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Journal of the Acoustical Society of America

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Apr 1993

Volume 93, Issue 4, pp. 1687-2427

Page 1 of 36 Pages Next Page | Jump to Page

Ultrasonic scattering from spherical shells including viscous and thermal effects

L. W. Anson and R. C. Chivers

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1687-1699 (1993); (13 pages) | Cited 6 times

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An analysis for sound scattering and attenuation by shell structures immersed in fluids is outlined. While the form of the analysis permits easy comparison with previous results for simple spheres, it includes novel features of viscoelasticity in the shell and core materials (which may be fluid or solid), viscosity in the suspending fluid, and thermal effects. The computational procedure adopted is outlined with particular reference to the avoidance of numerical instabilities at very low and very high values of ‘‘ka.’’ The testing of the program by comparison with previous results on simpler systems is reported, and a limited selection of numerical results is given. The program has been used successfully over the range of ka values between 10−6 and 200, its robustness needs closer definition.
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43.20.Fn Scattering of acoustic waves
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

A gradient formulation of the Helmholtz integral equation for acoustic radiation and scattering

David T. I. Francis

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1700-1709 (1993); (10 pages) | Cited 9 times

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A method of overcoming the problem of nonuniqueness in the discretized Helmholtz integral equation is described, based on a partial application of the Helmholtz gradient formulation of Burton and Miller [Proc. R. Soc. London, Ser. A 323, 201–210 (1971)]. The numerical implementation is designed to be compatible with a finite‐element structural analysis, and uses boundary elements of the quadratic isoparametric type. The method is illustrated for scattering from a sphere, and for radiation by a piston vibrating in the end of a cylinder, with consistent results being obtained across a wide frequency range. The additional computation is of the order of 35% of that required for the standard formulation.
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43.20.Fn Scattering of acoustic waves
43.20.Tb Interaction of vibrating structures with surrounding medium
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.20.Px Transient radiation and scattering

Eigenfrequencies of an acoustic rectangular cavity containing a rigid small sphere

John A. Roumeliotis

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1710-1715 (1993); (6 pages) | Cited 2 times

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Analytical expressions are derived for the eigenfrequencies of any mode in a hard‐walled acoustic rectangular cavity, containing an acoustically small rigid sphere. A straightforward and simple approach is employed to obtain a first‐order perturbation of the cavity eigenfunctions and the corresponding eigenfrequency shifts. Rectangular wave functions, as well as their expansion in terms of cylindrical wave functions and finally in terms of spherical ones, are used. The results are useful in problems connected with acoustic levitation and with excitation or probing of resonant cavities. Some suggestions are made about the best positioning of the probe, for more exact measurement of the eigenfrequency of any mode in the unperturbed cavity. Graphical results for some of the lower‐order modes are given, for various values of the parameters.
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43.20.Ks Standing waves, resonance, normal modes
43.20.Fn Scattering of acoustic waves

Ray tracing in a moving medium with two‐dimensional sound‐speed variation and application to sound propagation over terrain discontinuities

J. S. Lamancusa and P. A. Daroux

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1716-1726 (1993); (11 pages) | Cited 7 times

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The development of an efficient method for tracing rays and determining sound pressure levels in a moving medium is described. The medium is specified with horizontal and vertical variations in temperature and vectorial wind velocity. Reflections from a nonlevel ground surface of complex impedance are treated and an adaptive time step numerical integration is implemented for high accuracy. Two integration algorithms are compared for accuracy and computational efficiency. Recommendations are given for improved discretization of the medium and for accurate ray tracing through a ground reflection. This model is used to investigate the effect that terrain discontinuities, such as hills, have on atmospheric sound propagation. The importance of correct inclusion of the vectorial nature of wind is demonstrated.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.20.Dk Ray acoustics
43.50.Vt Topographical and meteorological factors in noise propagation

On the validity of the heuristic ray‐trace‐based modification to the Weyl–Van der Pol formula

Kai Ming Li

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1727-1735 (1993); (9 pages) | Cited 5 times

