Excitation of guided elastic wave modes in hollow cylinders by applied surface tractions

Abstract

The problem of the generation of guided elastic wave modes in infinite hollow circular cylinders by loading applied to the boundaries of the cylinder, apart from being an interesting problem in itself, has important applications in the field of nondestructive evaluation. Hollow cylinders are commonly used in the nuclear industry in heat exchangers and hence must be inspected for defects regularly to ensure continued safe operation. An exact, closed-form solution is given for the amplitude with which any propagating waveguide mode is generated due to the application of prescribed (time harmonic) surface tractions. Instead of using classical integral transform techniques to solve the problem, the normal mode expansion technique is used. In this technique, analogous to the expansion of a function in terms of an orthogonal (and complete) set of functions, the fields generated in the cylinder due to the application of the surface loading are expanded in terms of the normal modes of the cylinder. The general results are then specialized to loading configurations of practical importance in nondestructive testing.