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Journal of the Acoustical Society of America

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Jun 1994

Volume 95, Issue 6, pp. 3039-3689

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Generalized modal expansion: A Wiener–Hopf problem

Hossein Haj‐Hariri

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3039-3048 (1994); (10 pages)

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A method is presented that is suitable for studying linear wave‐scattering problems for guided waves in bounded or unbounded domains. The method is developed for the classical wave equation. The generality of the discussions show the promise of the method for studying scattering problems governed by linear equations more complicated than the classical wave equation (e.g., higher‐order, nonconstant coefficients). The method allows for modal expansion in cases where the spectrum of the governing operator may not be readily accessible. The well‐known example problem of sound propagation and scattering in a plane waveguide in the presence of a semi‐infinite splitter plate is studied using this technique. The results are in agreement with the analytical solutions obtained using the Wiener–Hopf and classical modal expansion methods. Whereas these latter two techniques are simple, they cannot be generalized easily; in contrast to the method proposed herewith.
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43.20.Bi Mathematical theory of wave propagation
43.20.Fn Scattering of acoustic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts

Acoustic coupling from a focused transducer to a flat plate and back to the transducer

Xucai Chen, Karl Q. Schwarz, and Kevin J. Parker

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3049-3054 (1994); (6 pages) | Cited 5 times

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An approximate solution for the acoustic coupling factor (the diffraction correction function) from a focused transducer to a flat plate and back to the transducer is provided. This function is useful for system calibrations where a pulse‐echo system or transmit–receive system is used. Numerical solutions are provided for the important case where the flat plate is placed near the focal plane of the transducer. The solution for a flat disk transducer is obtained as a limiting case. Experimental evidence for a focused transducer is provided.
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43.20.Fn Scattering of acoustic waves
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.20.Bi Mathematical theory of wave propagation

Formulation of short‐wavelength bistatically scattered fields in terms of monostatic returns

Miguel C. Junger

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3055-3058 (1994); (4 pages) | Cited 2 times

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The relation between short‐wavelength bi‐ and monostatically scattered fields of smooth scatterers, e.g., the sphere, is governed by the bistatic theorem. This relation is extended here to scatterers with marked edges, viz. finite cylinders and rectangular baffles. The formulation of the bistatic field in terms of the monostatic return does however depend on two parameters not relevant to the classical bistatic theorem: The product of the wave number times the characteristic dimension, and the bistatic angle between the incident and scattered wave.
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43.20.Fn Scattering of acoustic waves
43.30.Vh Active sonar systems

Simultaneous measurement of the acoustical properties of a thin‐layered medium: The inverse problem

V. K. Kinra, P. T. Jaminet, C. Zhu, and V. R. Iyer

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3059-3074 (1994); (16 pages) | Cited 4 times

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This paper presents a frequency‐domain ultrasonic technique for a simultaneous determination of the thickness (h) and wave speed (c) of the individual layers comprising a multilayered medium. The layers may be ‘‘thin’’; by thin we mean that the successive reflections of an ultrasonic pulse from the two faces of a layer are nonseparable in the time domain. Plane longitudinal waves which are normally incident upon the medium are considered. A systematic analysis of the sensitivity of the complex‐valued transfer function to the acoustical parameters of each layer has been carried out. An inverse algorithm, which utilizes either the Newton–Raphson or the Simplex method in conjunction with the incremental search method, has been developed to reconstruct simultaneously the thickness and phase velocity of each layer by minimizing the difference between the theoretical and the experimental results in the mean‐sum‐square sense; the entire complex spectrum, i.e., the amplitude as well as the phase spectrum, was used. The technique is fully automated and computer controlled and can be readily used for in situ NDE applications. Results are presented for several three‐layer specimens; aluminum/water/aluminum, aluminum/water/titanium, and titanium/water/titanium. Successful inversion was obtained for the following cases (1) simultaneous determination of h and c of any one of the three layers, given h and c of the remaining two layers; (2) simultaneous measurement of the three thicknesses, given the three wave speeds; (3) simultaneous measurement of the three wave speeds, given the three thicknesses; (4) simultaneous determination of all three thicknesses and one wave speed, given the remaining two wave speeds. The precision of our measurements was found to be excellent; typically, ±3 μm in h (for h of the order of 1 mm) and ± one part per thousand in c. The accuracy was found to be about one order of magnitude lower than the precision; typically, ±10 μm in h and ±2% in c.
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43.20.Fn Scattering of acoustic waves
43.20.Hq Velocity and attenuation of acoustic waves
43.35.Zc Use of ultrasonics in nondestructive testing, industrial processes, and industrial products
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants

