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

## 5aUW5. Coupling coefficient for leaky waves on thick spherical shells from
elasticity theory.

**Steven G. Kargl
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*Appl. Phys. Lab., Univ. of Washington, Seattle, WA 98105
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**Philip L. Marston
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*Washington State Univ., Pullman, WA 99164-2814
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An approximation of leaky wave scattering amplitudes for thick spherical
shells in water was previously demonstrated for backscattering and (through the
optical theorem) the total cross section [S. G. Kargl and P. L. Marston, J.
Acoust. Soc. Am. 88, 1103--1113 (1990); 89, 2545--2558 (1991)]. In the
convention of that formulation, it was sufficient to approximate the complex
leaky wave coupling coefficient G[sub l] for the thick shell by 8(pi)(beta)[sub
l]c/c[sub l] over the frequency range considered. In the present work,
calculations are given pertaining to that approximation that are based on full
elasticity theory and a generalization of Watson transformation results for
solid spheres. The computations [S. G. Kargl, Ph.D. dissertation, Wash. State
Univ. (1990)] show that while |G[sub l]| is well approximated as noted,
(phi)[sub l]=arg(G[sub l]) tends to negative values for low ka [roughly in
proportion to (ka)[sup -1]] for both the s[sub 0] wave and the supersonic
region of the a[sub 0] wave. At large ka, (phi)[sub l] becomes small in
agreement with the approximation. Over a range of ka above the coincidence
frequency the (phi)[sub l](ka) curves for the a[sub 0] and s[sub 0] waves are
similar and |(phi)[sub l]|<1 rad. [Work supported by ONR.]