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Backscattering from a cloaked submerged spherical shell is analyzed in the low, mid, and high frequency regimes. Complex poles of the scattered pressure amplitudes using Cauchy residue theory are evaluated in an effort to explain dominant features of the scattered pressure and how they are affected by the introduction of a cloak. The methodology used is similar to that performed by Sammelmann and Hackman [J. Acoust. Soc. Am. 85, 114-124 (1989); J. Acoust. Soc. Am. 89, 2096-2103 (1991); J. Acoust. Soc. Am. 90, 2705-2717 (1991)] in a series of papers written on scattering from an uncloaked spherical shell. In general, it is found that cloaking has the effect of diminishing the amplitude and shifting tonal backscatter responses. Extreme changes of normal and tangential fluid phase velocities at the fluid-solid interface when cloaking is employed leads to elimination of the 'mid-frequency enhancement' near the coincidence frequency for even modestly effective cloaks, while reduction of the 'high-frequency enhancement' resulting from the 'thickness quasi-resonance' near the cut-off frequency of the symmetric (S2B) mode requires more effective cloaking, but can be practically eliminated by employing a cloak that creates tangential acoustic velocities in excess of the S2B mode phase speed near cutoff. [ABSTRACT FROM AUTHOR]

An investigation into the applicability and accuracy of Pritchard's approximation for closely packed transducer arrays is undertaken. A new, 'modal' Pritchard approximation is developed, based upon normal modes of the acoustic medium, and is tested for arrays of acoustically hard spheres to ascertain its accuracy in determining the mutual acoustic radiation impedance between array elements. For ka≈1, it is found that the modal Pritchard approximation works quite well in approximating the mutual radiation impedance of a two-element array, even for relatively close spacing; but for arrays of three or more scatterers in close proximity the approximation may have relatively large errors. The effect of neglecting inter-element scattering is analyzed for the monopole-to-monopole scattering of various configurations of a three-element array and a sixteenelement double line array. © 2001 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A new method for solving the scattering problem of acoustic pulses by baffled membranes is described. It is an adaptation of the finite difference technique which uses an ''artificial'' boundary condition to mimic an infinite region. The numerical method is used on several problems involving a plane compact pulse. It is also used on a time-harmonic pulse of infinite extent. This pulse generates a time-harmonic response as t→∞; this is proved in the Appendix. The numerical scheme is marched out in time until the transients have decayed away and a time-harmonic solution has been established. This ''relaxation'' scheme yields accurate solutions in a reasonable amount of time without requiring heavy or light fluid loading assumptions. [ABSTRACT FROM AUTHOR]

Bi-orthogonality relationships are established for a vertically heterogeneous porous media in contact with a fluid, a solid, a second porous medium, and a free surface. Fraser's bi-orthogonality relation for propagation of Rayleigh-Lamb modes in a plate with traction-free surfaces is shown to be a special case of the bi-orthogonality relations derived herein in which the medium can be thought of as a porous slab with zero porosity. [ABSTRACT FROM AUTHOR]

The acoustical performance of a submerged linear array of spherical shells in shallow water is examined by combining the T-matrix method of solving for multiple acoustic interactions among separate bodies with a model for the ocean as a fluid layer over a half-space of a distinct fluid. The system of source and reflected waves is analyzed by standard approximate contour integration techniques, valid for the far field of the array. Calculations using the results show the effects of shallow water on array performance. [ABSTRACT FROM AUTHOR]

The scattering of a time harmonic acoustic wave by an array of N identical baffled membranes is considered in the limit as N→∞. The method of matched asymptotic expansions is used to construct an inner and outer expansion; the inner expansion contains the physics of the local periodic structure and the outer expansion has the proper behavior in the far field. The matching process is used to determine a set of unknown coefficients in the analysis and the result is a far-field pattern for the structure that blends the physics of both expansions. In particular, the far-field pattern is highly localized about the Bragg or mode angles of the inner representation. The maximum value of this function is directly proportional to the reflection coefficient determined numerically from the inner problem. Several numerical examples are presented illustrating these features. Moreover, it is observed that the asymptotic theory agrees quite well with the exact answer (obtained by using a finite difference scheme) when N=3. [ABSTRACT FROM AUTHOR]

The acoustical performance of a submerged linear array of spherical transducers is examined by combining the T-matrix method of solving for multiple acoustic interactions among separate bodies with a model for transducers as thin spherical elastic shells. This approach solves the fully coupled problem of the response of the array to internal forcing. The results show that the assumptions giving rise to the Chebyshev criteria for optimal arrays of point sources appear to apply well even for large spheres at low frequencies. However, at frequencies near or above the lowest resonant frequency, the directional pattern may be degraded, depending on the material of the shells. [ABSTRACT FROM AUTHOR]

This paper is concerned with the scattering from a submerged (heavy fluid) bilaminate spherical shell composed of an outer layer of steel, and an inner layer of radially polarized piezoelectric material. The methodology used includes separation formulas for the stresses and displacements, which in turn are used (coupled with spherical harmonics) to reduce the governing equations to linear systems of ordinary differential equations. This technique uses the full equations of elasticity rather than any of the various thin-shell approximations in determining the axisymmetric scattering from a shell, normal modes of vibration for the shell, as well as voltages necessary for annihilation of a scattered pressure due to insonification of the shell by an incident plane wave.