Nonspecular reflection of two‐ and three‐dimensional acoustic beams from fluid‐immersed plane‐layered elastic structures

Smaine Zeroug and Leopold B. Felsen

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3075-3089 (1994); (15 pages) | Cited 9 times

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This paper treats the interaction of two‐ and three‐dimensional acoustic quasi‐Gaussian beams with plane‐layered elastic configurations. Emphasis is placed on the regime of nonspecular reflection, which is characterized by strong coupling between the specularly reflected beam and leaky waves supported by the structure. The present analysis generalizes previously published studies of these phenomena by allowing for arbitrarily collimated two‐ and three‐dimensional beams as well as simultaneous excitation of multiple leaky waves. The substantially enriched range of nonspecular phenomena encountered under these generalized conditions is explained by examining the spectral content of the reflected and leaky wave constituents that participate in the interaction. By use of the complex source point (CSP) method for modeling quasi‐Gaussian beams, the reflection problems are solved rigorously by wave‐number spectral decomposition. Subsequent reduction by uniform asymptotic techniques yields physically meaningful wave‐field contributions, which explain the phenomenology and also allow efficient computation. The accuracy of the CSP asymptotic algorithms is assessed by comparison with purely numerically generated reference data. The results establish the accuracy and versatility of the CSP strategy for a broad range of beam‐interface conditions.
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43.20.Fn Scattering of acoustic waves

Direct measurements of edge diffraction from soft underwater acoustic panels

Jean C. Piquette

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3090-3099 (1994); (10 pages) | Cited 4 times

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Direct measurements of edge diffraction arising from the interaction of an acoustic wave with an underwater panel that satisfies soft‐body boundary conditions are reported. The measurements were obtained by utilizing a specially fabricated ‘‘airbox’’ sample, which is literally a ‘‘box of air,’’ fabricated using thin polycarbonate walls. The airbox theoretically would exhibit a typical insertion loss in excess of 60 dB (in the absence of edge diffraction), thus avoiding interference of the directly transmitted wave with the edge‐diffracted wave of interest. The validity of the edge‐diffraction measurements was established by demonstrating that the performance of a small sample panel fabricated from a closed‐cell foam material can be deduced by adding (frequency‐by‐frequency) measurements obtained from an airbox to diffraction‐free measurements obtained from a large sample of the same closed‐cell foam. This procedure simulates (from direct experimental measurements) the combined edge‐diffracted plus transmitted wave field that is present in the transmission region of the small sample. The results reported include the edge diffraction caused by the interaction of a spherically symmetric source with a soft sample panel and the edge diffraction caused by the interaction of an acoustic array with a soft sample panel. The frequency interval considered is 1–21 kHz.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.40.Le Techniques for nondestructive evaluation and monitoring, acoustic emission
43.40.Yq Instrumentation and techniques for tests and measurement relating to shock and vibration, including vibration pickups, indicators, and generators, mechanical impedance

A note on using the fast field program

Y. L. Li and Michael J. White

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3100-3102 (1994); (3 pages) | Cited 3 times

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The fast field program is a numerically efficient algorithm for computation of the sound pressure due to a time harmonic point source above a general boundary in a layered medium. In this method, the inverse Hankel transform for obtaining the pressure is approximated by two Fourier integrals. One of the Fourier integrals was treated as the incoming wave term and neglected in the computation of sound pressure. Actually, no one has theoretically proven that one of the Fourier integrals can be neglected. In this paper, it is shown that the neglected integral is necessary for the computation of low‐frequency sound pressure when a pressure‐release boundary is involved.
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43.28.-g Aeroacoustics and atmospheric sound
43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.20.Bi Mathematical theory of wave propagation

A note on short‐range ground characterization

Keith Attenborough

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3103-3108 (1994); (6 pages) | Cited 4 times