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The Weyl–Van der Pol formula from electromagnetic wave propagation theory is known to give tolerable predictions of sound levels over a wide range of ground surfaces in a homogeneous atmosphere. A ray‐tracing technique is perhaps the simplest approach to extend the applicability of the Weyl–Van der Pol formula to the inhomogeneous situation. Essentially one uses ray theory to determine the path lengths and the angle of incidence at the ground. These modified parameters are then substituted into the Weyl–Van der Pol formula for the overall sound levels. This heuristic approach may be criticized for its lack of mathematical rigor even though it is physically reasonable. By using a ray theory approximation in the wave equation, a closed‐form solution has been obtained for the sound field over an impedance plane in the presence of a sound‐speed gradient. It has been shown that the heuristic formula represents an approximation of the solution. The theory also suggests that there is a strong interaction between the sound‐speed profile and the ground surface, in particular, when the impedance is high. The solution is limited to a single reflection.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.20.Bi Mathematical theory of wave propagation
43.50.Vt Topographical and meteorological factors in noise propagation

A split‐step Padé solution for the parabolic equation method

Michael D. Collins

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1736-1742 (1993); (7 pages) | Cited 93 times

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A split‐step Padé solution is derived for the parabolic equation (PE) method. Higher‐order Padé approximations are used to reduce both numerical errors and asymptotic errors (e.g., phase errors due to wide‐angle propagation). This approach is approximately two orders of magnitude faster than solutions based on Padé approximations that account for asymptotic errors but not numerical errors. In contrast to the split‐step Fourier solution, which achieves similar efficiency for some problems, the split‐step Padé solution is valid for problems involving very wide propagation angles, large depth variations in the properties of the waveguide, and elastic ocean bottoms. The split‐step Padé solution is practical for global‐scale problems.
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43.30.Bp Normal mode propagation of sound in water
43.30.Dr Hybrid and asymptotic propagation theories, related experiments
43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics

Scattering enhancement by supersonic resonances of cylindrical shells

Miguel C. Junger

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1743-1746 (1993); (4 pages) | Cited 1 time

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Off‐beam backscattering peaks associated with supersonic resonances of a simply supported unstiffened shell are evaluated by means of a relatively unfamiliar powerful analytical technique conceived by H. Lamb [London Math. Soc. Proc. 32, 11–20 (1900)] and further developed by P. W. Smith, Jr. [J. Acoust. Soc. Am. 34, 640–646 (1962)]. Boundary conditions leading to a simple solution have been selected because they have only a minor effect on coupling between the fluid and supersonic resonances. Cross‐section peaks are effectively the same for the shear and compression families of shell resonances. Frequency dependence is associated only with a sin θi factor, θi being the angle of incidence measured from the cylindrical axis, associated with trace matching of the incident acoustic wave number and modal structural wave numbers. The level of sin θi for shells in water varies by no more than 1 dB with frequency. Within this range, the target strength maximum contributed by a shell resonance is TSr=20 log(2L)−9.4 dB±0.6 dB, where 2L is the shell length. Elastic parameters only affect the range of angles of incidence θi matched to the resonant mode’s configuration. The level is independent of the cylinder radius, though of course resonance frequencies are not.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.20.Fn Scattering of acoustic waves
43.40.Ey Vibrations of shells

Experimental investigation of sediment effect on acoustic wave propagation in the shallow ocean

Andrew K. Rogers, Tokuo Yamamoto, and William Carey

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1747-1761 (1993); (15 pages) | Cited 8 times

