Acoustic high‐frequency scattering by elastic cylindrical shells

Abstract

Acoustical scattering resulting from a high‐frequency plane‐wave incident upon an infinite aluminum circular cylindrical shell immersed in and filled with water is determined by applying the Sommerfeld–Watson transformation to the classical Rayleigh normal‐mode series solution. The resulting contour integrals are computed by both the saddle point method and by summing residues over poles which correspond to the zeros of a 6 ×6 determinant resulting from satisfying the necessary boundary conditions. The Bessel functions and their derivatives which appear in the 6 × 6 determinant are evaluated using asymptotic representations of both the Airy and Debye type depending upon the region of the complex plane. Emphasis is placed on the transitions in the scattering characteristics as the shell goes from a solid cylinder to a thin‐walled shell. This dual behavior will be discussed in terms of the number and trajectories of allowed modes of the scatterer, the dispersion curves of various modes, and the contributions of the various modes to the scattered pressure field.