Geometrical theory of acoustic scattering by thin elastic shells

Abstract

Based on ray concepts, a geometrical theory is developed for the analysis and synthesis of the pressure and velocity fields of source-excited smooth thin elastic shells with fluid loading. At mid frequencies, these fields are contributed mainly by shell guided leaky membrane waves and specular reflection, provided either the source or observer is away from the shell surface. The theory involves the ray divergence coefficients characterizing the evolution of ray tubes in the fluid or ray strips on the shell, as well as the excitation, radiation, and reflection coefficients, which depend on both the physical and the geometrical properties of the shell. The former may be found by geometrical considerations, while the latter are determined by comparison with the analytic solutions of appropriate canonical problems and subsequent generalization to the perturbed shell configurations. Utilizing circular cylindrical and spherical shells as the canonical examples, this paper demonstrates the construction of the scattered fields from cylindrical shells of arbitrary cross section and from shells of revolution. It extends the concepts of Keller and Karal’s geometrical theory for surface waves [J. B. Keller and F. C. Karal, Jr., J. Appl. Phys. 31, 1039–1046 (1960)].