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In shallow water the sediment layers have very strong effects on the propagation of acoustic waves. An effort to study the effects of the sediment has been made using 50‐ to 600‐Hz continuous wave acoustic propagation data taken by Carey [‘‘Experimental verification and application of bottom shear modulus profile (BSMP) method,’’ Oceans ’91 Proceedings (1991)] at the Atlantic margin coring project (AMCOR) borehole 6010 off the coast of New Jersey combined with sediment properties measured at that site by Yamamoto et al. of the University of Miami Geoacoustic Laboratory using the bottom shear modulus profiler (BSMP) method. Excellent agreement was found between the model and data indicating the acceptability of BSMP sediment values as input for acoustic propagation studies. The introduction of shear or tangential stresses in the model was found to have no effect upon which modes propagated but only on their modal intensity. The higher the order of the mode the greater the penetration in the seafloor and the stronger the shear effect on the intensity. A sub‐seafloor acoustic waveguide was investigated for the site and found to give possible explanation for enhanced intensity of modes that propagate strongly within that region. The intrinsic attenuation was determined using a method of matching modal intensity from model calculations with measured data. Biot theory was utilized and depth‐dependent intrinsic sediment attenuation profiles were found for seven frequencies between 50 and 600 Hz.
The depth‐averaged attenuation for the first mode at each frequency and the first mode that penetrates to 100 m was found. The frequency dependence of the mode attenuation was determined. The attenuation values agreed well with previous experimental acoustic reflection data taken by Mitchell and Focke [J. Acoust. Soc. Am. 67, 1582–1589 (1980)] but were much lower than values for attenuation in this frequency range determined by Hamilton’s [Geophysics 36, 266–284 (1971)] extrapolation of high‐frequency laboratory and field measurements to the ≤1‐kHz range. The effect of interface and volume scattering on transmission loss was determined using the acoustic model and a thin layer representation of the scattering interface. The result showed scattering to significantly contribute to energy loss beyond a kilometer or so and to have increased significance as frequency is increased.
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43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics
43.30.Bp Normal mode propagation of sound in water

Scattering by objects buried in underwater sediments: Theory and experiment

Raymond Lim, Joseph L. Lopes, Roger H. Hackman, and Douglas G. Todoroff

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1762-1783 (1993); (22 pages) | Cited 14 times

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The scattering of sound by objects buried in underwater sediments is studied in the context of an exactly soluble model. The model consists of two fluid half‐spaces separated by a planar, fluid, transition layer of arbitrary thickness. Attenuation is included in any of these regions by using complex wave numbers. A directional source field, generated in the upper half‐space by a continuous line array, insonifies an object placed in the lower half‐space. The scattered field detected by another line array placed anywhere in the system may be calculated. The solution is determined from the T matrix for the bounded scattering system and is exact (in linear acoustics) to all orders of multiple scattering among the interfaces and object. Numerical results are presented to investigate the effect of the local acoustic environment on the free‐field, in‐water scattering resonances of thin spherical shells. The field scattered by a shallowly buried object is discussed with emphasis on the importance of evanescent wave scattering in detection from above the sediment over an extended range. An initial set of experiments meant to verify the model are described. Results are presented and discussed for the measured scattering response of buried, spherical, evacuated, steel shells, that are 2.25% and 11% of the outer radius in thickness.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics
43.30.Ft Volume scattering
43.20.Fn Scattering of acoustic waves

Acoustic scattering from elemental Arctic ice features: Numerical modeling results

J. Robert Fricke

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1784-1796 (1993); (13 pages) | Cited 4 times

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In this paper acoustic scattering from Arctic ice is considered. No analytic scattering theories are able to explain the observed loss at low frequency (10–100 Hz) in long‐range propagation experiments. A finite difference method is used to solve the heterogeneous elastodynamic equations in two dimensions; this technique permits arbitrary roughness, unrestricted in slope, displacement, or radius of curvature and provides direct, physical insight into the rough ice scattering mechanism. Broadband numerical scattering simulations are conducted on pressure ridges. The specular loss due to a ridge is affected by three parameters: cross‐sectional area or mass of the ridge, excitation of plate waves, and a material‐dependent power law. The first two affect the magnitude of the loss, while the last affects the frequency dependence. Multi‐year ridges are completely frozen and are best modeled as elastic structures yielding a loss frequency dependence of ≊f9/2. Observed loss in field data, with a frequency dependence of ≊f3/2, is not explained by scatter from multi‐year ridges. In contrast, young pressure ridges are modeled as fluid structures since they are loose aggregations of ice blocks and cannot support shear strain. Scatter from fluid ridges has a loss frequency dependence of ≊f3/2 and yields a good match to the observed frequency dependence in field data. These results suggest that observed long‐range propagation loss is best explained by scatter from large, young pressure ridges.
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43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics
43.30.Hw Rough interface scattering

