotics leads to ray acoustic interpretations for the total field in terms of the conventional incident and reflected waves, augmented by shell‐guided creeping waves and leaky waves that are excited by phase matching on the shell surface, as well as trapped waves in the shell excited by evanescent tunneling from the source. The shell‐guided ray fields, which represent quasicompressional, quasiflexural, and quasishear phenomena, exhibit anisotropic behavior. In parameter regimes that emphasize axial guiding along the shell and the interior fluid [favoring (r,z)], the trapped waves, which are less important for the external processes, become the dominant constituents.

Nonlinear viscoelastic effects on the harmonic generation of a finite‐amplitude acoustic wave
View Description Hide DescriptionThe effect of fluid viscoelasticity on the second‐harmonic wavegenerated by a planar acoustic wave is considered. It is shown that the growth, decay, wavenumber, phase, and amplitude of the second‐harmonic wave are all modified by fluid viscoelasticity. The effect on the amplitude, the most readily measured property, is discussed in detail. It is found that viscoelasticity in the form of frequency thinning causes a shift in the maximum of the second‐harmonic amplitude to distances further from the acoustic source. Finite linear and nonlinear viscoelasticity are found to cause both harmonic suppression and harmonic enhancement, depending on the properties of the fluid and the dimensionless frequency of oscillation. The harmonic suppression predicted here may be associated with changes in the noise spectrum of cavitation that have been observed for dilute polymer solutions.

Acoustic radiation pressure on a rigid cylinder: An analytical theory and experiments
View Description Hide DescriptionSimple and general analytical expressions are derived for the acoustic radiation force on a long rigid cylinder with a small diameter, whose axis is perpendicular to the wave propagation. Results are expressed in terms of the time‐averaged densities of kinetic and potential energies of the incident sound field. For the case of a standing‐wave field, which was used in these experiments, the theoretical results agree well with the experimental observations.

Spectral reconstruction of uniformized wave fields from nonuniform ray or adiabatic mode forms for acoustic propagation and diffraction
View Description Hide DescriptionRay acoustic and adiabatic mode representations provide effective means for charting sound transmission in relatively complicated propagation and diffraction environments, under operating conditions that validate the use of such approximate waveforms. A principal limitation of these physically incisive and conveniently implemented algorithms is their failure in transition regions. For ray acoustics, transitions occur near caustics, foci, critical reflection angles, shadow boundaries, etc.; adiabatic modes undergo transitions when cutoff‐inducing or other smooth environmental changes transform their initially well trapped into radiated (leaky) energy. Instead of constructing the uniformized spectral representations required in transitional domains by an independent, more general, analysis, it is shown here that the uniformized spectral forms for a large variety of propagation and diffraction phenomena can be synthesized directly from ray acoustic or adiabatic mode data. This feature should be helpful in generalizing existing acoustic ray or adiabatic mode algorithms to accommodate transitional wave processes. The theory is presented for two‐dimensional configurations and fluid media, but the same considerations apply also in three dimensions and for multiwave effects due to elasticity or anisotropy.

The normal‐mode theory of air‐to‐water sound transmission in the ocean
View Description Hide DescriptionThe normal‐mode theory is presented for the transmission of sound from a stationary source in a homogeneous, stationary, air layer into an arbitrarily stratified ocean. Transmission loss calculations are performed for a Pekeris‐type shallow‐water environment consisting of an isospeed water layer over a uniform elastic solid seabed. Notable features of the results are: the sensitivity of transmission loss to bottom type, the weak dependence of incoherent transmission loss upon source height, and a 25 log r range dependence of average transmission loss in the mode‐stripping region. Finally, some approximate intensity‐range relations are proposed for shallow‐water propagation.

A parabolic wave equation based on a rational‐cubic approximation
View Description Hide DescriptionA parabolic wave equation based on a rational‐cubic approximation of the square root operator is presented. The equation yields accurate solutions in cases with angles of propagation up to about 89 deg. In the homogeneous case an analytic solution to the equation has been found.The correspondence between approximating the square root operator and the modal wavenumbers of the exact solution of the Helmholtz equation is shown. By using the analytic solution of the rational‐cubic parabolic equation (PE), comparisons are made with the rational‐quadratic PE and the Helmholtz equation.

