Asymptotic Analysis of the Axisymmetric Vibrations of Shells

Abstract

An asymptotic analysis is carried out for the equations of axisymmetric vibrations of thin shells, somewhat analogous to the procedure by which geometrical optics is obtained from electromagnetic theory. It is found that two types of asymptotic solutions are obtained, roughly classifiable as high-frequency membrane solutions and bending solutions. Two explicit representations of these solutions are obtained, one for the shallow region of a shell and the other for the nonshallow region. A number of interesting conclusions emerge from the analysis.