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Short‐range measurements of the excess attenuation spectrum from a point source can be used to characterize the acoustical properties of the ground surface but they are influenced by turbulence as well as the ground surface. The geometry used for ground characterization should be a compromise between greatest sensitivity to the acoustical properties of the ground surface and avoidance of turbulence effects. Compromise geometries are suggested together with a method of estimating the effective flow resistivity of the ground surface from the frequency of the first maximum in the excess attenuation spectrum. The use of this method is illustrated for a particular grass‐covered farmland.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.58.Bh Acoustic impedance measurement

Diffraction by a screen in downwind sound propagation: A parabolic‐equation approach

Erik M. Salomons

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3109-3117 (1994); (9 pages) | Cited 10 times

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The parabolic‐equation method is used to study sound diffraction by a screen on an absorbing ground. For a homogeneous atmosphere, results are in good agreement with an analytical diffraction theory, showing that the proposed method to include a screen in the parabolic‐equation method is accurate. Results are presented for inhomogeneous atmospheres with logarithmic sound‐speed profiles, representative of downwind sound propagation. The results show that meteorology has large effects on sound diffraction by a screen at a frequency of 1000 Hz, and small effects at a frequency of 100 Hz.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.20.Fn Scattering of acoustic waves

A comparison of measured and predicted broadband acoustic arrival patterns in travel time–depth coordinates at 1000‐km range

Peter F. Worcester, Bruce D. Cornuelle, John A. Hildebrand, William S. Hodgkiss, Jr., Timothy F. Duda, Janice Boyd, Bruce M. Howe, James A. Mercer, and Robert C. Spindel

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3118-3128 (1994); (11 pages) | Cited 19 times

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Broadband acoustic signals were transmitted from a moored 250‐Hz source to a 3‐km‐long vertical line array of hydrophones 1000 km distant in the eastern North Pacific Ocean during July 1989. The sound‐speed field along the great circle path connecting the source and receiver was measured directly by nearly 300 expendable bathythermograph (XBT), conductivity‐temperature‐depth (CTD), and air‐launched expendable bathythermograph (AXBT) casts while the transmissions were in progress. This experiment is unique in combining a vertical receiving array that extends over much of the water column, extensive concurrent environmental measurements, and broadband signals designed to measure acoustic travel times with 1‐ms precision. The time‐mean travel times of the early raylike arrivals, which are evident as wave fronts sweeping across the receiving array, and the time‐mean of the times at which the acoustic reception ends (the final cutoffs) for hydrophones near the sound channel axis, are consistent with ray predictions based on the direct measurements of temperature and salinity, within measurement uncertainty. The comparisons show that subinertial oceanic variability with horizontal wavelengths shorter than 50 km, which is not resolved by the direct measurements, significantly (25 ms peak‐to‐peak) affects the time‐mean ray travel times. The final cutoffs occur significantly later than predicted using ray theory for hydrophones more than 100–200 m off the sound channel axis. Nongeometric effects, such as diffraction at caustics, partially account for this observation.
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43.30.Pc Ocean parameter estimation by acoustical methods; remote sensing; imaging, inversion, acoustic tomography
43.30.Cq Ray propagation of sound in water

Analysis of pulse propagation in a bottom‐limited sound channel with a surface duct

Charles L. Monjo and Harry A. DeFerrari

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3129-3148 (1994); (20 pages) | Cited 3 times

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Measurements of acoustic transmission in a bottom‐limited sound channel with a surface duct, are compared with model predictions using broadband ray, normal mode, fast‐field, and parabolic approximation methods. At a range of 42 km, six surface‐ducted arrivals are evident in the data set and are predicted by all models except simple ray theory. Surface‐ducted propagation is compared to propagation without a surface duct. The surface duct is found to generate a series of modes which display a resonance between the highly dispersive surface reflected bottom reflected (SRBR) propagation and less dispersive refracted bottom reflected (RBR) propagation. The six arrivals contain energy from three types of propagation paths. Faster precursors are purely diffracted energy, while slower precursors have RBR and SRBR contributions. Ray theory predicts the SRBR contribution, but not the diffracted energy. The precursors are generated at discrete ranges where RBR and SRBR phase fronts exchange energy with the RSR phase front in the duct. Energy leaking from the duct also reenforces the slower precursors. Since range‐independent models were used, mode coupling cannot be the cause of energy exchange.
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43.30.Bp Normal mode propagation of sound in water
43.30.Pc Ocean parameter estimation by acoustical methods; remote sensing; imaging, inversion, acoustic tomography
43.30.Es Velocity, attenuation, refraction, and diffraction in water, Doppler effect

