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Apr 1982

Volume 71, Issue S1, pp. S1-S113

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back to top Session V. Physical Acoustics III: Reflection and Scattering
Invited Paper
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K‐space formulation of the scattering problem in the time domain (A)

Norbert N. Bojarski

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S44-S44 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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The arbitrary direct scattering problem is solved numerically in closed form in the time domain and spatial Fourier transform space. This solution consists of casting the general basic global laws (i.e., the second‐order partial differential wave equation or its integral representation) as a local algebraic equation in the spatial Fourier transform space, and leaving the specific local constitutive equations (i.e., the algebraic boundary conditions, which specify a given structure, which are conventionally imposed on the differential or integral representation of the general basic global wave equation) as a local algebraic equation in real space, thereby reducing the scattering problem to a statement of two simultaneous local algebraic equations in two unknowns (the fields and the induced sources) in two spaces connected by the spatial Fourier transform. A temporally local representation in both spaces is obtained with the aid of an introduced auxilliary field and two propagators. By virtue of causality, a numerically efficient closed form solution to this set of equations is obtained that utilizes the fast Fourier transform algorithm as the transformations between the two spaces. By virtue of the numerically efficient fast Fourier transform algorithm and the local algebraic representations, the number of required complex multiply‐added operations and storage allocation is of the order of N log2 N and N per temporal discretization, respectively (where N is the number of spatial cells into which the scattering problem is discretized). It is shown that the solution is only of the order of log2 N slower than an ideal solution. The solution is thus practical for very large one‐, two‐, and three‐dimensional scattering problems. Numerico‐experimental results for a variety of refrective index profiles, including perfect reflectors, are presented, thus verifying the presented algorithm.
Contributed Papers
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Ultrasonic wave scattering from solids with periodic surfaces: Theory and experiment (A)

Alain Jungman, Laszlo Adler, Robert Roberts, and Jan Achenbach

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S44-S44 (1982); (1 page) | Cited 1 time

Online Publication Date: 12 Aug 2005

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The problem of an ultrasonic wave scattered from solids with periodic surfaces is formulated analytically. This analysis uses an integral representation of the scattered elastodynamic field in terms of the surface displacement of a suitable canonical problem. A digitized ultrasonic spectrum analysis system is used to measure the frequency components of broadband pulse backscattered from periodic surfaces of various solids. Features of the observed amplitude spectra are analyzed based on theoretical predictions.
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Scattering behavior of a solid with a periodic rough surface (A)

Richard K. Johnson and Shun‐Lien Chuang

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S44-S44 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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A theoretical approach based on the extended boundary condiiton for wave scattering from a liquid and solid periodic interface has been presented and compared with experimental data by Chuang and Johnson [J. Acoust. Soc. Am. Suppl. 1 70, S80 (1981)]. This theory is now applied to study scattering effects in water for several cases in order to demonstrate the physics of the problem. (1) The scattering from two different surface profiles: sinusoidal and triangular. (2) The diffraction efficiencies as functions of the frequency. (3) The effect of viscoelasticity on the diffraction efficiencies. The effects of frequency are also compared with experimental data measured for an acrylic block with a triangular surface profile. We observe peaks in the specular diffraction efficiency at two incidence angles both theoretically and experimentally. One peak occurs near the critical angle of the compressional wave of the solid. The second peak occurs at the angle of incidence such that the surface wave of the liquid and solid is excited. Changing the frequency will change the position of the second peak. The diffraction efficiencies of the peaks are also found to be sensitive to viscoelasticity in the solid.
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Reflection from and transmission through a periodically stratified ideal fluid half‐space (A)

Michael Schoenberg and Pabitra N. Sen

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S44-S45 (1982); (2 pages)

