The acoustic scattering by thin-walled, evacuated, elastic spherical shells immersed in water is studied. The analytic structure of the scattering amplitude in the complex-k plane is directly analyzed using Cauchy's residue theorem, and dispersion curves are presented for the lowest elastic modes of the fluid-loaded shell. It is found that fluid loading has a profound effect on the vacuum dynamical characteristics of the shell; the spherical equivalent of the first antisymmetric, fiat-plate Lamb wave for the fluid-loaded shell bifurcates into two distinct modes near the frequency that the vacuum dispersion curve transitions from a subsonic to a supersonic phase velocity. By way of contrast, the spherical equivalent of the first symmetric Lamb wave is essentially unaffected. The salient features of the free-field scattering process are also analyzed in terms of the resonance excitation of these modes. , PACS numbers: 43.30. Gv, 43.20.Fn, 43.40.Ey INTRODUCTIONThe study of the acoustic scattering from submerged, elastic targets has become increasingly fashionable in the last decade. Much of the more recent work has been concerned with resonance scattering theory and its implications for the inverse scattering problem. However, advances in this area will also have an impact on the more general question of fluid-elastic structure interactions, which have much more diverse applications. In this context, we note that the fluidloaded, elastic spherical shell is the simplest, nontrivial, three-dimensional example of such a dynamical system amenable to a numerical/analytical treatment over an extended frequency range. A solid physical understanding of the scattering from this target will surely yield dividends when the subtleties associated with more complicated structures are encountered. This acoustic scattering problem, which is the subject of the present article, thus takes on special significance.The earliest investigation of the acoustic scattering from an elastic spherical shell was apparently by Junger. • This article was quite modern in perspective in that it touched on a number of issues of current interest. For example, it was in this article that the concept of the separation of the scattering solution for shells into two terms, a "rigid body scattering" (background) contribution and a "radiation scattering" (resonant) contribution, was first introduced. While Junger's analysis also underscored the profound effects of fluid loading on the dynamical characteristics of the shell in vacuum, 2 this analysis must be regarded as incomplete; the thin shell theory employed by this author was later found to be inadequate for the bending modes of a spherical shell. 3 A scattering formalism utilizing the full linearized, elastic equations of motion for the spherical shell was later given by Goodman and Stern 4 and subsequently employed by Hickling • in a theoretical study of steady state and transient solutions. Hickling's analysis of the scattering of short transient pulses led him to propose that the component of the sc...

The acoustic scattering from an elastic spherical shell in a homogeneous, range-independent waveguide is studied. New phenomena are observed that have no counterpart in free-field scattering. First, the free-field resonance spectrum exhibits fine structure, that is, the l th resonance splits into (l + 1 ) distinct components. This splitting is most pronounced near the waveguide l•oundaries. Second, "superresonances" are observed. It is found that at certain water column heights and scatterer depths, significant enhancements of the resonance strength occur. In some cases, more than 100-fold enhancement is observed.PACS numbers: 43.20.Mv, 43.30.Gv

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A transition matrix formalism is developed for the acoustic scattering from a target in a layered, inhomogeneous waveguide. The connection is made with the normal mode model of propagation and the total acoustic wave is expressed as a sum over waveguide modes. For a target in a deep ocean environment, the scattering solution may be expressed in terms of the free-field T matrix and the normal mode wavefunctions for the empty waveguide. Both homogeneous and inhomogeneous layers are considered. PACS numbers: 43.20.Fn, 43.20.Mv, 43.30. Gv

A multiple scattering analysis is presented for a target in a range-independent oceanic waveguide. The multiple scattering series is explicitly summed and a solution is obtained in closed form. The solution agrees with that presented earlier [R. H. Hackman and G. S. Sammelmann, J. Acoust. Soc. Am. 80, 1447–1458 (1986)] for all cases that were checked. The method provides an attractive alternative to the previous formalism in two regards. First, this approach provides insight into the algebraic structure of the solution. The individual terms in the final solution may be simply interpreted in terms of single scattering processes. And, second, there is less algebra involved when relatively simple waveguides are considered. Numerical examples are given that illustrate the importance of contributions involving rescattering among the target and the waveguide boundaries.