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Journal of the Acoustical Society of America

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May 1989

Volume 85, Issue S1, pp. S1-S156

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back to top Session T. Underwater Acoustics III and Structural Acoustics and Vibration III: Commonality Between the Fields of Underwater Acoustics and Structural Acoustics
Invited Papers
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Radiation and scattering from laminated spherical shells (A)

Henrik Schmidt

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S49-S49 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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The solution in terms of spherical harmonics to acoustic and elastic wave propagation problems in spherically stratified media is well established. However, except for very low ka values, a direct numerical implementation is unstable. Propagator matrix approaches have been applied for moderate ka values, whereas environment transformations have been developed to represent the spherical stratification by a plane stratification at higher ka values, in particular in relation to long‐range seismic propagation in the solid earth. Here, it is demonstrated that, by introducing a proper normalization of the spherical Bessel functions, unconditional stability can be obtained by using the Global Matrix approach [H. Schmidt and F. B. Jensen, J. Acoust. Soc. Am. 77, 813–825 (1985)]. This SAFARI code has therefore been modified to treat propagation in spherically stratified elastic media. The algorithm is stable at least up to ka = 103, allowing modeling of stratifications alternating between high‐ and low‐speed layers, traditionally problematic for propagator approaches. Examples will be given for high‐frequency scattering from coated shells as well as simulations of array signal processing performance in relation to structural acoustics experiments. [Work supported by ONR.]
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Three‐dimensional Green's function for fluid‐loaded thin elastic cylindrical shell: Formulation and solution (A)

L. B. Felsen, J. M. He, and I. T. Lu

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S49-S49 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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This paper treats sound radiation from a time‐harmonic point pressure source located either inside or outside a thin, homogeneous, infinitely long circular cylindrical elastic shell, which is immersed in different interior and exterior fluid media. This Green's function problem is attacked by a combination of the method of separation of variables and the method of images applied to an infinitely extended azimuthal (ϕ) domain. The reduced one‐dimensional problems in the cylindrical (r, ϕ, z) coordinates are solved by general spectral techniques in terms of one‐dimensional characteristic Green's functions gr, gϕ, gz, which depend on one or both of the two complex spectral separation parameters (spatial wavenumbers) λ1 and λ2. While the one‐dimensional problems in the ϕ and z domains are straightforward, the presence of the shell in the radial domain introduces substantial complexity. The solution is obtained by defining the discontinuities in the pressure and normal displacement across the shell via recourse to the dynamical equations of motion inside the shell. The synthesis problem is made unique through a complete analysis of the spectral singularities gr,ϕ,z in their respective complex planes, which permits selection of appropriate integration contours. A host of alternative representations, whose choice (concerning utility) is motivated by the parameter range of interest, can be derived from the fundamental spectral form, and asymptotic reductions lead to a variety of wave processes that have a cogent ray acoustic interpretation. [Work supported by ONR.]
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Coherence theory in volume scattering and structural acoustics (A)

Mark J. Beran and John J. McCoy

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S49-S49 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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In this paper, the use of the two‐point coherence function, defined for arbitrarily positioned points, to study wide‐angle volume scattering problems in the ocean and wave propagation in cylindrical shells subject to random forcing is considered. Although the basic equations of the two phenomena are different, it will be shown that the basic approach developed 30 years ago in optics is a useful way to study these and similar problems. First, the theory of partial coherence developed in optics for free‐space propagation from random sources is reviewed. Then, the coherence equations for the cylindrical shell propagation case are formulated, and it is shown how the equations may be solved when the two‐point statistics of the forcing function are known.
Contributed Papers
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Frequency wavenumber analysis of seismoacoustic waves in an ice layer (A)

G. Giellis and T. C. Yang

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S50-S50 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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Seismoacoustic waves traveling in an ice layer over a deep Arctic Ocean are studied using frequency wavenumber analysis. Ice‐ridge‐generated noise can travel in the ice via ice‐trapped waves and water‐borne waves coupled to the ice. {Previous hydrophone data [B. Buck and J. H. Wilson, J. Acoust. Soc. Am. 80, 256–264 (1986)] indicated that the noise originated from the bottom of a ridge.} The data are simulated by a point source in the water (for the water‐borne waves) and a point source in the ice (for the ice‐trapped noise) using the SAFARI numerical code with a planar receiver array of vertical axis geophones. Frequency wavenumber analysis is applied to the simulated data to determine the wavenumber of the various waves traveling in the ice. The methodology and preliminary results of this analysis will be reported.
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Low‐frequency diffraction from a free surface coupled to a semi‐infinite elastic surface as modeled by sea ice properties (A)

Peter H. Dahl and George V. Frisk

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S50-S50 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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This paper discusses the solution of a low‐frequency plane wave incident upon a semi‐infinite elastic plate, such as an Arctic ice lend or free edge, using the Wiener‐Hopf method. By low‐frequency it is meant that the elastic properties of the plate are adequately described by the thin plate equation. For example, in a floating ice sheet, this translates into frequency‐ice thickness products that are ≲ 150. A key issue here is the fluid loading pertaining to sea ice and low‐frequency acoustics, which cannot be characterized by simplifying heavy or light fluid loading limits. An approximation to the exact kernel of the Wiener‐Hopf functional equation is used here, which is valid in this midrange fluid loading regime. The farfield diffracted pressure is found, which includes a fluid‐loaded, sub‐sonic (relative to the water) flexural wave in the ice plate. Comparisons are also made with the locally reacting approximation to the input impedance of an ice plate. The combined effects of the ice lead diffraction process represent loss mechanisms that contribute to the transmission loss in long‐range Arctic acoustic propagation.
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Low‐frequency SAW sensors for the detection of shear stresses in the turbulent boundary layer (A)

Yongrae Roh, Vasundara V. Varadan, and Vijay K. Varadan

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S50-S50 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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To simulate a low‐frequency SAW device, surface wave propagation at the boundary between water and a thin film of PZT‐SH on steel was investigated extensively through numerical analysis. Two‐ and three‐dimensional dispersion curves, attenuation mechanism, and displacement variation were obtained for each of the propagation modes of all types of the surface waves (Rayleigh, Scholte, and Love) in the medium. The energy distributions of the Rayleigh and Scholte waves have also been obtained. With these results, the optimum geometry (crystal cut, propagation direction, and nondimensional wavenumber) for maximum launching efficiency was determined. The acoustic fluid was replaced by a turbulent flow, and the variation of the propagation velocity of the SAW due to turbulence was investigated. These results show a new method to distinguish the effect of shear stress fluctuations from that of normal pressure in a turbulent flow.
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