Lamb waves and fluid-borne waves on water-loaded, air-filled thin spherical shells

Abstract

The results of a recent study of fluid-borne waves on plates with one-sided fluid loading [M. Talmant, Ph.D. thesis, University of Paris VII (1987)] allow the prediction of the corresponding waves and their resonances (as well as of the Lamb-wave resonances) on thin submerged spherical shells. Similar fluid waves and the ensuing ‘‘bifurcation’’ in the dispersion curves of the first antisymmetric vibration mode on cylindrical shells were previously described [J. V. Subrahmanyam, Ph.D. thesis, Catholic University of America (1983); J. L. Rousselot, Acustica 58, 291 (1985)] and the fluid waves were observed by Talmant et al. [J. Acoust. Soc. Am. 84, 681–688 (1988)]. The resonances predicted by the plate model for spherical shells are confirmed here by comparison with scattering cross-section calculations using surface integral equation radiation and scattering (SIERRAS) and T-matrix codes.

Circumferential-wave phase velocities for empty, fluid-immersed spherical metal shells

“…For the case of evacuated tungsten carbide ͑WC͒ shells immersed in water, the literature contains calculated dispersion curves for 1% and 2.5% shell thicknesses, 2 Our results are shown in Fig. 6.…”

“…For the water-loaded, evacuated shell, the A 0 curve now tends toward zero, however. An additional surface wave A ͑also called 16 a 0Ϫ and generally referred to as the ''Scholte-Stoneley wave'' 2,5,6,10 ͒ now appears here, being present due to the water loading of the shell, and it is now the dispersion curve of this A wave that shows the lowfrequency upturn. At first thought, the A 0 wave, since existing on the shell with or without fluid loading could be expected to be shell-borne throughout, and the A wave which exists only with the presence of fluid loading could be considered to be fluid-borne throughout ͑especially since its dispersion curve at ka→ϱ tends towards the sound speed in the ambient fluid͒.…”

“…11͒. In Ref. 2, Eq. ͑1͒ has been used in order to obtain some limited portions of circumferential-wave dispersion curves for evacuated, water-immersed thin shells of aluminum, stainless steel, and tungsten carbide ͑WC͒, based on the calculated resonance frequencies up to kaϭ8 ͑Al͒, 3͑WC͒, and 2.3 ͑steel͒ that were available at that time.…”

“…Application of the phase matching procedure which furnishes the resonance/dispersion curve connection has been initiated by Talmant et al 2 for the case of spherical aluminum shells. In this reference, the Scholte-Stoneley wave ͑called the A wave͒ has first been identified on spherical shells, simultaneously with the work of Sammelmann et al 17 where it was called the a 0 -wave͒, see Fig.…”

Fluid-structure effects of cloaking a submerged spherical shell

“…They include the works of Marston and co-workers, 10-14 € Uberall and co-workers, [15][16][17][18][19][20][21] and the excellent three papers by Sammelmann and Hackman. [22][23][24] The present work specifically addresses scattering from heavy fluid-loaded, cloaked spherical shells.…”