Sound scattering from elastic objects and their complex eigenfrequencies

Abstract

A variety of surface waves is created at a smooth elastic target during acoustic scattering, including internal Rayleigh‐and whispering‐gallery type elastic waves, and external Franz‐type creeping waves. Previously, we studied these using a Watson transformation, searching for poles of the scattering amplitude in the complex mode‐number plane. The Singularity Expansion Method (SEM) of radar scattering instead characterizes the amplitude by its poles in the complex frequency plane. It is shown that each surface wave contributes a well‐defined set of complex‐frequency poles, and that the phase and group velocity dispersion curves of both elastic‐type and Franz‐type waves may be obtained from this set of poles. This approach is here carried through for the case of spherical and infinite‐cylindrical elastic targets, and the ensuing dispersion curves are shown to characterize the surface waves as to Rayleigh or whispering gallery type. [H. Überall is also at Catholic University, Washington, DC, sponsored by the Office of Naval Research.]