Plane acoustic wave diffraction at a semi-infinite thin elastic plate

Abstract

The problem of plane acoustic wave diffraction at a thin semi-infinite elastic plate was first stated, and an approach to its solution described, by G. D. Malyuzhinets at the Fourth All-Union Conference on Acoustics, Moscow, 1958. It was not possible at that time to complete the solution, first because the theory of Malyuzhinets functional equations was still incomplete, second because no methods had been developed for analyzing the diffraction fields corresponding to the solutions of these equations, and third, because no detailed analysis had been made of the behaviour of the Brewster angles corresponding to a thin elastic plate. A more complete theory of Malyuzhinets functional equations was later developed [1, 2], together with methods for analyzing diffraction fields in an irregular region [3–5]. As a result, it was possible to finalize the solution of the problem described, and to analyze the solution in detail; the present paper describes the results obtained. Notice that a solution of a problem similar to that described was recently obtained by the Wiener-Hopf-Fock method in [6].