### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 2pSA7. Reflection and transmission of structural waves at a corner of an
arbitrary angle.

**Jane B. Lawrie
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*Dept. of Mathematics, Brunel Univ., Uxbridge UB8 3PH, UK
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**I. David Abrahams
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*Keele Univ., Keele ST5 5BG, UK
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This talk is concerned with an analytic investigation into the reflection,
transmission, and scattering of fluid-coupled structural waves by a corner of an
arbitrary angle. The fluid domain is an open wedge, the surfaces of which are
described by high-order boundary conditions (that is, containing derivatives
with respect to variables both normal and tangential to the boundary).
Maliuzhinets (1958) obtained an exact solution for a wedge with impedance faces.
However, until the works of Osipov (1994) and Abrahams and Lawrie (1995), little
progress was made on adapting his method to problems with more realistic
wave-bearing boundaries. The model comprises a compressible fluid wedge bounded
by two plane elastic surfaces. An unattenuated surface wave, incident from
infinity along one wedge face, is scattered at the apex. Several different edge
conditions are discussed, including configurations which excite in-plane plate
motions. Explicit application of these constraints allows the boundary value
problem to be formulated as two inhomogeneous coupled difference equations which
are solved using Maliuzhinets' special functions. An analytical solution is
obtained for an arbitrary wedge angle.