Steven L. Means
Allan D. Pierce
Graduate Prog. in Acoust., Penn State Univ., 157 Hammond Bldg., University Park, PA 16802
At frequencies somewhat below the ring frequency, a fluid-loaded cylindrical shell supports a surface wave, the energy of which is predominantly in the surrounding fluid. The possible propagation directions are limited to those close to the axial direction. For such waves the inertia of the elastic material is unimportant and the shell behaves nearly as a Winkler foundation, such that the ratio of the external acoustic pressure to the inward displacement is Eh/R[sup 2]. The present paper seeks to quantify the physical phenomena associated with reflection of such a wave from a free end of a shell, but to make the analysis tractable, the shell is regarded as a semi-infinite locally reacting cylinder extending from -(infinity) to 0, followed by a rigid cylindrical baffle, also of radius R, extending from 0 to (infinity) along the x axis. A known surface wave is incident from x=-(infinity) and one seeks the amplitude and phase shift of the reflected surface wave along with any acoustic field radiating into the fluid that originates in the vicinity of the shell end at x=0. An exact solution involving contour integrals is derived using the Wiener--Hopf technique and applicable asymptotic results are extracted.