### ASA 126th Meeting Denver 1993 October 4-8

## 4pSA1. Convolution formulation of leaky wave contributions to scattering
by plates and by cylinders and shells of variable curvature.

**P. L. Marston
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*Appl. Res. Lab., Univ. of Texas, Austin, TX 78713-8029 and Phys. Dept.,
Washington State Univ., Pullman, WA 99164-2814
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A novel high-frequency formulation is investigated that approximates the
leaky wave amplitude at the scatterer in terms of a spatial convolution of the
local incident wave pressure and a one-sided line response function h(s(greater
than or equal to)0)=-j(alpha) exp(-(alpha)s+ik[sub l]s). Here, s is the
propagation distance along the flat or curved surface, (alpha) is the
reciprocal of the attenuation length, k[sub l] the real part of the wave
number, and j=1 for equal fluid loading on both sides of a plate but j=2 for
one-sided fluid loading of a shell or for Rayleigh waves on a solid.
Application to plane waves incident on cylindrical surfaces (empty shell or
solid) of slowly varying curvature yields the following far-field amplitude
from a leaky ray propagating a distance S on the surface: p[sub
l]=-2(alpha)p[sub inc](2(pi)a[sub 1]a[sub 2]/ kr)[sup 1/2]
exp(-(alpha)S+i(pi)/4+i(eta)), where a[sub 1] and a[sub 2] are the radii of
curvature at the launching and detachment regions and (eta) is a geometrical
phase accumulation. When a[sub 1]=a[sub 2], the coupling coefficient G[sub l]
for a circular cylinder derived previously is recovered. The result can be
modified to situations where (alpha) varies weakly with curvature. [Work
supported by ARL:UTIR&D Program and by ONR.]