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A Three-Dimensional Wiener-Hopf Technique for General Bodies of Revolution: Part 1—Theory

[+] Author Affiliations
Rudolph Martinez, Brent S. Paul, Morgan Eash, Carina Ting

Alion Science and Technology Corporation, Mystic, CT

Paper No. IMECE2009-13344, pp. 65-79; 15 pages
doi:10.1115/IMECE2009-13344
From:
  • ASME 2009 International Mechanical Engineering Congress and Exposition
  • Volume 15: Sound, Vibration and Design
  • Lake Buena Vista, Florida, USA, November 13–19, 2009
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4388-8 | eISBN: 978-0-7918-3863-1
  • Copyright © 2009 by ASME

abstract

This work, the first of two parts, presents the development of a new analytic solution of acoustic scattering and/or radiation by arbitrary bodies of revolution under heavy fluid loading. The approach followed is the construction of a three-dimensional Wiener-Hopf technique with Fourier transforms that operate on the finite object’s arclength variable (the object’s practical finiteness comes about, in a Wiener-Hopf sense, by formally bringing to zero the radius of its semi-infinite generator curve for points beyond a prescribed station). Unlike in the classical case of a planar semi-infinite geometry, the kernel of the integral equation is non-translational and therefore with independent wavenumber spectra for its receiver and source arclengths. The solution procedure begins by applying a symmetrizing spatial operator that reconciles the regions of (+) and (−) analyticity of the kernel’s two-wavenumber transform with those of the virtual sources. The spatially symmetrized integral equation is of the Fredholm 2nd kind and thus with a strong unit “diagonal” — a feature that makes possible the Wiener-Hopf factorization of its transcendental doubly-transformed kernel via secondary spectral manipulations. The companion paper [1] will present a numerical demonstration of the new analysis for canonical problems of fluid-structure interaction for finite bodies of revolution.

Copyright © 2009 by ASME

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