Propagating and evanescent elastic waves in cylindrical waveguides of arbitrary cross section

Abstract

We study waves in elastic waveguides, with a view toward the nondestructive evaluation of slender structures by means of imposed vibrations. Envisioned applications demand an accurate understanding of both propagating and evanescent guided waves in waveguides of arbitrary cross section. Accordingly, we develop a theoretical framework in which energy principles and finite element discretization lead to a discrete set of solutions representing both wave types. We examine the solutions in great detail, with a particular emphasis on the accuracy of the finite element discretization. Results are compared with analytic solutions of the Pochhammer–Chree equations for the special case of a circular cross section, determining the combination of mesh parameters and frequency regimes for which the code yields accurate results. Convergence studies are conducted for the case of a more complex cross section, that of a typical railroad rail.