Scattering of Sound by an Elastic Prolate Spheroid

Abstract

The scattering of a plane wave by an elastic prolate spheroid at arbitrary angle of incidence is formulated by means of an expansion in spheroidal wave functions. The structural response of the spheroid is expressed in terms of a surface impedance operator. Even for a homogeneous elastic solid or shell, the impedance operator generally couples the spheroidal modes of the acoustic medium, and hence numerical solutions involve the inversion of an infinite set of linear equations. However, a number of special cases are considered here for which direct solutions can be obtained. These include resonant mode scattering and low-frequency scattering. When one of the structural modes is excited by the incident wave at its resonant frequency, it may radiate with such intensity as to mask radiation by other modes. The conditions under which this type of scattering can take place are shown to be very restrictive. When the acoustic wavelength is large and the frequency is small compared to the lowest natural frequency of the structure, the scattered field can be analyzed into uncoupled monopole and dipole fields. Simply asymptotic expressions, not involving spheroidal functions, are presented for a spheroid with finite compressibility and inertia as well as for the limiting cases of rigid and fixed boundary and pressure-release boundary.