Acoustic scattering by a closed semi-infinite fluid-loaded elastic cylindrical shell

A plane sound wave is obliquely incident upon a semi–infinite elastic circular cylindrical shell, closed at one end by a rigid but movable disk, with exterior fluid loading. Expanding the unknown pressure on the end plate as a Dini series and applying half–range Fourier transforms allows the problem to be formulated as a Wiener–Hopf equation with unknown coefficients which satisfy a system of simultaneous linear equations. The solution is presented for the axisymmetric, n = 0 harmonic, component of the scattered sound, which in the far–field consists of the cylindrically spreading waves, in appropriate regions, which would have been present if the shell had been infinitely long, together with a spherically spreading component which is due to the semi–infinite length of the shell. Some numerical results are presented for the spherically spreading component of the scattered field.