Selected topics in computational ray methods

Abstract

Several selected topics intimately involved with the application of ray theory to acoustic scattering are discussed. The first topic is the application of quantitative ray theory to the low-frequency acoustic scattering from large aspect ratio solids. In this approach, the scattering amplitude is developed as a time-ordered perturbation series. The series for the elastic response is explicitly summed to obtain a closed form expression that is analogous to results obtained for spherical and infinite cylindrical geometries through application of the Sommerfeld–Watson transformation. Emphasis is placed on novel features that have no counterpart on these simpler geometries (e.g., ‘‘bipolar’’ coupling phenomena) and their implications for resonance excitation. A second topic deals with a near-field/far-field target strength model for more complicated geometrical shapes that is under development at CSS. But theoretical and experimental results are presented. A third topic is the high-frequency ‘‘quasi-resonance’’ phenomenon of thin shelled structures. The structure of the ‘‘quasiresonance’’ mode is obtained for both complex wave number (real frequency) and complex frequency (real wave number) extensions of the reflection coefficient for a fluid loaded flat plate. The results are used to synthesize the scattering amplitude for spherical shells using forms previously derived for the Sommerfeld–Watson transform.