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Nov 1990

Volume 88, Issue S1, pp. S1-S200

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back to top Session 2PA: Physical Acoustics: Scattering
Contributed Papers
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Comparisons of backscattering from cylindrical shells described by shell and elasticity theories (A)

Ronald P. Radlinski, Richard D. Vogelsong, and Louis R. Dragonette

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S15-S15 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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For kah < 1, where k is the fluid wave number, a is the radius of the cylinder, and h is the wall thickness, scattering from infinite cylindrical shells at normal incidence can be described by a combination of specular reflection and the zeroth‐order symmetric Lamb wave (S0). Thin‐shell theory is found to closely describe the resonance behavior from this two‐wave interaction. At higher values of kah, additional scattering from the antisymmetric Lamb modes above the plate coincidence frequency of the shell material is predicted by elasticity theory. For materials with longitudinal wave speeds greater than the fluid, and shear wave speeds less than for the fluid, no coincidence frequency is predicted by plate nor shell theory. Accordingly, backscattering from this class of materials described by shell theories, which include bending, show no evidence of the antisymmetric Lamb wave. For materials where both the compressional and shear wave speed are greater than the sound speed in fluid, the adequacy of the shell theory to describe the antisymmetric Lamb wave response is determined by comparison with full elasticity theory and with the results of Veksler and Korsunskii [J. Acoust. Soc. Am. 87, 943–962 (1990)].
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Comparison of backscattered echoes predicted from exact theory and from thin‐shell theories (A)

C. E. Dean and M. F. Werby

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S15-S15 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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It is not difficult to predict how sound scatters from a fluid‐loaded elastic shell based on exact elastodynamic theory, provided the shell is a sphere or an infinite cylinder. Problems arise for more general shapes, however, and although some success has been obtained for spheroids and cylinders with hemispherical end caps, the results are rather tedious, if not disappointing, when one wishes to extend the frequency range or aspect ratio of the target. Some progress has been made for results predicted from thin‐shell theories either utilizing finite‐element methods in two and three dimensions or T matrices based on thin‐shell theories. In this study, some common thin‐shell theories that are employed for spherical elastic shells with exact normal mode theory are examined, with the goal of extending the results to elongated targets. Limitations of the various thin‐shell theories are explored for both the frequency range and thickness.
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Anomalies in the ray synthesis of backscattering from hollow elastic spherical shells (A)

Steven O. Kargl and Philip L. Marston

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S15-S15 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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When the form function for backscattering f(θ = πka) from a hollow spherical shell is described by a ray synthesis based on a generalized surface ray theory [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)], two anomalies occur in the vicinity of the first axial longitudinal resonance within the shell. The first anomaly is the manifestation of the longitudinal resonance and a ray synthesis of the specular reflection contribution fsp, which includes a novel curvature correction fcc, seems to properly describe one effect of longitudinal resonances on f [S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 88, 1114–1122 (1990)]. The fundamental longitudinal resonance occurs at ka = πcL/[c(1 − b/a)], where k is the wave number of the incident wave, b/a is the inner‐to‐outer radii ratio of the shell, and cL and c are the longitudinal sound speed of the elastic material and speed of sound in water, respectively. The present ray synthesis contains leaky Lamb wave contributions that account for the circumnavigation of Lamb waves about the shell. The second anomaly occurs where the s1 leaky Lamb wave has a negative group velocity and is highly radiation damped. This occurs for ka slightly below that of the fundamental resonance. It is plausible that the second anomaly may be the result of a direct ray contribution not currently contained in the ray synthesis. [Work supported by ONR.]
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Analysis of thickness “resonances” when scattering from submerged elastic shells at high frequency (A)

