Acoustic high-frequency scattering by elastic cylinders

Abstract

Acoustic scattering from an infinite elastic cylinder in a fluid is described by using the Sommerfeld–Watson transformation. The wavenumbers for the surface and transmitted waves are determined by poles or saddle points, respectively, of the scattering amplitude in the complex wavenumber plane. Dispersion and attenuation curves for the dominant surface wave modes have been obtained from the pole positions and given in our previous work. The present study gives the amplitudes of all the known contributions to the scattered field by evaluating the corresponding residues and the saddle-point amplitudes. The results indicate that the individual surface wave modes (i.e., Franz, Rayleigh, Stoneley, and Whispering Gallery), remain comparable to the transmitted-wave contributions to the scattered field (all these being plotted versus scattering angle at several frequencies) through frequencies at least as high as ka=200. This indicates that sound scattering from an elastic body does not tend to become predominantly geometrical-diffractive in the short-wavelength limit. Finally, some surface wave modes are plotted versus frequency, and are shown to contain a series of narrow resonances corresponding to the excitation of eigenvibrations of the elastic cylinder.