Vibrations of a heavily loaded, semi-infinite, cylindrical elastic shell. I

A mixed boundary-value problem is formulated to describe the axisymmetric coupled motion between an inviscid, compressible fluid and a semi-infinite cylindrical elastic shell. The shell is rigidly bonded to a hollow cylindrical duct, which acts as a waveguide for the plane acoustic wave that forces the system. An exact solution, in terms of contour integrals, is obtained by means of the Wiener-Hopf technique, and this is then interpreted in the limit of heavy fluid loading and long waves.