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Nov 1980

Volume 68, Issue S1, pp. S1-S116

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back to top Session QQ. Physical Acoustics VII: Scattering II
Contributed Papers
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T‐matrix formulation of Acoustic wave scattering by layered elastic obstacles immersed in water (A)

V. K. Varadan, B. Peterson, V. V. Varadan, and T. A. K. Pillai

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S80-S80 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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The subject of wave scattering from layered elastic obstacles of arbitrary shape immersed in a fluid finds many potential applications in underwater acoustics. In spite of the mathematical unity present in the description of the three classical wave fields, namely acoustic, electromagnetic and elastic, due to the coupling by boundary conditions of the rotational and irrotational parts of the elastic field that propagate at distinct wave speeds, many problems with layered elastic bodies defied solution. With solid‐fluid interfaces, the problem is even more difficult since the wave equations governing the regions in the solid and fluid are different, admitting different solutions that must be coupled at the interface through continuity conditions of pressure and particle velocity. The available results are limited to this elastic shells in water using shell theory approximations. In this paper, we propose a T‐matrix approach to study acoustic wave scattering from layered elastic objects such as oblate and prolate spheroids, finite cylinders, infinite two dimensional cylinders, etc., and present numerical results for bistatic, backscattering and total scattering cross sections for a range of frequencies and for different angles of incidence, and for different thickness of the layer.
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Computation of rigid body scattering by spheroids and finite cylinders using T‐matrix approach (A)

V. K. Varadan, V. V. Varadan, T. A. K. Pillai, L. R. Dragonette, and L. Flax

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S80-S80 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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The periodic structure of the backscattered spectrum of elastic and acoustic waves from smooth obstacles has been indicative of diffraction effects similar to the geometrical diffraction concepts in optics. The waves do go around the obstacle (diffraction) and consequently one observes periodic multiple echo returns. Such circumferential waves have been named Franz waves, after W. Franz who first discussed the existence of such creeping waves in his work on the diffraction of electromagnetic waves by conducting spheres and cylinders. In the present paper we present a Franz wave analysis of the backscattered spectrums of spheroids and finite cylinders of various aspect ratios. The backscattered spectrum is calculated using the T‐matrix approach, and a Franz wave velocity is predicted for spheroidal and cylindrical obstacles. Comparisons of the acoustic and elastic cases are made wherever possible.
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T‐matrix analysis of the resonances in sound scattering from elastic spheroids in water (A)

L. R. Dragonette, Lawrence Flax, Vijay K. Varadan, and Vasundra V. Varadan

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S80-S80 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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The acoustic scattering by elastic prolate spheroids in water is computed by the T‐matrix method. Resonances in the range ka < 10, where k is the wavenumber of the incident sound wave and a is the length of the semi‐major axis, are isolated by comparing the rigid and elastic solutions. The effects of circumferential waves on the frequency response of the elastic target are derived.
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Elastic wave scattering from multiple and compound flaws (A)

V. V. Varadan, V. K. Varadan, and B. Tittmann

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S81 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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If the nondestructive evaluation (NDE) of flaws in structural materials it is often important to distinguish between a single flaw or cavity, two cavities separated by a finite distance and a compound flaw when two cavities intersect. Using the T‐matrix method, numerical results have been obtained for P waves incident on such geometries as a function of incident wave frequency and the scattering geometry. In each case, results have been obtained using several approaches. Approximate solutions including only single scattering effects are compared with exact results as the distance between the scatterers change. The compound flaw can be treated as a single flaw or as two flaws in contact. The above results will be compared with experimental results showing good agreement.
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Glory contribution to backscatter from large elastic spheres (A)

P. L. Marston and L. Flax

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S81 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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Partial wave theory for backscatter by large aluminum spheres and cylinders in water give a form function for spheres several times greater than that for cylinders when each is normalized to the geometric scattering of a rigid reflector of the same size and shape [L. Flax, J. Acoust. Soc. Am. 62, 1502 (1977)]. The physical‐optics approximation is used in the present work to show that twice‐reflected, twice‐refracted glory rays are a significant contribution to the largeness of the backscatter by elastic spheres. These rays lead to a back‐facing toroidal wavefront which appears to originate at a virtual ring‐like source of radius b < the sphere radius a. The modulus of the glory contribution to the normalized form function obtained by computing the farfield diffraction of this wavefront is ∣fa∣  =  (ka)1/2G∣J0 (kb sin γ)∣, where k is the wavenumber in water, G is a function of material properties, γ = 180° − θ, and θ is the scattering angle. When all glory rays in aluminum are S waves, b/a ≃ 0.27 and ∣fa ≃ 2.8 for backscatter with ka = 938. The sum of 2.8 and the geometric form function of 0.8 due to reflection from the first surface is similar to the prediction of partial wave theory; however, a complete physical‐optics calculation should include the phase of these terms and other reflections. The (ka)1/2 enhancement is not present in cylinders. [Work supported by ONR. P. Marston is an Alfred P. Sloan Research Fellow.]
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Weak multiple scattering by a linear array of randomly sized spheres (A)

