Evidence for the existence of strong bending modes for signals scattered at oblique incidence from spheroidal shells

Abstract

In an earlier work [Werby etal., J. Acoust. Soc. Am. 85, 2365 (1989)] it was established that bending (flexing) modes are excited for signals scattering at oblique incidence from solid spheroidal shells. This was accomplished by comparing the exact T-matrix resonance predictions with those predicted from Timoshenko beam theory which accurately predicts the bending modes of a bar. One must then ask, do such modes exist for shells? One would expect that for fairly thick shells such modes do, but do they exist for thin shells too? In this study scattering of acoustical signals from elastic shells of various materials, aspect ratios, and shell thicknesses are examined. The study does indeed demonstrate the presence of bending modes even for very thin shells. It is interesting that for thick shells the resonance’s manifest themselves as maximum amplitude returns while for thin shells they manifest themselves as minimum amplitude returns. The effect with the transitional nature of a rigidlike background is associated to a softlike background for the two extremes so that the return signals vary in their coherence from adding constructively to adding destructively over the thickness variation. The sensitivity of resonance locations as a function of the elastic parameters is also presented. [Work sponsored by NRL and ONR.]