Ray Solutions on Surfaces of Revolution

Abstract

Our concern is the development of techniques for the analysis of wave propagation and general transient response of thin shells to local loading. In general, ray methods are useful for such problems. In the present work, the ray solutions are obtained for a shell of revolution with high prestress, for which the bending stiffness of the shell wall can be neglected. The equation is that for an inhomogeneous, anisotropic medium with a non-Euclidean metric. Of special interest in the present shell problem is the global connectivity of ray paths. For an example the conical shell is considered. The rays for uniform pressure are shown to deviate substantially from geodesics. A ray emitted from a point on the cone may make several spirals around the small end of the cone before moving toward the large end in an almost straight line. The implication is that high focusing of energy can occur from a mild impact on the side of a conical shell.