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.

The use of mechanic waves for assessing structural integrity is a well-known non-destructive technique (NDT). The ultrasound applied in the guided wave in particular requires significant effort in order to understand the complexities of the propagation so as to develop new methods in damage detection, in this case, knowing the interaction between the wave propagation and the geometry of the waveguides is mandatory. In the present work, the wave propagation in rectangular steel rod is presented. In this study, the section dimensions were fixed as 5 × 15 [mm], a typical element of the flexible riser structural amour commonly used in the offshore oil industry. The studies here presented were restricted to [0, 100 KHz] frequencies. This frequency interval is in the range of commercial waveguide equipment commonly applied in ducts in NDT applications. The computation of the dispersion curves is performed by using three different methodologies: (i) analytical solutions, (ii) a method that combines analytical approaches with finite element methods (SAFE), and (iii) experimental method that extracted information from the rod using laser vibrometers and piezoelectric actuators. Finally, two applications based on the dispersion curves determined in the rectangular waveguide are presented to illustrate the possibilities of the curve dispersion knowledge related to the specific geometry in the development and application linked to NDT. The first application consists on showing the possibilities of the techniques that use a fiber grating Bragg cell (FGB) to measure the wave displacement and the second application involves the simulation of pre-fissured prismatic waveguide aimed at searching to induce three characteristic acoustic events. The model was built combining the finite element method and a version of the discrete element method.

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