Multipole character of the large-amplitude, low frequency resonances in the sonar echoes of submerged spherical shells

• Published in: International journal of solids and structures 1992, Vol.29 (1), p.121-130
• Main Authors: Strifors, Hans C., Gaunaurd, Guillermo C.
• Format: Article
• Language: English
• Subjects: Acoustics; Air bubbles; Backscattering; Band spectra; Bubbles; Coalescing; Cross sections; Dispersion (wave); Echo surveys; Exact sciences and technology; Fluids; Fundamental areas of phenomenology (including applications); Lamb waves; Mathematical analysis; Physics; Plates (structural members); Position (location); Shells (structural forms); Sonar; Spectra; Underwater sound; Vacuum; Waves
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/0020-7683(92)90100-8

We analyze the large-amplitude resonance features, which arc present at low frequencies in the backscattering cross-sections (BSCS) of air-fillcd, spherical, elastic shells submerged in water. By means of partial-wave expansions we demonstrate the multipole character of those features. For the materials and thicknesses investigated, it is confirmed that about half-a-dozen modes contribute to their formation. As the shell thickness decreases we note that : (i) fewer modes are seen to contribute to the BSCS. Ultimately, as the shell thickness approaches zero, only the monopole,n = 0. mode has an effect, just as for an air-bubble in water. (ii) In the bubble case, the large amplitude becomesgiant. the various peaks coalesce into one. and its spectral location shifts down tok1a ∼ 10−2. (iii) The narrow, low-amplitude set of overtones caused by the internal air remains present at all thicknesses, as the shell thickness decreases. Finally, we give a physical interpretation for these large features. They seem to he caused by a pseudo-Lamb wave denoted here bya01, investigated earlier by Junger (1967), by means of Donnell's shell theory. This wave is slower than the generalized zeroth-order antisymmetrica0, lamb wave for a shell. Its dispersion plot—which we display—exists only in the same narrow, low-frequency spectral band where the large echo features in question also occur. We investigate here its cause and effect by means of an exact, threedimensional elasticity description of the shell motions, which was derived earlier by Ayreset al (1987). We emphasize that what we have called, here and in the referenced paper, thea0-wave, is really a “generalized” antisymmetric zeroth-order Lamb wave for ashell, fluid-loaded on both sides by dissimilar fluids (and not for aplate in vacuum, as is often done). Thea01 is a companion type of generalizeda0-wave for shells that emerges from the roots of the same characteristic equation, and which has no counterpart for Hat plates.