Matched mode processing for sparse three‐dimensional arrays

T. C. Yang and Christopher W. Bogart

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3149-3166 (1994); (18 pages) | Cited 2 times

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Matched mode processing (MMP) has been demonstrated to localize underwater sound sources with vertical hydrophone arrays. Two new MMP algorithms for arbitrarily shaped three‐dimensional arrays in a range‐independent environment are presented. The first algorithm, exact matched mode processing (EMMP), is a generalization of vertical array MMP; its mode decomposition depends on source bearing. The second algorithm, approximate matched mode processing (AMMP), ignores bearing dependence during mode decomposition, reinserting it afterward. The AMMP azimuth beam pattern is similar to that of matched field processing (MFP) and conventional beamforming. The performance of the EMMP and AMMP algorithms is investigated and compared with MFP using simulated data. A slanted vertical array, a horizontal array, and a T‐shaped array composed of horizontal and vertical segments were considered. It was found that the AMMP and MFP yield similar peak‐to‐sidelobe ratio (PSR) and peak‐to‐average‐sidelobe ratio (PASR) in range and depth localization. In contrast, the EMMP yields higher PSR and PASR in range and depth localization for known source bearings. Its bearing search properties were not investigated; they may be less robust than AMMP, MFP and conventional beamforming.
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43.30.Wi Passive sonar systems and algorithms, matched field processing in underwater acoustics
43.60.Gk Space-time signal processing, other than matched field processing

Overcoming ray chaos

Michael D. Collins and W. A. Kuperman

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3167-3170 (1994); (4 pages) | Cited 5 times

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Computational difficulties associated with chaos may be overcome by solving eigenray problems with boundary‐value techniques rather than the initial‐value technique of shooting. The nonlinear differential equation for the ray paths is therefore somewhat analogous to stiff linear differential equations. The boundary‐value problem is solved using the bending method and simulated annealing. Numerical results are presented for problems that are ill‐posed as initial‐value problems but well posed as boundary‐value problems.
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43.30.Cq Ray propagation of sound in water

Sound emissions by a laboratory bubble cloud

M. Nicholas, R. A. Roy, L. A. Crum, H. Og̃uz, and A. Prosperetti

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3171-3182 (1994); (12 pages) | Cited 11 times

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This paper presents the results obtained from a detailed study of the sound field within and around a cylindrical column of bubbles generated at the center of an experimental water tank. The bubbles were produced by forcing air through a circular array of hypodermic needles. As they separated from the needles the ‘‘birthing wails’’ produced were found to excite the column into normal modes of oscillation whose spatial pressure‐amplitude distribution could be tracked in the vertical and horizontal directions. The frequencies of vibration were predicted from theoretical calculations based on a collective oscillation model and showed close agreement with the experimentally measured values. On the basis of a model of the column excitation, absolute sound levels were analytically calculated with results again in agreement with the measured values. These findings provide considerable new evidence to support the notion that bubble plumes can be a major source of underwater sound around frequencies of a few hundred hertz.
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43.30.Ft Volume scattering
43.30.Nb Noise in water; generation mechanisms and characteristics of the field
43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance

Bubble population measurements with a parametric array

Marc Gensane

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3183-3190 (1994); (8 pages) | Cited 2 times

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This paper presents a method that estimates gas bubble density in water versus range. A bubble cloud being insonified with a highly directive acoustic transducer, this method combines backscattering and attenuation measurements. It relies on the linear theory of bubble resonance, and the so‐called first‐order multiple scattering approximation. Here it is applied to some measurements performed with a parametric array (primary frequency: 210 kHz; secondary: 8 to 40 kHz). The application of this method to the secondary frequencies fails, because the backscattered levels are much higher than the saturation level. This failure is imputed to the nonlinear scattering occurring at the secondary frequencies by the bubbles whose resonance is close to the primary frequency. From this assumption, minimum ranges are deduced under which the measurements of bubbles resonating at the secondary frequencies cannot be stated as reliable.
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43.30.Pc Ocean parameter estimation by acoustical methods; remote sensing; imaging, inversion, acoustic tomography
43.30.Es Velocity, attenuation, refraction, and diffraction in water, Doppler effect
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

