Acoustic backscattering from fluid‐filled submerged prolate spheroidal shells

Abstract

The equations of motion for nonaxisymmetric vibration of prolate spheroidal shells of constant thickness were derived using Hamilton’s 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. The fluid‐filled shell is insonified by a plane wave with an arbitrary angle of incidence. The external and internal fluid loading impedances were computed using an eigenfunction expansion of prolate spheroidal wavefunctions. Far‐field backscattered acoustic pressure spectra are presented as a function of the angle of incidence 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). A comparison of the backscattering from fluid‐filled and empty shells is presented at selected plane wave incident angles. [Work supported by the ONR/ASEE Summer Faculty Research Program and the NAVSEA Newport ILIR Program.]