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Nov 1979

Volume 66, Issue S1, pp. S1-S89

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back to top Session LL. Physical Acoustics VII: Scattering and Related Phenomena
Contributed Papers
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The resonances of a finite‐length fluid cylinder and their interpretation in terms of surface waves (A)

G. C. Gaunaurd, E. Tanglis, and H. Überall

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S80-S80 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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We consider a finite‐length fluid cylinder surrounded by either a very tenuous or a very dense exterior fluid. This amounts to respectively considering either Dirichlet or Neumann boundary conditions on the cylinder's surface. The eigenfrequencies of such finite‐length cylinders are interpreted in this paper as the resonances caused by phase matching of circumferential waves that circumnavigate the cylinder along certain helicoidal Fermat paths, and that get reflected back and forth from its top and bottom flat surfaces. We have obtained the dispersion curves of these circumferential (i.e., “creeping”) waves which are seen to correspond to a series of well‐defined pitch angles of their helix, for different values of the cylinder's length‐to‐radius ratio. We generate and display graphs pertaining to various cylinder sizes, boundary conditions, and pitch angle of each of the resulting surface waves. [H. Überall is also at Catholic University, Washington, DC, and was additionally supported by Code 421 of ONR.]
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Critical angle diffraction in high frequency scattering by fluid spheres and cylinders (A)

P. L. Marston

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S80-S80 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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When plane waves are reflected from a flat surface between ideal fluids, the reflection is total when the angle of incidence θ exceeds θc  =  sin−1(c1/c2) where c2 > c1; c1 and c2 are the sound speeds, respectively, of the fluid from which the wave is incident and of the second fluid. For an interface of constant curvature, ray acoustics predicts that the scattered intensity has an unphysically divergent angular derivative as the scattering angle ϕ approaches the critical scattering angle ϕc  =  π − 2θc. This divergence is removed by diffraction which is important in an angular region near ϕc. The width of this region exceeds (a/λ)1/2, where a is the radius of curvature and λ is the wavelength. A simplified approximation for the diffraction, similar to the optical analog described in “Critical angle scattering by a bubble: physical‐optics approximation and observations” [P. L. Marston, J. Opt. Soc. Am. 69, 1205–1211 (1979)], is derived. As ϕ approaches ϕc, a ringing and decay of the far‐field intensity is predicted which may be observable in scattering by fluid spheres and cylinders.
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Ultrasonic nonspecular reflectivity near longitudinal critical angle (A)

T. D. K. Ngoc and W. G. Mayer

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S80-S80 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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The intensity profile of an ultrasonic beam reflected from a liquid‐solid interface is determined by a numerical integration method. This numerical approach takes into account the influence of absorption in the media and is valid for all angles of incidence. The reflected profile is calculated for a specific case: incidence near the longitudinal critical angle for a water‐Plexiglas interface. The calculated results demonstrate the existence of nonspecular reflectivity near this particular critical angle and provide a quantitative description of its basic features. Theoretical results and experimental measurements are compared. [Work supported by the Office of Naval Research, U.S. Navy.]
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Scattering of sound from a randomly rough solid‐liquid interface (A)

S. K. Numrich

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S80-S81 (1979); (2 pages)

Online Publication Date: 11 Aug 2005

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Measurements have been made of sound scattered by submerged surfaces with Gaussian height and slope statistics. A wide range of roughness was spanned through the use of transient pulse analysis. In terms of the ratio of the rms surface height (σ) to sound wavelength (λ), the range included 0.03 < (σ/λ) < 5.0. Coherent and incoherent terms were separated digitally. In the region of small roughness, the coherent reflection coefficient was compared with two theoretical models. Comparisons with theory were also made using the incoherent term when large values of roughness were involved. At both extremes of the range, the experimental data agreed well with the theoretical predictions. Of particular interest in this experiment is the intermediate region in which the coherent and incoherent terms are explained in detail. Here the coherent term decreases rapidly and the incoherent term begins to dominate the scattering return. No adequate theoretical model exists for this transition region. [Work supported by ONR, Code 461, and NOSC, San Diego.]
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Backscattering of short ultrasonic pulses by solid elastic cylinders at large ka (A)

