Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-02T21:09:35.745Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction of sound by a surface inhomogeneity at a fluid-solid interface

Published online by Cambridge University Press:  16 July 2009

R. H. Tew
R. H. Tew
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The diffraction of a plane sound wave in a fluid by an adjacent elastic solid containing a surface flaw is analysed using ray techniques. By solving the eikonal equation with suitable boundary data, the pattern of the rays leaving the boundary and propagating into the fluid and solid respectively is established, with the corresponding amplitudes being furnished by the appropriate system of transport equations. For the acoustic and elastic cylindrical bulk waves that emanate from the flaw itself, the amplitude directivities cannot be found from this ray analysis alone.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 2 , June 1992 , pp. 115 - 145
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brekhovskikh, L. 1980 Waves in Layered Elastic Media (2nd edn). Academic Press, New York.Google Scholar
Briggs, G. A. D. 1985 An Introduction to Scanning Acoustic Microscopy. Oxford University Press/Royal Microscopical Society.Google Scholar
Crighton, D. G. 1971 Acoustic beaming and reflexion from wave-bearing surfaces. J. Fluid Mech. 47, 625–38.CrossRefGoogle Scholar
Crighton, D. G. 1979 The free and forced waves on a fluid-loaded elastic plate. J. Sound Vib. 63, 225–35.Google Scholar
Crighton, D. G. 1983 The Green function of an infinite, fluid loaded membrane. J. Sound Vib. 86 (3), 411–33.CrossRefGoogle Scholar
Howe, M. S. 1990 Scattering by a surface inhomogeneity on an elastic half-space, with application to fluid-structure interaction noise. Proc. R. Soc. Lond. A429, 203–26.Google Scholar
Howe, M. S. 1990 Diffraction of sound by a surface scratch on an elastic solid. Euro. Jnl. Applied Math. 1 (4), 353–69.Google Scholar
Hulson, J. A. 1980 The Excitation and Propagation of Elastic Waves. Cambridge University Press.Google Scholar
Ilett, C., Somekh, M. G. & Briggs, G. A. D. 1984 Acoustic microscopy of elastic diseontinuities. Proc. R. Soc. Lond. A393, 171–83.Google Scholar
Keller, J. B., Lewis, R. M. & Seckler, B. D. 1956 Asymptotic solution of some diffraction problems. Comm. Pure Appl. Math. 9, 207–65.CrossRefGoogle Scholar
Keller, J. B. 1957 Diffraction by an aperture. J. Appl. Phys. 28, 426–44.CrossRefGoogle Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill, Kogakusha.Google Scholar
Rowe, J. M., Kushibiki, J., Somekh, M. G. & Briggs, G. A. D. 1986 Acoustic microscopy of surface cracks. Phil. Trans. R. Soc. Lond. A320, 201–14.Google Scholar
Sneddon, I. 1957 Elements of Partial Dfferential Equations. McGraw-Hill.Google Scholar
Somekh, M. G., Bertoni, H. L., Briggs, G. A. D. & Burtoni, N. J., 1985 A two-dimensional imaging theory of surface diseontinuities with the scanning acoustic microscope. Proc. R. Soc. Lond. A401, 29–51.Google Scholar
Tew, R. H. 1987 An imaging theory of surface-breaking discontinuities. D.Phil thesis, University of Oxford.Google Scholar
Tew, R. H. 1990 Ray theory of the diffraction of sound by an inhomogeneous membrane. IMA J. Appl. Math. 44, 95–110.CrossRefGoogle Scholar
Troup, I. E. A. 1977 Analysis of a fluid-plate interaction problem. MSe. dissertation, University of Oxford.Google Scholar
Whittaker, E. T. & Watson, G. N. 1927 A Course of Modern Analysis. Cambridge University Press.Google Scholar