Broadband source localization and signature estimation

T. C. Yang

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1797-1806 (1993); (10 pages) | Cited 9 times

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The temporal signature and source location of a broadband impulse propagating in an ocean waveguide are estimated using matched mode processing and illustrated using simulated data in an Arctic sound channel. Matched mode processing provides a simple method for broadband signal detection and localization; the peak‐to‐sidelobe ratio is significantly improved using broadband data compared with the narrow‐band case. The range and depth ambiguity function evaluated at the source location yields directly the source spectrum, which is inverse Fourier transformed to estimate the original signal waveform. For the simulated data, the reconstructed signal, compensated for spreading loss and array signal gain, agrees rather well with the original waveform. The estimated spectrum/waveform is weaker than the original spectrum/waveform due predominantly to the fact that the Arctic wave guide is lossy. A method for coherent broadband processing is proposed to improve signal localization and detection when the original source spectrum is known. Multiplying (correlating) the original spectrum with the range and depth ambiguity function, the product can be coherently summed over the frequency band of the signal. Near theoretical processing gain is achieved for the simulated data. Broadband signal detection is proposed using a frequency versus depth plot in addition to the commonly used frequency versus bearing plot.
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43.30.Wi Passive sonar systems and algorithms, matched field processing in underwater acoustics
43.20.Mv Waveguides, wave propagation in tubes and ducts

Normal mode wave‐number estimation using a towed array

Harish M. Chouhan and G. V. Anand

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1807-1814 (1993); (8 pages) | Cited 3 times

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In the analysis of the null‐steering technique of normal mode filtering presented by the authors previously [H. M. Chouhan and G. V. Anand, J. Acoust. Soc. Am. 89, 735–744 (1991)], it was assumed that the modal wave numbers km are known a priori. In practice, the waveguide parameters upon which the modal wave numbers depend are normally not known and are difficult to measure accurately. In order to use the null‐steering technique of mode filtering, or in applications such as source localization and waveguide characterization, it is necessary to estimate the modal wave numbers. An estimation procedure using a towed horizontal line array is presented in this article. The method entails eigendecomposition of the range‐averaged array signal correlation matrix. Range‐averaging effectively decorrelates the normal mode signals and enables the use of high‐resolution spectral estimation techniques such as MUSIC for estimating the modal wave numbers. Simulation results for the Pekeris model of the ocean are presented.
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43.30.Bp Normal mode propagation of sound in water

A two‐way parabolic equation for elastic media

Michael D. Collins

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1815-1825 (1993); (11 pages) | Cited 14 times

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The parabolic equation (PE) method is extended to handle wave propagation and scattering in range‐dependent elastic waveguides, which are approximated by a sequence of range‐independent regions. The two‐way elastic PE involves an efficient PE‐based scattering method for computing reflected and transmitted fields at the vertical interfaces separating range‐independent regions. The one‐way elastic PE is used to propagate the outgoing and incoming fields through the range‐independent regions with two‐way range marching. In addition to providing the backscattered field, the two‐way PE provides a correction to the outgoing field. The self‐starter is generalized to handle a source in a solid layer.
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43.30.Bp Normal mode propagation of sound in water
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics

Wave solutions in three‐dimensional ocean environments

C. H. Harrison

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1826-1840 (1993); (15 pages) | Cited 3 times