On determination of orthotropic material moduli from ultrasonic velocity data in nonsymmetry planes

Y. C. Chu, A. D. Degtyar, and S. I. Rokhlin

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3191-3203 (1994); (13 pages) | Cited 7 times

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This paper reports analysis of the reconstruction of elastic constants from ultrasonic velocity measurements in nonsymmetry planes of unidirectional composite materials. It is shown that the nonlinear least‐square optimization method is stable to initial guess selection and data scatter and can be used routinely to measure the full set of nine elastic constants for orthotropic materials. Simple analytical expressions are derived for phase velocities in arbitrary directions in an orthotropic material with low transverse‐to‐fiber anisotropy. Using these, coefficients of sensitivity of phase velocities to elastic constants are obtained in closed form and used to find the optimal wave propagation directions for elastic constant measurement. The changes in velocity due to elastic constant variation calculated by the exact theory agree well with the predictions from the sensitivity coefficients. When all nine elastic constants are reconstructed from velocity data in nonsymmetry planes, the inversion is highly dependent on the initial guesses and susceptible to random data scatter. When seven elastic constants are found from velocity data in planes of symmetry, the remaining two (C12 and C66) can be found from nonsymmetry‐plane data independently of initial guesses and scatter levels. This is especially important since the elastic constants C12 and C66 cannot be determined from immersion velocity measurements in two accessible planes of symmetry.
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43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.35.Yb Ultrasonic instrumentation and measurement techniques

Comparative analysis of through‐transmission ultrasonic bulk wave methods for phase velocity measurements in anisotropic materials

Y. C. Chu and S. I. Rokhlin

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3204-3212 (1994); (9 pages) | Cited 10 times

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In this paper a critical evaluation of ultrasonic bulk wave velocity measurements by the through‐transmission and the recently introduced self‐reference methods is reported. The major difference in these two techniques is the reference acoustic path: through‐water for the through‐transmission method and through‐sample at normal incidence for the self‐reference method. The error introduced by geometrical imperfection of the sample is compared theoretically and experimentally for two methods. Composite materials with different anisotropies are used in the experiment, including ceramic matrix (SiC/Si3N4) and graphite/epoxy composites. Both analytical and experimental studies show that the self‐reference method has advantages over the through‐transmission method, which is susceptible to geometrical imperfections in the sample. The effect of temperature fluctuation on the accuracy of ultrasonic phase velocity measurements is discussed and different compensation techniques are proposed.
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43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.35.Yb Ultrasonic instrumentation and measurement techniques

Ultrasonic nonlinear properties of lead zirconate‐titanate ceramics

Jeong K. Na and Mack A. Breazeale

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3213-3221 (1994); (9 pages) | Cited 10 times

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A systematic study of the nonlinear properties of lead zirconate‐titanate (PZT) ceramics is presented. The velocity, attenuation, and nonlinearity parameter of PZT ceramics were measured from room temperature to temperatures above the Curie temperature. The velocity goes through a minimum near the Curie temperature. In spite of a maximum in attenuation near the Curie temperature, the nonlinearity parameter exhibits a maximum whose behavior is affected by polarization. Frequency dependence of the nonlinearity parameter at room temperature is reported for the first time. Large third harmonics of an initially sinusoidal ultrasonic wave at room temperature suggest that either the effect of the fourth‐order elastic constants is anomalously large or that the nonlinear equation used to describe the behavior of single crystals is only approximately valid for description of PZT. Strain gradients are assumed to cause the frequency dependence of the nonlinearity parameter as well as the large third harmonic.
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43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.25.Dc Nonlinear acoustics of solids
43.38.Fx Piezoelectric and ferroelectric transducers

Attenuated leaky Rayleigh waves

Quan Qi

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3222-3231 (1994); (10 pages) | Cited 3 times

