BACKGROUND CONTRIBUTIONS AND COUPLING-COEFFICIENTS FOR BACKSCATTERINGBY THICK SHELLS

Approximations for leaky wave coupling coefficients and background sca ttering contributions are usually derived by assuming the shell respon se is governed by thin shell theory. Comparisons are described with ap proximations derived by other methods for a thick spherical shell at f requencies above coincidence. The variation of the phase of the coupli ng coefficient from numerical evaluation of the Watson transformation residue by Kargl [Ph.D. thesis, Washington State University (1990)] is evident in an analytical approximation. The phase of the background i ncludes inertial and wave-kinematic contributions and is related to re search by Gaunaurd and Werby [J. Acoust. Sec. Am. 90, 2536-2550 (1991) ]. The inertial contribution to the background phase is derived direct ly from the reflectivity of a plate in the limit of small phase shift for propagation across the thickness of the shell. The frequency and a ngle dependence of the phase of the exact reflection coefficient of a plate (having the same thickness as the shell) is also examined. (C) 1 997 Acoustical Society of America.