J. W. Young and K. S. Ma

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S81 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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Scattering of an incident plane wave by a linear array of randomly sized spheres exhibits both deterministic and stochastic features. For the case of noninteracting spheres, moments of the scattering cross section are determined by moments of the sphere size distribution function multiplied by the geometrical pattern function of the linear array. When interaction between spheres (multiple scattering) is included, this simple product relationship is modified. In this paper, we evaluate the effect of weak multiple scattering on the moments of the scattering cross section of a linear array of small spheres. Both hard and soft boundary conditions are considered in the limit of kti kā ≪ I and d̄ where ā is the mean radius and d̄ is the mean separation.
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Inversion of acoustic and elastic scattering data with the time domain ramp function (A)

Bill D. Cook, Ronald L. McKinney, and Shelford E. Wilson

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S81 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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Scattering data at low frequencies contains sufficient information upon inversion to yield the basic shape of the scatterer. By shaping the incident wave to have the form of a time domain ramp function, this information can be extracted directly in the time domain. An approximate theory states that the backscattered time signal appropriately corrected for range is proportional to the crossectional area of the scatterer as a function of distance along the line of sight from transducer to target. We are testing the approximate theory with calculations of the exact theory for elastic and acoustic spherical scatterers. The results are encouraging in that in most cases, the size of the scatterer can be inferred.
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Radiation and attenuation of waves in a random medium: The mean energy flux (A)

Alan R. Wenzel

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S81 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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A theoretical analysis of the wave field radiated by a point source in a weakly inhomogeneous one‐dimensional random medium has been carried out. The analysis is based on a perturbation technique and includes all single‐ and double‐scattering terms, as well as some scattering terms of higher order. An approximate expression, valid when the absorption of the medium is small, has been obtained for the mean energy flux of the wave as a function of propagation range. This expression shows that, as a consequence of backscattering by the random inhomogeneities of the medium, the mean energy flux decreases more rapidly with range than it would due to absorption alone. This more rapid rate of decrease of the mean energy flux with range can be regarded as an excess attenuation of the wave as a result of the randomness of the medium. An interpretation of this result in terms of energy conservation is given. [Work sponsored by NORDA.]
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Anomalies in the spectrum of scattered ultrasonic waves from periodic interfaces (A)

A. Jungman, Gerard Quentin, and Laszlo Adler

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S81 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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Scattering of broadband ultrasonic waves from water‐solid, solid‐air and solid‐solid interfaces with periodic structures was investigated by ultrasonic spectroscopy. The interface is a periodic grating (of triangular shape) with periodicity ranged from 100 to 1800 μ. Both infinite and finite surfaces are studied. The spectrum of the scattered wave shows sharp minima (anomalies) at certain frequencies which are characteristic of the materials and parameters of the grating. These “missing” frequencies are identified as diffracted orders along the interface with bulk or surface wave velocities. Studying bondings between two surfaces with the aid of these spectral anomalies is suggested. [This work was supported jointly by the French CNRS and by the Center for Advanced NDE operated by the Science Center, Rockwell International, for ARPA and AFML.]
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Ultrasonic scattering from rough cracks in solids (A)

Laszlo Adler, D. Kent Lewis, M. de Billy, F. Cohen‐Tenoudji, and Gerard Quentin

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S81-S82 (1980); (2 pages)

Online Publication Date: 11 Aug 2005

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The problem of ultrasonic scattering from cracks with random rough surfaces such as a fractured surface in solids is considered. The rough crack is embedded in diffusion bonded titanium. From ultrasonic measurements (both in the time and in the frequency domain) parameters of the crack are determined and compared to actual values. These parameters include: size, shape, orientation, rms roughness, spatial correlation, length, and density distribution of roughness. [This work was supported jointly by the French CNRS and by the Center for Advanced NDE operated by the Science Center, Rockwell International, for ARPA and AFML.]
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An interrelationship between self‐consistent fields and effective scattering parameters (A)

P. W. Jameson

J. Acoust. Soc. Am. Volume 68, Issue S1, pp. S82-S82 (1980); (1 page)

Online Publication Date: 11 Aug 2005

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Various authors [V. Twersky, J. Acoust. Soc. Am. 36, 1314 (1964)], [Keller, Proc. Symp. Appl. Math. 16, 145 (1964)], [Ishmirau, Proc. IEEE 65, 1030 (1977)], [A. J. Devaney, submitted to J. Math. Phys.] have derived a dispersion relation for the propagation of the coherent wave through a medium containing scatterers. The expression involves forward scattering amplitudes. We show how for the case of spherical scatterers this expression can be interpreted in terms of the effective dynamic parameters of a unit spherical cell containing the scatterer. These effective parameters are derived by integrating stresses and strains over the surface of the unit sphere.
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