Analysis of localized edge vibrations of cylindrical shells using the Stroh formalism

Abstract

We consider localized edge vibrations of isotropic cylindrical thin shells that are described by the Kirchhoff–Love theory. This problem is mathematically similar to the surface-wave problem but has so far not benefited from the elegant general theory developed for the latter. We first reformulate the governing equations into a Stroh/Hamiltonian form and then derive a matrix Riccati equation and an integral representation for the edge-impedance matrix, the use of which we wish to promote. We show how to use the Riccati equation and the integral presentation to compute the vibration frequency efficiently.