Complex eigenfrequencies of rigid and soft spheroids

The complex eigenfrequencies of impenetrable or penetrable target objects form a pattern which is characteristic for a given target, as far as its shape and/or composition is concerned. They manifest themselves as poles (resonances) in the amplitude of waves scattered from the object. We here obtain the eigenfrequency patterns of acoustically rigid and soft prolate spheroids in the complex frequency plane, and study their displacement when the eccentricity of the spheroids is varied. The eigenfrequencies were obtained numerically by subjecting spheroidal wavefunctions to the Neumann or Dirichlet boundary condition, respectively. Poles of both m = 0 (axial vibrations) and m ≠ 0 (vibrations with azimuthal components) were obtained, and axes ratios of 1:1 (sphere), 1.33:1, 2:1, 3:1, 5:1, and 10:1 were considered. Increasing axes ratios lead to increasing splittings between poles with different m values. [Supported in part by the David W. Taylor Naval Ship R&D Center, Annapolis, MD 21402.]