Gerry R. Wickham
Dept. of Math., Univ. of Manchester, Manchester M13 9PL, England, UK
The scattering of sound of wavelength 2(pi)/k by a circular elastic plate of radius a in an infinite planar contrasting baffle is exactly formulated in terms of a singular integral equation of the second kind using a novel extension of the Wiener--Hopf technique. The exact solution of this equation is easily derived analytically as a rigorous convergent expansion that is also asymptotic in the limit ka->(infinity). Thus it is possible to derive explicit asymptotic formulas for the scattered field in terms of the factorization of the standard Wiener--Hopf kernel corresponding to the canonical diffraction problem for two adjoining semi-infinite compliant surfaces. The special cases of an elastic plate in a rigid baffle and a rigid plate in an elastic baffle are considered in detail. It turns out that the asymptotic forms for the diffracted far fields may be simplified dramatically using a factorization procedure devised by the author and Andrew Norris and that these results are uniform in the fluid loading parameter.