### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5aUW11. Kirchhoff scattering for fourth-order structural wave systems.

**R. Martinez
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*Cambridge Acoust. Associates, Inc., 200 Boston Ave., Ste. 2500, Medford,
MA 02155
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Real structures always contain discontinuities that act as scattering
agents for the smooth-geometry elastic wave systems that they otherwise
support. A typical such structural-wave diffractor of continuing interest is a
partial arc frame on a thin cylindrical shell. This paper aims to turn that
mathematically unseparable problem into a canonical one by developing a
Kirchhoff scattering theory for the shell's fourth-degree wave systems: both
for the plate-like flexural motion and for the in-plane ``membrane'' fields,
which are each governed by the operator ((del)[sup 2]+k[sub p][sup 2])
((del)[sup 2]+k[sub s][sup 2]) at high frequencies. The suggested
quasidecoupling of the radial motion from the other two (which remain coupled)
is the result of an intermediate perturbation expansion of the shell equations
in terms of two parameters. The structurally diffracted field of the radial
motion, delivered analytically by the new structural Kirchhoff scattering
theory, becomes an extended source of sound that is now likewise available
analytically. The predictions to be presented of the target strength of an
internal partial frame in a cylindrical shell generalize those made by Rumerman
for a full end frame [J. Acoust. Soc. Am. 93, 55--65 (1993)].