P. J. Welton, M. De Billy, A. Hayman, and G. Quentin

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S81-S81 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Backscattering measurements from solid brass, aluminum, and Lucite cylinders in water have been performed at a ka of approximately 240 using short acoustic pulses. Numerous discrete echoes are received due to multiple internal reflections of the acoustic pulse at the boundary of the cylinders. Excellent agreement between the measured echo arrival times and the echo arrival times predicted by the theory of Brill and Überall [D. Brill and H. Überall, J. Acoust. Soc. Am. 50, 921–939 (1971)] is obtained for all of the cylinders. The amplitudes of the backscattered echoes from the brass and aluminum cylinders were also compared with theory and fair agreement is obtained.
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The scattering of an obliquely incident plane acoustic wave from a cylindrical object (A)

Lawrence Flax, Vasundara V. Varadan, and Vijay K. Varadan

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S81-S81 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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A mathematical model is developed to predict the scattering of a plane acoustic wave incident upon an elastic cylinder immersed in water at any angle relative to the cylindrical axis. Solutions to the elastic problem are constructed using scalar and vector potentials. There are three important angular regions of interest. These are at the longitudinal, shear, and Rayleigh critical angles. The scattering amplitude at these angles is derived and will be discussed.
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The T‐matrix approach to scattering of waves by finite elastic and viscoelastic cylinders immersed in water (A)

Vasundara V. Varadan, Vijay K. Varadan, and Lawrence Flax

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S81-S81 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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In this paper, the T‐matrix or null field approach is applied to make scattering and absorption calculations for finite elastic and viscoelastic cylinders in water. Various difficulties which so far have prevented the use of such a formalism for a solid‐fluid interface will be discussed. The complication due to the appearance of only curl free basis functions in water which in turn makes some of the matrices involved nonsquare has been overcome by considering additional representation of the scattered and refracted fields and using a series of matrix manipulations. Numerical results displaying the scattering cross sections for a range of frequencies for various aspect ratios are presented. These results are then compared with those of a prolate spheroid of the same overall dimensions to study how the shape is critical in determining the absorption characteristics.
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“Zeroes,” “ridges,” and poles, in the scattering amplitudes of elastic waves echoing from resonating fluid spheres in solids and liquids (A)

D. Brill, G. Gaunaurd, and H. Überall

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S81-S81 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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We study the “resonance parts” of the scattering amplitudes of compressional or shear waves, returned when compressional or shear waves are incident on fluid spheres contained in either solids or in dissimilar fluids. The resonance parts are obtained after suitable smooth backgrounds are subtracted from each composite partial‐wave amplitude. The starting point of the analysis is the three‐dimensional graph of any of the modular surfaces ∣a−1fnPP∣, ∣a−1fnPS∣, ∣a−1fnSP∣, and ∣a−1fnSS∣ plotted versus mode order n, and nondimensional frequency ka. We found simple expressions for the (not necessarily straight) lines of zeros that constitute the boundaries or demarcation lines of each of the “ridges” that appear so evidently in the plots. These “ridges,” which are inclined with respect to the n and ka axes, exhibit marked cleavages, and the “peaks” present in them (i.e., the resonances) are spaced in a peculiar way that is, (a) predictable from the analysis, and (b) that yields information about the material composition of the scatterer. The analytic expressions for the lines connecting the tips of the peaks along a given ridge has also been determined. Each “ridge” is shown to be associated with a “creeping wave” and it is the graphic visualization of the elastic analog of a “Regge pole.” [H. Überall is also at Catholic University, Washington, DC, and was additionally supported by Code 421 of ONR.]
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The Mittag‐Leffler expansion and the interpretation of poles in the scattering amplitudes of waves echoed from fluid spheres (A)

