Scattering of sound by a semi-infinite elastic plate with a soft backing; a matrix wiener-hopf problem

This paper looks at the acoustic edge scattering of a semi-infinite thin elastic plate. The plate is backed by an acoustically soft layer, so that pressure fluctuations vanish on one side. This is an example of a problem where the influence of an absorbent liner may reduce the acoustic far-field pressure levels, and has obvious applications in the area of jet-noise research. The problem is formulated into a matrix Wiener-Hopf equation for which no general method of solution has yet been found. However, studies have been made for restricted classes of these equations, and this paper shows that an exact solution is obtainable in the present case. The exact solution is found using a technique whereby the Wiener-Hopf equation is converted into a scalar Hilbert problem. The asymptotic form of this solution is determined when the influence of the fluid on plate deflections is very large. © 1986 Oxford University Press.