M. F. Werby and G. C. Gaunaurd

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S15-S15 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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When sound scatters from an elastic spherical shell submerged in water at suitably high frequencies, it is noted that backscattered returns, when plotted as a function of frequency, display unusually large signals over a broad frequency range. The point at which this occurs is a function of both shell thickness and material properties. This effect is illustrated for five elastic materials and three shell thicknesses (15 distinct examples). Simple expressions that predict the location of the strong returns in ka (the ka values, where k is the wave number in the fluid and a is the radius of the sphere) for all 15 examples are then given. The results are also examined in partial wave space and are explained within the context of flexural waves and half‐integral wavelengths that correspond to the thickness of the sphere.
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Form function dependence at low ka (A)

Louis R. Dragonette and Charles F. Gaumond

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S15-S16 (1990); (2 pages)

Online Publication Date: 14 Aug 2005

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The form function of an infinite cylindrical shell has been solved and previously studied as a function of ka, shell thickness, and material parameters, e.g., density, longitudinal velocity, and shear velocity. However, at values of ka below 1.5, physical intuition suggests that the principal motions involved in scattering are uniform compression and undeformed body motion, the monopole and dipole terms, respectively. The backscattered form function at a fixed value of ka was therefore computed as a function of compressibility and mass of the cylinder, with thickness and one material parameter held constant. The effects of varying the remaining constant, as well as the effect of higher‐order modes, were also found.
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Elastic wave scattering from large linear arrays of bounded obstacles (A)

Raymond Lim and Roger H. Hackman

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S16-S16 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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At a previous meeting of the Society [R. Lim and R. H. Hackman, J. Acoust. Soc. Am. Suppl. 1 87, S40 (1990)], an improved transition matrix formulation for multiple scattering calculations was suggested, capable of exact numerical results at low to moderate ka. Exact results for acoustic scattering from finite linear arrays of up to ten spherical shells were presented. In the far field, comparisons with the field due to truncated infinite arrays showed remarkable agreement. Hence it is possible to approximate the acoustic far field due to moderate to large finite groups of scatterers with fast calculations involving infinite arrays. In this presentation, results for the scattering from finite and infinite linear arrays imbedded in elastic hosts will be given. Here the strong coupling, possibly due to the host's shear degrees of the freedom, causes end effects to be more important. Energy cross sections for both compressional and shear wave incidence are presented and discussed.
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Complex resonance frequencies in acoustic wave scattering from impenetrable spheres and elongated objects (A)

X. L. Bao and Herbert Überall

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S16-S16 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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Complex resonance frequencies of impenetrable (rigid or soft) elongated objects, namely, spheroids and cylinders with hemispherical endcaps, including the spherical limit of the latter, are studied. Complex resonance frequencies are obtained from the principle of phase matching of surface waves. Substantial differences are found between the two mentioned objects, and are explained physically. For the case where the surface waves are generated by plane acoustic waves at broadside incidence, the simultaneous presence of cylindrical circumferential‐wave resonances and of the resonances of meridionally propagating surface waves is discussed; this effect is also known from the observation of elastic surface wave resonances on hemispherically endcapped elastic cylinders (G. Maze and J. Ripoche).
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Analysis and comparison of three‐dimensional angular distributions of rigid, soft, and elastic spheroidal targets (A)

J. George and M. F. Werby

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S16-S16 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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Three‐dimensional angular distributions are calculated for rigid, soft, and elastic spheroidal targets. The elastic targets also include resonance locations and the results of the predictions of the three classes of targets are compared at both resonance values (for the elastic target) and non‐resonance values. Both similarities and differences of the patterns are outlined over a broad frequency range and explained.
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Resonant acoustic scattering as a singular perturbation phenomenon (A)

Andrew Norris

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S16-S16 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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The resonant scattering of acoustic waves from very rigid or dense elastic targets can be viewed as a singular perturbation from the case of a perfectly rigid scatterer that displays no interior resonances. The method of matched asymptotic expansions is used to develop the scattered field as a combination of the rigid background with an “inner” solution valid for frequencies close to the modal frequencies of the target in vacuo. The general form of the inner solution shows that the strength of the response at a given modal frequency is very sensitive to the spatial distribution of the mode, with the strongest resonances occurring if the modal displacement is confined to the vicinity of the exterior surface. These general conclusions are illustrated for a spherical target, and a comparison of the matched asymptotic results with the predictions of the resonant scattering theory for the sphere sheds some light on the asymptotic validity of the latter.
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The thin‐shape breakdown (TSB) of the Helmholtz integral equation (A)

