R. Martinez
Cambridge Acoust. Associates, Inc., 200 Boston Ave., Ste. 2500, Medford, MA 02155
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)].