Scattering of fluid loaded elastic plate waves at the vertex of a wedge of arbitrary angle, I: analytic solution

This article is the first part of an investigation into thescattering of fluid coupled structural waves by an angular discontinuityat the junction of two plates of different material properties.These two thin elastic plates are semi-infinite in extent thereforeforming the faces of an infinite wedge, the interior of whichcontains a compressible fluid. A plane unattenuated structuralwave is incident along the lower face of the wedge and is scatteredat the apex. The edges of the elastic plates may be joined ina variety of different ways, for example, they may be pin-jointedto an external structure or welded to each other. In the formercase, the plates will experience only the usual flexural vibrationswhereas in the latter case longitudinal (in-plane) disturbanceswill be generated and will propagate away from the wedge apex. An exact explicit solution is sought in terms of a Sommerfeldintegral representation for the fluid velocity potential. Thispermits the boundary-value problem to be recast as a functionaldifference equation which is easily solved in terms of the Maliuzhinetsspecial function (Maliuzhinets, Soviet Phys. Dokl. 3 1958).The chosen ansatz for the solution is of a different form fromthat used previously by the authors for the less complicatedmembrane wedge problem. The new ansatz has several analyticand numerical advantages which enable the reflection and transmissioncoefficients to be expressed explicitly in a compact form thatis ideal for computation. In the second part of this study a full numerical investigationof the reflection and transmission coefficients will be presentedfor a variety of interesting parameter ranges and edge conditions.     

Scattering of Sound by Large Finite Geometries

Diffraction problems with finite geometries do not usually haveexact solutions and so asymptotic methods, which require a largeor small parameter, are employed to obtain approximate results.This paper presents a formal method for approximating the acousticpotential when the finite length in the geometry is large comparedto an acoustic wavelength. The method presented is exactly analogousto other approaches, including the modified Wiener-Hopf technique,but is advantageous because of its relative ease of use andapplicability to many problems. This is shown by using the methodon problems with resonances and complicated geometries.