The interaction of elastic waves incident on an elastic spherical inhomogeneity is studied in detail, particularly in the resonance scattering regime. Incident and scattered compression and shear waves in lossless elastic media separate into three modes: a p mode for the compression wave, and s and t modes for the shear wave. A description of how the acoustic energy redistributes among these modes during the scattering process is contained in the scattering matrix that we separate here into background and resonance portions for the two extreme cases of a nearly soft and a nearly rigid elastic sphere. This produces farfield scattering amplitudes which are a superposition of a background contribution felt to contain reflected and Franz-type circumferential waves and a resonance contribution that seems to contain refracted, Rayleigh, and whispering gallery waves. Limiting cases (a fluid sphere in an elastic medium, an elastic sphere in a liquid medium, and a fluid sphere in a fluid medium) are extracted from these results to show agreement with previous work. Plots show the background and resonance portions of the scattered amplitudes and their connections with the poles of the scattering amplitude in the complex frequency plane. The methodology of the resonance scattering theory (RST) is summarized with a very general yet basic example of importance in acoustic/ultrasonics and elastodynamics/NDE, which contains all earlier situations.
The vector potential for an arbitrarily polarized shear wave in an elastic (lossless) medium incident on, and scattered by, a spherical fluid occlusion is expanded in vector spherical harmonics. The boundary conditions are dealt with for this incident vector potential in terms of two (scalar) Debye shear potentials ψ and χ giving rise to what we have termed ’’s and t waves,’’ respectively. The s wave scatters into both another s wave and also mode-converts into a compressional p wave. The t wave scatters only into another t wave with no mode conversion. Scattering amplitudes are cast in a series of resonance terms. The scattered p and s waves exhibit resonances; however, the t wave does not. We exhibit monostatic and bistatic plots of the first few partial-wave amplitudes (n=1,2,3,...) for the sp, ss, and tt scattering modes. When the background amplitude corresponding to scattering from an evacuated spherical cavity is removed from each partial-wave contribution, the remaining portion of the amplitudes is a clear series of liquid-sphere resonances. We display these resonances as functions of the acoustic size kda of the cavity, and of the order n of each mode. This work completes the determination of the scattering matrix elements for a fluid sphere in an elastic medium which was commenced by us earlier with the study of resonance effects in pp and ps scattering.
A large set of dolphin-emitted acoustic pulses ("echolocation clicks") have been examined, which were reflected from various elastic shells that were suspended, underwater, 4.5 m in front of the animal in a large test site in Kaneohe Bay, Hawaii. A carefully instrumented analog-to-digital system continuously captured the emitted clicks and also the returned, backscattered echoes (A/D conversion at 500 kHz). Using standard conditioning techniques and food reinforces, the dolphin is taught to push an underwater paddle when the "correct" target-the one he has been trained to identify-is presented to him. He communicates his consistently correct identifying choices in this manner. Many echoes returned by three types of cylindrical shells in both the time and frequency domains as well as in the joint time-frequency (t-f) domain, by means of Wigner-type distributions have been examined. It will be shown exactly how specific features observable in these displays are directly related to the physical characteristics of the shells. This processing takes advantage of certain fundamental resonance principles to show which echo features contain information about the size, shape, wall thickness, and material composition of both the shell and its filler substance. In the same fashion that these resonance features give the identifying characteristics of each shell, it is believed they may also give them to the dolphin. These echo features may allow him to extract the target properties by inspection without any need for computations. It is claimed that this may be the fundamental physical explanation of the dolphin's amazing target ID feats, upon which they base their recognition choices. This claim may be substantiated by the detailed analysis of many typical echoes returned by various shells, when they are interrogated by several dolphins. Thus far, this analysis of many echoes from many shells has only been carried out for a single dolphin.
We present a study of the resonance scattering undergone by an air-filled hollow elastic cylinder excited by an incident plane acoustic wave. We construct the boundary value problem, obtain its classical solution, the solution based on the Resonance Scattering Theory (RST), and generate a variety of useful computed results, some of which are later compared to experimental observations recently performed in France. We present highly accurate expressions for the phase and group velocities and for the phase and group attenuations of the first few surface waves circumnavigating (the extreme cases) of rigid and soft cylinders, and display these dispersion plots in all instances. We analyze the modal backgrounds and modal resonances of the shell, display them in a wide spectral band, determine the SEM-type pole-position diagram in the complex k•a plane, and obtain and display the background-suppressed cross section of the tube. This result serves to generate the acoustic spectrogram of the shell as well as to show the excellent agreement of this theoretical prediction with the experimental observations carried on in France. We analyze cross-sectional poles and cross-sectional dips, and reduce many of the present shell results to particular cases for impenetrable cylinders and solid elastic cylinders. For these latter ones, we obtain the dispersion plots for the phase and group velocities of the internal surface waves revolving around them. We determine expressions for the nearfield shell cross sections at different ranges, and compare them to the usual farfield results. We determine the sound pressure levels transmitted into the shelfs interior, and exhibit the controlling role the tube resonances have on the isobaric contours. We display extensive computerized calculations to illustrate all these points. Comparisons with experimental observations are shown to be quite favorable, particularly for the background-suppressed shell cross section, and for its acoustic spectrogram.
We study the normal-mode amplitudes for the scattering of (compressional and shear-type) elastic waves returned by a fluid-filled spherical cavity in a solid in the absence and presence of mode conversion, and examine their unitarity properties. The moduli of the resonance portions of these amplitudes are exhibited in the form of a two-dimensional ’’response surface’’ in a three-dimensional graph, where the two independent variables are (nondimensional) frequency and mode order. For various combinations of incident and scattered waves we note, display, and explain the various distinctive features of the response surface, namely, the loci of the zeroes, the series of ridges which give rise to modal resonances and to Regge poles (circumferential waves), and a series of tips along each ridge, which correspond to resonances in the circumferential waves due to phase matching. These informative features, graphically displayed at a glance in the plots of the response function, are useful in the interpretation of the scattering process taking place around fluid-filled cavities in solids, and in the identification of the material composition of the cavity contents, if the fillers were not known a priori.
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