Reflection and transmission of structural waves at a corner of an arbitrary angle

Abstract

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). Malyuzhinets (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 Malyuzhinets’ special functions. An analytical solution is obtained for an arbitrary wedge angle.