G. Gaunaurd and H. Überall

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S81-S81 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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We consider the cases of acoustic and elastic wave scattering from fluid (possibly viscous) spheres contained within either solids (i.e., coatings) or dissimilar fluids (i.e., bubbles), and study the resulting scattering matrix Sn and the poles in the associated scattering amplitude (s). The one‐term Taylor series we used in the past to obtain the “one‐level approximation” to Sn, which was so valuable in our earlier development of the resonance theory of viscoelastic wave scattering from cavities, can now be replaced by the exact Mittag‐Leffler expansion of the quantity Fn. This quantity is proportional to the system's mechanical impedance and since all of its singularities are simple poles, it admits a meromorphic function (i.e., Mittag‐Leffler) series representation. The locations of the “new” resonances and the value of their widths are found to be shifted from the values we found using our earlier approach, even in the absence of absorption in the fluid interior to the sphere. Absorption introduces further shifts and the unitarity property of Sn is lost in both instances. The new representation is not only exact, but reduces properly to the right asymptotic limits and our earlier “backgrounds” and “resonances” can be re‐interpreted in the light of these new (and simpler to obtain) poles. Plots of the poles and their shifts are displayed in various cases. [H. Überall is also at Catholic University. Washington, DC., and was additionally supported by Code 421 of ONR.]
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A simple scattering model for finite objects (A)

J. C. Nelander and A. D. Matthews

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S82-S82 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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A model for acoustic scattering from finite objects is described in terms of a three‐dimensional Fourier wave space. This wave space representation, adapted from x‐ray diffraction analysis, provides a convenient method for depicting aspect and frequency dependence simultaneously. Physical observables are interpreted by means of the Ewald construction. The method is illustrated for a rigid right circular cylinder. A procedure which eliminates mathematical difficulties which arise from surface discontinuities for finite objects when one‐dimensional models are employed is discussed. Incorporation of impedance boundary conditions can alter details of the cylinder's scattering cross section. Examples are discussed and illustrated for aluminum and brass cylinders in water. Dominant observed features are related to the large phase shift which occurs at the shear critical angle. The model provides a useful simulation tool and also suggests a method for analyzing experimental data in detail.
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Creeping wave description of surface wave modes on elastic cylindrical shells (A)

J. W. Dickey, D. A. Nixon, and E. D. Breitenbach

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S82-S82 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Dispersion and attenuation curves are given for identified surface modes in the scattered pressure from elastic cylindrical shells insonified by a normally incident plane wave. The results are derived using two different techniques for air‐filled aluminum shells of several different wall thicknesses, b/a (ratio of inner to outer radius). The first series of numerical results are calculated using the Sommerfeld‐Watson transformation and determining the roots of a 6 × 6 secular determinant. The second method is used to derive similar results by analysis of the partial wave responses. The second method results, for a thick shell, are favorably compared with previously obtained creeping wave results for a solid elastic cylinder. For low values of b/a, the Rayleigh and Stoneley waves on the shell are shown to approach limiting values for increasing ka which correspond to the Rayleigh and Stoneley wave speeds defined for the infinite half‐space, and the Franz and Whispering Gallery modes approach the bulk wave velocities for the external and shell materials respectively. For thin shells (b/a → 1), Whispering Gallery and Rayleigh modes have vanished and the symmetric and antisymmetric Lamb modes are prevalent over limited regions of ka. Calculations are carried out over the range 0.1 ⩽ ka ⩽ 200, the first method valid for higher ka, and the partial wave method valid at lower ranges of ka.
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Scattering of elastic waves by an elliptical cylindrical shell (A)

M. M. Simon and R. P. Radlinski

J. Acoust. Soc. Am. Volume 66, Issue S1, pp. S82-S82 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Much work has been accomplished in the analysis of the dynamics of an elliptical cylindrical shell. Recently, solutions have appeared for acoustic scattering from a submerged elliptical shell [Brigham, Libuha, and Radlinski, J. Acoust. Soc. Am. 61, 48–59 (1977)]. The problem of scattering of arbitrarily polarized elastic waves from an elliptical cylindrical shell is even more difficult because the basis functions for the fields in a separable coordinate system are not orthogonal for the different wave speeds. Recent advances [Pao and Varatharjulu (Varadan) J. Acoust. Soc. Am. 59, 1361–1371 (1976)], in the application of the extended boundary condition method to elastic wave propagation has led to solutions for elastic wave scattering from elliptical inclusions that are stress‐free, rigid, fluid, or solid elastic. Varadan and Varadan have worked on the case of a layered elastic inclusion. This presentation deals with coupling of thin shell theory to the elastic scattering problem as described by the extended boundary condition method. The theory is ideally suited to such applications since the formulation is given in terms of normal and tangential stresses and displacements on the elliptical surface.
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