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A three‐dimensional wave solution is developed for variable depth but isovelocity environments by transforming the wave equation into a suitable coordinate system. These solutions can be compared with existing known solutions derived from a ray point of view where the vertical modes propagate like horizontal rays. A general approach for arbitrary profiles is used to give explicit analytical solutions for various particular topographies including troughs and ridges. The behavior of these solutions is well known since they all have analogs in ordinary two‐dimensional refracting media. Because this approach does not invoke the adiabatic approximation or ray invariants but evidently has similar limitations it throws some light on the limits of validity of these alternative approaches. In passing, some interesting problems in normalization are encountered, and investigations into slope and curvature restrictions reveal some general relations between average slope, curvature or higher derivatives for realistic surfaces. Numerical modelers, who currently only have the ocean wedge as a 3‐D benchmark solution, now have an extended repertoire of benchmarks.
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43.30.Bp Normal mode propagation of sound in water

Broadband matched‐field processing of transient signals in shallow water

S. M. Jesus

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1841-1850 (1993); (10 pages) | Cited 3 times

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Range and depth source localization in shallow water amounts to the estimation of the normal‐mode structure of the acoustic field. As ‘‘seen’’ by a vertical array, and from a modeling point of view, the normal‐mode structure appears as a set of nonplane coherent waves closely spaced at a vertical angle. This paper presents a full‐wave‐field narrow‐band high‐resolution technique that uses the spectral decomposition of the sample covariance matrix to resolve the vertical arrival structure of the harmonic acoustic field. The broadband processor is obtained by weighted averaging of the narrow‐band range‐depth ambiguity estimates within the source signal frequency band. Results obtained on synthetic data show that its performance is always better than or equal to that of the generalized minimum variance processor, which itself largely outperforms the conventional matched‐field processor. It is shown, using both simulated and experimental data, that the effect of the broadband processor is to increase the stability of the source location estimate. Results obtained with this processor on short transient pulses collected during the North Elba’89 experiment with a 62‐m‐aperture vertical array, showed stable and accurate localizations over long time intervals. It is also shown that the sound field, received over a given frequency band, is relatively stable over time and is in agreement with the predictions given by a standard normal‐mode propagation model.
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43.30.Wi Passive sonar systems and algorithms, matched field processing in underwater acoustics

Applications of optimal time‐domain beamforming

Michael D. Collins, Jonathan M. Berkson, W. A. Kuperman, Nicholas C. Makris, and John S. Perkins

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1851-1865 (1993); (15 pages)

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Applications to ocean acoustic data from a towed array and to speech processing are presented for an improved optimal time‐domain beamformer, which involves optimizing over all possible source bearings and time series for multiple sources using simulated annealing. The convergence of the parameter search is accelerated by accepting time series perturbations only when the energy decreases. A comparison with the conventional delay‐and‐sum beamformer illustrates that the optimal beamformer handles larger receiver spacing and larger source‐to‐receiver ratio. Periodic ambiguities are essentially eliminated by using irregular receiver spacing and the improved search algorithm. Weak sources are handled with fractional beamforming. Noise cancellation is possible if the parameters of the noise are included in the search space. Two‐dimensional localization is performed for nearby sources.
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43.30.Yj Transducers and transducer arrays for underwater sound; transducer calibration
43.60.Gk Space-time signal processing, other than matched field processing

Stable marching schemes based on elliptic models of wave propagation

George H. Knightly and Donald F. St. Mary

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1866-1872 (1993); (7 pages)

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A marching numerical scheme is applied to a far‐field elliptic model of underwater wave propagation. General stability conditions are derived for the scheme in the case of varying parameter functions. Several examples are presented to demonstrate the capacity of the method to detect backscattered energy. In these examples the elliptic equation is cast as an initial value problem with assumed correct initial data. The ill‐posed nature of initial value problems for elliptic problems is discussed.
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43.30.Bp Normal mode propagation of sound in water
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

An experiment on matched‐field acoustic tomography with continuous wave signals in the Norway Sea

Valerii V. Goncharov and Alexander G. Voronovich

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1873-1881 (1993); (9 pages) | Cited 2 times

