Abstract

The equations of motion for nonaxisymmetric vibration of prolate spheroidal shells of constant thickness were derived using Hamiltons principle [S. I. Hayek and J. E. Boisvert, J. Acoust. Soc. Am. 114, 2799–2811 (2003)]. The shell theory used in this derivation includes shear deformations and rotatory inertias. The shell displacements and rotations were expanded in infinite series of comparison functions. These include associated Legendre functions in terms of the prolate spheroidal angular coordinate and circular functions in the azimuthal angle coordinate. For axisymmetric vibration of a submerged shell, the external (heavy) fluid loading impedance was computed using expansions of prolate spheroidal wavefunctions. The shell was excited by axisymmetric normal surface forces, including a point load at the shell apex and ring load at other locations. Far-field radiated pressure spectra are presented for several shell thickness-to-half-length ratios ranging from 0.005 to 0.1, and for various shape parameters, a, ranging from an elongated spheroidal shell (a=1.01) to a spherical shell (a∼100). The far-field directivity of acoustic radiation is presented at selected frequencies. [Work supported by the NUWC ILIR Program and the ONR/ASEE Summer Faculty Research Program.]

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