### ASA 124th Meeting New Orleans 1992 October

## 2pSA7. Reflection of axial surface waves from the end of a fluid-loaded
cylindrical shell: A Wiener--Hopf analysis.

**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.