Online Publication Date: 12 Aug 2005

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The problem of the reflection of acoustic waves from a periodically layered acoustic half‐space is solved exactly at all frequencies. Pass and stop bands and the associated complex slowness surfaces for propagation through the periodic medium are found. In the low‐frequency limit, when the wavelength normal to the layering is much greater than one period, it is shown that there always exists a homogeneous ideal fluid with the same reflection properties as the layered medium. The effective acoustic medium that models transmission as well as reflection at low frequencies has a bulk modulus, Keff, given by 〈K−1〉−1, where the brackets denote a volume weighted average. However, for the inertial density appearing in the equations of motion, the effective medium has an anisotropic density tensor with ρ∥, the density component parallel to the layering, given by 〈1/ρ〉−1, and ρ⟂, the density component perpendicular to the layering given by 〈ρ〉. The slowness surface for such an anisotropic acoustic medium is the usual ellipse with a speed that is always greater parallel to the layering than normal to the layering.
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Acoustical behavior of a submerged steel plate coated with an elastomer layer that contains perforations (A)

Anthony J. Rudgers and Christine A. Solvoid

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S45-S45 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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The reflection and transmission characteristics of an infinite steel plate submerged in water are analyzed for a normally incident plane acoustic wave. The plate is coated on one side by a layer of styrene‐butadiene rubber (SBR) perforated by a doubly periodic array of rectangular holes. A second, thin, homogeneous SBR layer covers the perforated layer so as to exclude water from the holes. Numerical analyses are presented that compare two different models describing the perforated layer—the “effective‐modulus” model and an alternative model derived using an approximate elasticity‐theory analysis. In the effective‐modulus model, only the volume concentration of the perforations in the SBR affects the elastic properties of the layer. However, in the alternative model, the layer elastic properties are affected by the size, shape, and pattern of the perforations, in addition to their concentration. The effects of perforation size, shape, and pattern are illustrated by comparing computed results for different perforation schemes having the same volume concentration of perforations. [This abstract appears in the program of the 102nd Meeting. The paper, which was to have been presented as paper HH3 at that Meeting, was cancelled.]
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Reflection of Waterborne acoustic waves from a viscoelastic layer on a rigid hacking with perforations (A)

J. Jarzynski

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S45-S45 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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The reflection coefficient is calculated for a plane acoustic wave normally incident on a viscoelastic rubber cover layer submerged in water. The rubber layer is mounted on a rigid backing with air‐filled cylindrical perforations. Acoustical losses are attributed to motion of the layer over the perforations. This motion is calculated by treating the layer above each perforation as a vibrating circular viscoelastic plate. Different boundary conditions are assumed, and in each case the sound reflection coefficient is calculated. The results are compared with the experimental data of R. Lane [Ultrason. 19, 28–30 (1981)].
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A novel lining for an anechoic water tank (A)

Thomas E. Burton

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S45-S45 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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A novel method for achieving excellent reflection loss and transmission loss in a layer was presented at the previous meeting [T. E. Burton, J. Acoust. Soc. Am. Suppl. 1 70, S72 (1981)]. This theoretical concept is now applied to the design of an anechoic water tank. The previous paper considers only coherent reflection and assumes convenient but unrealistic properties for the layer's materials. The present paper assumes more realistic properties, contends with both coherent and incoherent reflections, and also treats the effects of curvature of the wavefronts.
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Acoustic wave scattering by highway noise barriers (A)

V. K. Varadan, V. V. Varadan, and S. Hayek

J. Acoust. Soc. Am. Volume 71, Issue S1, pp. S45-S45 (1982); (1 page)

Online Publication Date: 12 Aug 2005

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Barriers are commonly constructed beside highways to screen residential areas from traffic noise. The effectiveness of the barrier depends on its shape and height, the material with which it is constructed and its distance from the source of noise. In this paper we wish to analyze acoustic wave scattering by highway barriers of different shape and height. The sources considered will be harmonic point and line sources. The T‐matrix method and the finite element approach will be used to solve the scattering problem taking into consideration the effect of the ground. Comparisons with scale model experiments will be made.
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