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The propagation of leaky Rayleigh waves under the influence of viscous damping and heat conduction in boundary layers is studied using the matched asymptotic method. Viscosity of the fluid is considered unimportant except in a thin viscous boundary layer at the interface. A new characteristic equation is obtained in which the effect of boundary layer is shown by terms associated with R−1/2=(ων)1/2/ct, where R is the Reynolds number, ω is the frequency, ν is the kinematic viscosity of the fluid, and ct is the shear velocity of the solid substrate. One of the numerically obtained solutions gives the leaky Rayleigh wave speed and the attenuation coefficient. It is shown that, together with radiation, viscosity and heat conduction in the boundary layer also affect the attenuation of the leaky Rayleigh waves. Furthermore, it is shown that, because of the effect of the viscous boundary layer, the attenuated leaky Rayleigh wave speed can be smaller than the Rayleigh wave speed at the interface of a vacuum and a solid substrate. A critical Reynolds number of about 2500 is found beyond which a viscous boundary layer stops influencing leaky Rayleigh wave propagation. Finally, a new wave mode sustained by the viscous boundary layer alone is found in the limit of a small fluid–solid density ratio. This mode exists for appropriate frequency and layer thickness combinations. For air, the corresponding propagation speed is shown to be higher than the sound speed and the corresponding attenuation is significant. These results may be used to improve our interpretation of acoustic signature of materials.
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43.35.Pt Surface waves in solids and liquids

Determinations of anisotropic elastic constants using laser‐generated surface waves

J.‐F. Chai and T.‐T. Wu

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3232-3241 (1994); (10 pages) | Cited 11 times

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This paper studied the recovery of elastic constants of anisotropic solids from measured surface wave energy velocities. The calculations of surface wave phase and energy velocities of anisotropic solids were based on an efficient forward formalism. In the experiment, the surface waves were generated by a pulsed laser and detected by using the PS/PR technique, where the source and receiver were located on the same surface of a specimen. The inverse problem was solved successfully by the simplex optimization method. Following the simplex iteration rules, the orientation and the elastic constants can be recovered from the measured surface wave energy velocities. The wave fronts and the caustic effects of the skimming shear waves have also been observed in the laser ultrasound experiment.
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43.35.Ud Thermoacoustics, high temperature acoustics, photoacoustic effect
43.35.Pt Surface waves in solids and liquids
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
62.20.D- Elasticity

Acoustic double‐reflection and transmission at a rough water–solid interface

James H. Rose, Mehmet Bilgen, and Peter B. Nagy

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3242-3251 (1994); (10 pages) | Cited 5 times

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The double interaction of a wave with a rough interface is important in many acoustic measurements. An acoustic beam that reflects twice from a rough water–solid interface is considered. The second reflection from the rough surface is accomplished after the transducer’s buffer rod is used as an acoustic mirror. Changes in the spatially averaged specular reflection are related to the phenomenon of ‘‘enhanced backscatter,’’ previously observed for diffuse scattering. Simple, approximate closed‐form analytic formulas for the strength of the specular double reflections are given as a function of frequency and the stand‐off distance of the transducer. As one application of the analytic results, a method is proposed for determining the surface correlation function from the specular double reflections. The same physics (and appropriately modified analytic formulas) apply to doubly transmitted waves. Experimental measurements have been made of acoustic double reflection with a normally oriented broadband piezoelectric transducer near a rough water–solid interface. Measurements of (1) the wave reflected once from the rough interface, and (2) the wave reflected twice from the rough interface are given. The strength of the specular reflections was measured as a function of frequency and the transducer’s distance from the surface. It was observed that for large distances between the transducer and the rough surface and at low frequencies the scattering‐induced loss of the doubly reflected wave was twice the loss of a singly reflected wave. However, for small distances between the transducer and the surface and at high frequencies the scattering‐induced loss of the doubly reflected wave was four times the loss of a singly reflected wave.
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43.35.Zc Use of ultrasonics in nondestructive testing, industrial processes, and industrial products
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

Advanced time domain wave‐number sensing for structural acoustic systems. I. Theory and design

J. P. Maillard and C. R. Fuller

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3252-3261 (1994); (10 pages) | Cited 12 times

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This paper discusses new work concerned with developing structural sensors and associated signal processing techniques that provide time domain estimates of far‐field pressure or structural wave‐number information. The sensor arrangement consists of multiple accelerometers whose outputs are passed through an array of linear filters. The impulse response of each filter is constructed from the appropriate Green’s function for the elemental source area associated with each sensor. The outputs of the filter array are then summed in order to predict far‐field pressure or wave‐number information somewhat analogous to the well‐known boundary element technique. A major significance of the approach is that it provides time domain information and can thus be efficiently applied to active structural acoustic control approaches.
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43.40.At Experimental and theoretical studies of vibrating systems
43.40.Yq Instrumentation and techniques for tests and measurement relating to shock and vibration, including vibration pickups, indicators, and generators, mechanical impedance
43.60.Gk Space-time signal processing, other than matched field processing