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An acoustic tomography experiment in the Norway Sea with continuous wave (cw) signals is described. Measurements were made using a point source and a vertical 560‐m‐long array 55 and 105 km apart. The tomography scheme was based on matched‐field and matched‐mode principles and consisted in ‘‘fitting’’ the media to the measured acoustic signal at the array. The sound‐speed profiles were described at some points by empirical orthogonal functions and linear interpolation between these points was applied. Two‐ and six‐parameter descriptions of the medium were in fact used. The results of tomography reconstruction of the sound‐speed field agreed well with the spot measurements and demonstrated the feasibility of the tomography schemes applied.
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43.30.Pc Ocean parameter estimation by acoustical methods; remote sensing; imaging, inversion, acoustic tomography
43.60.Rw Remote sensing methods, acoustic tomography

The use of inhomogeneous waves in the reflection–transmission problem at a plane interface between two anisotropic media

Patrick Lanceleur, Helder Ribeiro, and Jean‐François De Belleval

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1882-1892 (1993); (11 pages) | Cited 4 times

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A mathematical form is proposed for the study of the problem of reflection–transmission of monochromatic ultrasonic plane waves at the interface between two arbitrary anisotropic semi‐infinite media. The method used leads to a complete determination of all characteristics of the studied waves for all possible configurations, i.e., their directions of propagation, polarizations, and magnitudes. In particular, cases are taken into account where the waves generated by the existence of the interface are evanescent or more generally inhomogeneous. Applying this method to the calculation of several practical cases typically encountered in ultrasonic nondestructive evaluation fields, this paper points out the existence of phenomena that cannot be interpreted by classical methods usually used for the resolution of this kind of problem.
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43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.20.Fn Scattering of acoustic waves

On the crossing points of Lamb wave velocity dispersion curves

Qigao Zhu and Walter G. Mayer

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1893-1895 (1993); (3 pages) | Cited 3 times

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See Also: Erratum

Show Abstract
Standard dispersion curves relating the phase velocity of Lamb waves to the frequency‐plate thickness parameter fd indicate that in some cases symmetrical and antisymmetrical mode velocity curves cross each other. Viktorov’s equations are used to show that the crossing points are points where the dispersion curves are discontinuous so that no distinct Lamb mode exists for these particular velocity‐fd combinations. Procedures are given to predict how many such points exist and where they are located in a given range of fd.
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43.35.Pt Surface waves in solids and liquids

Experimental investigation of minimization of the dynamic response of mass‐loaded beams using vibration absorbers

Dhanesh N. Manikanahally and Malcolm J. Crocker

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1896-1907 (1993); (12 pages)

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An experimental verification of the theoretical analysis of the use of discrete vibration absorbers consisting of spring–mass–damper systems, to attenuate the response of a mass‐loaded cantilever beam, is presented. Ten different beam systems that are similar except for the location of the masses were studied both theoretically and experimentally. Initially, eigenvalues, eigenfunctions, and generalized masses were obtained for each beam system without absorbers. Then, an experimental investigation was conducted on these beam systems without absorbers, to determine the hysteretic damping factor for each system. With this information, two discrete vibration absorbers were designed using theoretical methods to suppress the first and second resonances of the beam systems under consideration in the frequency range below 100 Hz. Absorber I was designed to attenuate the first resonance and absorber II, the second resonance. The interaction of the absorbers was accounted for in the analysis. Ten different sets of absorber parameters, damping coefficients of the viscous damper, and spring stiffnesses of the springs were obtained for both absorbers I and II. Ten different sets of absorbers were designed corresponding to the ten different beam systems described above. The mass of the absorbers was kept constant for all the different beam systems. The stiffness and damping coefficients of absorbers I and II were found to be of the same order of magnitude for all of the ten absorber sets designed for the ten beam systems. Therefore, a single set of vibration absorbers was fabricated and used for each of the ten beam systems. The parameters of the vibration absorbers used for the experiment were similar to the theoretical values.
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43.40.Cw Vibrations of strings, rods, and beams
43.40.Tm Vibration isolators, attenuators, and dampers

The flexural wave‐number response of a string and a beam subjected to a moving harmonic force

Mauro Pierucci

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1908-1917 (1993); (10 pages)

