# Abstract

The early detection of failures in structures is a subject of great interest in engineering; several of these techniques are linked with the elastic wave propagation, using guided waves is one of these alternatives. Several structures of interest in engineering are laminar arrangements; the wave propagation in this type of structures depends not only on the material properties, but also on the geometric parameters, such as the plate thickness. Tubular structures, pressure vessels, tanks and also parts of ships hulls could be considered laminar. The elastic wave propagation in laminar structures could be considered as a sum of modal shapes that have its wave length and frequencies defined. These mode families are characteristics of each structure and could be represented through the dispersion curves. The definition of these dispersion curves is of crucial importance to understand the propagation of guided waves in the structure studied. In the present work the dispersion curves were generated using three different methodologies, specific for metallic rectangular stems that compound the strengthening armor in flexible riser duct. Each approach presented in the analysis were carried out using standard finite element commercial packages and an experimental verification, as well. The premise is to present the topics in the simplest way, not only to understand how the dispersion curves are built but also how these curves must be interpreted.

**Keywords**

Dispersion curves; guided waves; nondestructive test; laminar structures; Finite Element Methods