Advanced time domain wave‐number sensing for structural acoustic systems. II. Active radiation control of a simply supported beam

J. P. Maillard and C. R. Fuller

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3262-3272 (1994); (11 pages) | Cited 6 times

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A real time structural acoustic sensor and associated signal processing is developed and applied to the active control of sound radiated by a simply supported beam. The sensor consists of multiple accelerometers mounted on the structure. An array of FIR filters processes the measured structural information to provide an estimate of the structural wave‐number component coupled to acoustic radiation in a prescribed direction. This time domain signal is used as the error information in a feedforward adaptive control approach. The single channel filtered‐X LMS algorithm is implemented here. Computer simulations in the discrete time domain demonstrate the ability of the sensor to replace the use of error microphones in the far field. The described sensor represents a significant alternative to the use of distributive structural sensors (for example piezoelectric material) by providing accurate radiation information over a broadband frequency range.
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43.40.At Experimental and theoretical studies of vibrating systems
43.40.Cw Vibrations of strings, rods, and beams
43.40.Yq Instrumentation and techniques for tests and measurement relating to shock and vibration, including vibration pickups, indicators, and generators, mechanical impedance
43.60.Gk Space-time signal processing, other than matched field processing

Vibration of two concentric submerged cylindrical shells coupled by the entrained fluid

Shigeru Yoshikawa, Earl G. Williams, and Karl B. Washburn

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3273-3286 (1994); (14 pages) | Cited 5 times

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The vibrational characteristics of a point‐driven ‘‘double shell’’ (two concentric submerged cylindrical shells coupled by the entrained fluid) are investigated theoretically and experimentally. Of particular interest are the shielding effects, if any, of the outer shell upon the inner shell. The theory on the double shell is based on Flügge’s infinite‐shell equations, the Helmholtz wave equation, and boundary conditions at the fluid–structure interfaces. This theory is used to model a finite double‐shell structure in wave number‐frequency space. Experiments are carried out in which generalized near‐field acoustical holography (GENAH) is employed to provide the experimental vibration characteristics in wave number‐frequency space of the finite double shell. It is confirmed theoretically and experimentally that the outer shell of the double shell exhibits two separate dispersion curves: A higher‐frequency dispersion curve exhibits in‐phase vibrations with respect to the inner shell, and a second lower‐frequency curve, out‐of‐phase vibration. The higher‐frequency dispersion curve of the double shell is very similar to the dispersion curve of the single shell (the inner shell without the outer shell), and thus is identified as a forced wave number response. The lower‐frequency curve seems to be dependent on the free wave number response of the outer shell alone of the double shell. A double‐shell structure can usually reduce its vibrational amplitudes by splitting the response of single‐shell’s forced vibration into the responses of inner‐shell’s forced vibration and outer‐shell’s induced vibration. However, it radiates low‐frequency underwater sounds inevitably according to the lower‐frequency dispersion curve. Furthermore, the appearance of the inner shell’s dispersion curve on the outer shell seems to indicate that the shielding influence of the outer shell is not completely effective.
Show PACS
43.40.Ey Vibrations of shells
43.30.Ky Structures and materials for absorbing sound in water; propagation in fluid-filled permeable material

Transient waves in a thick disk

Michael El‐Raheb and Paul Wagner

J. Acoust. Soc. Am. Volume 95, Issue 6, pp. 3287-3299 (1994); (13 pages) | Cited 2 times

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Transient elastic waves in a free thick disk are analyzed by a modal method. Eigenfunctions are determined by applying the Galerkin technique to trial functions which satisfy the differential equations and shear free conditions on all boundaries. The disk is forced concentrically by a trapezoidal pulse of short duration. The excitation is treated in two ways. The first approximates normal pressure by a body force acting over a vanishingly thin layer adjacent to the boundary. The second superimposes an inhomogeneous static problem on a homogeneous dynamic problem. In this way, stress close to the excitation is modeled accurately. Transient stress history matches closely that from a finite element and a finite difference simulation.
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43.40.Dx Vibrations of membranes and plates
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