We study the elastodynamic spectral response of thick and thin shells in water when they undergo resonance scattering caused by the incidence of sound waves that impinge upon them at selected aspects. All the shells considered are elastic, air‐filled, and of cylindrical and prolate spheroidal shapes. Their thickness is intentionally varied three orders of magnitude from very thick (i.e., h≡1−b/a=90%) to very thin (i.e., h=0.1%), so that the effects of shell stiffness on their scattering behavior can be quantitatively analyzed and understood. The quantities a and b are the outer and inner shell radii, respectively. Material composition effects are studied by comparing various metals such as steel and aluminum. The shell motions are described by the exact equations of elastodynamics in all cases, so that comparisons may be drawn concerning the regions of applicability of pertinent shell theories. For the spheroidal shells no exact solution is possible, thus, we have presented results based on an extended T‐matrix method that still makes use of the exact 3‐D equations of elastodynamics to describe the shell vibrations.
For a wide range of shell thicknesses and compositions, we have computed the positions of the poles of the scattering amplitudes, in the complex frequency plane x1. Here, x1 is k1a, where k1=ω/c1, ω is the angular frequency of the incident wave, c1 is the sound speed in the outer medium, and a is the shell’s outer radius. These poles group themselves in certain families and give rise to surface waves that circumnavigate the shell, either in the water side (Franz or SEM‐type poles or waves) or inside the shell metal (Rayleigh/whispering gallery waves for solid bodies, or Lamb momentless and flexural waves for shells). This latter set of waves is the least attenuated and the most dominant. We have shown how the pole families affect the spectral shape of the form function, and that of it’s partial waves, with their interacting modal backgrounds and resonances. As the shells become thinner, only one‐pole family is shown to remain within the displayed boundary of the complex x1 plane. This single‐pole family becomes responsible for the generation of the first‐order set of symmetric/antisymmetric Lamb waves in the shell. All these concepts are illustrated with many examples which show the crucial importance of the pole‐position diagrams to understand the spectral behavior of the form function, and the way it reveals information about the shell and the types of waves it supports on its surfaces. A transition from the rigid to the soft background is observed as the shells become very thin, and it is used to properly isolate the resonances of very thin shells. Extensions of these spectral results to the time domain are forthcoming.