One‐way wave equations for seismoacoustic propagation in elastic waveguides
View Description Hide DescriptionOne‐way or parabolic wave equations for time‐harmonic propagation in two‐dimensional elastic waveguides are considered. It is shown that the direct application of a rational linear approximation with real coefficients to the elastic wave propagation case results in exponential growth in the numerical solutions. Elementary analysis demonstrates that this kind of approximation does not treat properly the modes with complex wavenumber which can exist in elastic waveguides. A new bilinear square‐root approximation with complex coefficients is introduced that accommodates all mode types and leads to stable numerical solutions. In the case of thick elastic layers (such as sea‐bottom sediments), this new approximation gives accurate total field prediction. When thin elastic layers (such as ice on the sea surface) are present, however, the method introduces excessive damping to modes with wavenumbers significantly different from a reference wavenumber.

Range and depth‐averaged fields in ocean sound channels
View Description Hide DescriptionBy use of the generalized phase‐integral approximation of the mode depth function and representing the square of the depth function as a sum of slow‐varying and fast‐varying components, a concise expression of the average intensity in an ocean channel is obtained by smooth averaging the intensities over range and depth. This expression is not divergent and will degenerate into the Brekhovskikh, Smith, and Weston one when the frequency approaches infinity. The caustic corrections in the vicinity of the source and its conjugate depths and the contributions of inhomogeneous waves are discussed and the numerical results for the linear, bilinear, and canonical channels are given.

Interference patterns in shallow‐water reverberation
View Description Hide DescriptionEcho‐ranging experiments off Perranporth, England, have shown diffuse patterns in the reverberation, a major cause being interference between the normal modes of propagation. There are interference modulations in the strength of the echoes from close‐range areas of bottom roughness, from daytime fish shoal tracks, and from general reverberation due to fish at night—the latter two effects going out about 56 km. At 1 kHz we can get regular patterns, with typical spacing 6.0 km at 20‐km range, and good agreement is demonstrated between experiment and a theory based on two modes. At 2 kHz we can get only irregular patterns, with typical spacing 3.0 km, due to a multiplicity of modes. These patterns follow the tidal variation in water depth, but are sometimes confused by other patterning that follows the tidal streaming. Changes in the phase of the patterns due to the vertical movement of fish in the water column have also been observed; this together with other phenomena can provide a crude measure of echoer depth.

Bubble noise spectra
View Description Hide DescriptionWhen bubbles are formed by the enclosure of pockets of air, they must first undergo extreme distortions before settling down into a spherical shape. In two recent papers [M. S. Longuet‐Higgins, J. Fluid Mech. 2 0 1, 525–541 (1989); 2 0 1, 543–565 (1989)] it has been shown that the shape oscillations of bubbles will, at second order, contain radially symmetric ‘‘monopole’’ terms, having double the fundamental frequency. These terms can resonate with the radial, ‘‘breathing’’ mode to produce significant levels of sound in the ocean. In the present paper it is shown that any broad spectrum of bubble‐generated sound may be expected to show peaks at the corresponding resonance frequencies. A first examination of the available oceanic data does indeed show evidence of such resonances, particularly at the even‐numbered mode frequencies. The same mechanism may also help to explain certain resonances observed in laboratory experiments by Medwin and Beaky [J. Acoust. Soc. Am. 8 6, 1124–1130 (1989)].

Deconvolution applied to high‐frequency echograms in sea bottoms
View Description Hide DescriptionThe echo‐sounding technique visualizes the marine subbottom by a cascade representation of consecutive traces resulting from the medium response to a normal‐incidence sonar pulse train. The resolution, i.e., the possibility of resolving close targets, depends on the sonar pulse widths. Similar to seismics, this resolution can be remarkably increased by applying deconvolution techniques. This paper analyzes the design of spiking deconvolution filters in the frequency domain and its performance in improving the resolution of real echograms collected from Buendia reservoir, 45 m deep. The effects of bandpass filtering and stabilization in the deconvolution process are also considered.

Modal shading coefficients for high‐resolution source depth localization
View Description Hide DescriptionIn this article the minimum variance principle is applied to the modal shading coefficients to improve source depth localization. It is shown that for a long, well‐populated vertical array, the source depth localization function based on the minimum variance principle is approximately the same as the depth function based on normal mode theory. For a limited aperture vertical array, the modes are spatially undersampled. In this case, the modal shading coefficients based on the minimum variance principle are shown to significantly improve the depth resolution assuming sufficient signal‐to‐noise ratio. But, as the signal‐to‐noise ratio decreases, the depth resolution for the minimum variance case approaches the (conventional) modal beamformer result.