Scattering from a coated cylindrical shell comparison of ray and exact computations

Abstract

We discuss sequentially the following: a homogenized shell theory and how it differs from uniform shell theory; high-frequency analysis of the quasi-P and S membrane wave solutions; the application of ray and coupling theory to the coated shell to predict the scattered response for oblique plane wave incidence; and numerical benchmarking against the exact code for thick coated shells. The shell theory is based on composite plate theory, with shell stresses modeled by the Kirchhoff assumption. The ray theory generalizes the theory developed for uniform thin shells, and accounts for the simultaneous P and S supersonic waves, and resulting resonances. The numerical comparisons demonstrate that the ray theory is accurate for undamped coatings, for which the excited resonances are strong. With damping present in the coating two unexpected discrepancies arise in the ray theory predictions. First, the damping of the excited structural waves is underestimated, even for relatively low damping in the coating, on the order of 0.1. At higher damping, e.g. 0.5, the same problem persists and is exacerbated by the degeneration of the background or specular approximation that is used in the asymptotic ray theory model. Refinements of the model to successfully address these is discussed.