R. Martinez

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S16-S16 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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A number of numerical implementations of the Helmholtz integral equation exist today that can predict routinely the field scattered by a volume‐holding body, such as the ellipsoidal “core” of a typical airborne or submerged vehicle stripped of its thin appendages, i.e., stripped of control surfaces, etc. The reason for these exclusions has often been an inherent limitation of the cited modeling tools, rather than a rational dismissal of the potential effect of the neglected protrusions on the complete body's expected scattering cross section. The limitation of existing techniques is this: The standard form of Gauss' theorem on which they are based, which leads to the Helmholtz integral, becomes meaningless when the volume of the shape addressed tapers down to zero even over only part of the structure. This paper explains, analytically, the origin of this thin‐shape breakdown (TSB), and develops an alternate boundary element formulation for its cure.
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Observations of transverse cusp diffraction catastrophes produced by reflecting long and short ultrasonic bursts from a curved metal surface in water (A)

Carl K. Frederickson and Philip L. Marston

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S16-S17 (1990); (2 pages)

Online Publication Date: 14 Aug 2005

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Transverse cusp caustics are predicted to be produced when sound or light from a point source is reflected by a smooth curved surface having the general shape h(x,y)  =  h1x2 + h2xy2 + h3y2 + h4x + h5y (with h2≠0) [P. L. Marston, in Acoustical Imaging (Plenum, New York, 1988), Vol. 16, p. 579]. The transverse cusp curve partitions space into regions where either one or three rays contribute to the wave field. The diffraction pattern exhibited by a cusp caustic is proportional to the Pearcey function. Experiments were conducted that produced a transverse cusp using a focused source of 1‐MHz sound and a smooth curved metal surface as a reflector. The shape of the reflector was measured to determine the parameters in h(x,y) for that particular surface. Long tone bursts were used to simulate a steady‐state signal in order to image the acoustical wave field in a plane distant from the reflector. Experimental and calculated diffraction patterns are in fair agreement when the measured values of h1 and h2 were used in the calculation. Single‐cycle bursts were used to show the transition from the three‐ray to the one‐ray region across the cusp curve. Temporal records manifest the transition expected for slices through the imaged wave field. An optical source and receiver replaced the acoustical source and receiver to image the corresponding optical wave field. A distinct optical cusp curve was visible as expected for the short wavelength limit. [Work supported by ONR.]
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Reflection tomography in the presence of wave front distortion (A)

James F. Smith, III, Robert C. Waag, and Charles F. Gaumond

J. Acoust. Soc. Am. Volume 88, Issue S1, pp. S17-S17 (1990); (1 page)

Online Publication Date: 14 Aug 2005

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The performance of an imaging algorithm [P. B. Abraham and C. F. Gaumond, “Reflection tomography,” J. Acoust. Soc. Am. 82, 1303–1314 (1987)] that replaces a scattering object by an equivalent source or reflectivity distribution is investigated in the presence of wave front distortion arising from sound‐speed variations in the path between the scattering object and the detectors. The wave front distortion is modeled by weighting the expression for the far field pressure, which is the Fourier transform of the effective source distribution, with a phase factor. The phase factor is determined by the travel time change produced by the sound‐speed variations. Travel times are computed by ray tracing. Measured scattering from a solid aluminum sphere is employed in a geometry in which the detectors are below the sphere, and span a plane in a half‐space out to the reliable acoustic path. The incident wave is assumed to travel in a direction parallel to the surface of the detector plane and the sound‐speed variations are assumed to depend only on the distance between the scattering object and the detector plane. Images obtained using the algorithm with and without wave front distortion show the degrading effect of a sound speed that varies with depth.
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