High-Frequency Response of Point-Excited Submerged, Spherical Shells

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Abstract
The classical, modal formulation of the harmonic vibrations and radiation loading of submerged elastic shells requires extensive calculations for high-frequency excitations. An alternative formulation in terms of attenuated traveling waves similar to the “creeping-wave” formulation commonly used in high-frequency diffraction analyses, is adapted to thin spherical shells excited by a radial point force. Applying Watson's transformation to the normal-mode series for the radial velocity and to the associated wave-harmonic series for the surface pressure, the shell response is expressed as the sum of (1) a primarily structure-borne field consisting of three modes, two of them rapidly attenuated, characterized by the wavenumbers of point-excited effectively infinite, submerged plane plates; and (2) a diffracted field, resembling “creeping waves” on “pressure-release” spheres. A single structure-borne mode suitably represents shell response and surface pressures except in the vicinity of the drive point (within 5° for the parameters used here).

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