Scattering of fluid loaded elastic plate waves at the vertex of a wedge of arbitrary angle .1. Analytic solution

J B Lawrie, I D Abrahams

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    Abstract

    This article is the first part of an investigation into the scattering of fluid coupled structural waves by an angular discontinuity at the junction of two plates of different material properties. These two thin elastic plates are semi-infinite in extent therefore forming the faces of an infinite wedge, the interior of which contains a compressible fluid. A plane unattenuated structural wave is incident along the lower face of the wedge and is scattered at the apex. The edges of the elastic plates may be joined in a variety of different ways, for example, they may be pin-jointed to an external structure or welded to each other. In the former case, the plates will experience only the usual flexural vibrations whereas in the latter case longitudinal (in-plane) disturbances will be generated and will propagate away from the wedge apex. An exact explicit solution is sought in terms of a Sommerfeld integral representation for the fluid velocity potential. This permits the boundary-value problem to be recast as a functional difference equation which is easily solved in terms of the Maliuzhinets special function (Maliuzhinets, Soviet Phys. Dokl. 3 1958). The chosen ansatz for the solution is of a different form from that used previously by the authors for the less complicated membrane wedge problem. The new ansatz has several analytic and numerical advantages which enable the reflection and transmission coefficients to be expressed explicitly in a compact form that is ideal for computation. In the second part of this study a full numerical investigation of the reflection and transmission coefficients will be presented for a variety of interesting parameter ranges and edge conditions.
    Original languageEnglish
    Pages (from-to)1-23
    Number of pages23
    JournalIMA Journal of Applied Mathematics
    Volume59
    Issue number1
    Publication statusPublished - 1997

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