Diffraction by a semi-infinite membrane in the presence of a vertical barrier

I. D. Abrahams

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this paper the scattering of sound by a semi-infinite membrane when joined to a semi-infinite absorbent (pressure release) surface is examined. The angle between the two surfaces is 3π/2 and the forcing for the problem is supplied by an incident surface wave. By using the Kontorovich Lebedev transform the problem is reduced to finding the solution of a sixth order difference equation derived from the membrane boundary condition. The general solution of this equation is obtained and eigensolutions of the problem (homogeneous solutions of the difference equation) are found to be required to give the correct edge behaviour. The exact solution to the problem is found both when the membrane is taken as having zero displacement at the edge, and also when the slope of the membrane vanishes at this edge. The reflection coefficients are determined for both edge conditions and these expressions are given explicitly when a fluid loading parameter in the problem is large. The applicability of this method to a wide class of wave bearing surfaces is discussed. © 1986 Academic Press Inc. (London) Limited.
    Original languageEnglish
    Pages (from-to)191-207
    Number of pages16
    JournalJournal of Sound and Vibration
    Volume111
    Issue number2
    Publication statusPublished - 8 Dec 1986

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