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The effect of a moving harmonic force that acts upon either a string or a beam is analyzed according to its spectral wave‐number components and the decaying components of the flexural vibrations. The speed of motion of the force is nondimensionalized with respect to the wave flexural speed. For a string, the wave number of the right traveling disturbance increases monotonically at subsonic speeds; at supersonic speeds both wave numbers lead to left traveling waves which decrease as a function of Mach number. For a beam, the effect of the motion is to produce one right traveling wave, with an everincreasing wave number, and three disturbances which propagate and decay behind the forcing function. The decaying modes, at a Mach number of two, become traveling modes. The critical Mach number of two corresponds to a speed of the force equal to the group velocity at that frequency.
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43.40.Cw Vibrations of strings, rods, and beams

Vibration and damping analysis of a scarf‐jointed beam in flexure

Mohan D. Rao and Haiming Zhou

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1918-1926 (1993); (9 pages)

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In this paper, an analysis for the determination of resonance frequencies, modal loss factors, and complex mode shapes of a simply supported beam with a scarf joint is presented. The system consists of a pair of isotropic or orthotropic beams that are scarf‐jointed with a certain angle by a viscoelastic adhesive. The governing equations of motion of the system, for a general case of forced vibration under transverse distribution load, are first derived using the energy method and Hamilton’s principle. The adhesive material is modeled using the complex modulus approach. By using a finite‐difference method, the numerical solutions of the governing equations for free vibration are obtained. A parametric study has been conducted to study the effects of various material and geometric parameters on the system’s dynamic stiffness and modal loss factors. It has been shown that there exists an optimum scarf angle for a given configuration that maximizes the system damping.
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43.40.Cw Vibrations of strings, rods, and beams
43.40.At Experimental and theoretical studies of vibrating systems

Constrained‐layer damping analysis for extensional waves in infinite, fluid‐loaded plates

Pieter S. Dubbelday

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1927-1935 (1993); (9 pages) | Cited 1 time

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This study concerns the mathematical analysis of constrained‐layer damping of extensional waves in plates of infinite extent, with and without fluid loading. Previous work was mostly limited to flexural waves. Some aspects of fluid loading for flexural waves may be understood by means of thin‐plate theory. Therefore, a similar theory was developed for extensional waves. The description and examples presented here are based on three models: The first is an extension of Kerwin’s 1959 model [E. M. Kerwin, J. Acoust. Soc. Am. 31, 952–962 (1959)], the second is a hybrid model in which the base plate is described by exact elasticity theory and the other two layers by Kerwin’s concepts, and the third uses exact elasticity theory for all three layers. It is shown that the extended Kerwin model is useful in the design of constrained‐layer damping for extensional waves as well as for flexural waves.
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43.40.Dx Vibrations of membranes and plates

Sound scattering from cylindrical shells with internal elastic plates

Y. P. Guo

J. Acoust. Soc. Am. Volume 93, Issue 4, pp. 1936-1946 (1993); (11 pages) | Cited 6 times

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This paper examines sound scattering from cylindrical shells with internal structural loading. Here, the internal system is modeled by elastic plates, which support both longitudinal and flexural waves. It is shown that an internal plate may affect the scattering process in two ways: it may interact with shell waves at the attachment points and it may resonantly respond to the incidence excitation. For the former, the acoustic effects are the same as those caused by any other forms of internal loading, such as mass–spring systems, or by inhomogeneities of the shell itself, such as material imperfection. For the latter, it is shown that internal plate resonances may result in large amplitude coupling forces at the attachment points connecting the plate with the shell, which in turn affect the scattered field. It is shown that this resonance effect is clearly seen in the acoustic field only for light structural loading. Both pinned and clamped plates are examined, which only reveals small differences in the low‐ to mid‐frequency domain. The effects of attachment locations are also examined. Three different regions on the shell surface are identified, in each of which the loading interacts with different kinds of shell waves, resulting in different scattering characteristics.
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43.40.Dx Vibrations of membranes and plates
43.20.Fn Scattering of acoustic waves
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