###### Abstract  
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 \(5\times 15\) [mm], a typical element of the flexible riser structural amount 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. steel rectangular rods; guided wave; dispersion curves; nondestructive techniques (NDT) +
Footnote †: journal: Applied Soft  
The prismatic bar could be considered simplified components of a flexible pipe (riser) used commonly in the offshore oil industry, more specifically when forming the structural amount layer of this system (see Figure 1a). The original motivation of the present work consists on developing an non-destructive technique (NDT) using a wave propagation framework that allows detecting damage in a critical region of the riser close to the platform connection (see Figure 1b). Details about the application of the NDT based on guided waves in this kind of structure can be seen [1,2]. The advance of NDT has increasingly allowed the service failures prediction, consequently reducing the maintenance cost and raising the structure reliability throughout its useful life [3, 4, 5]. The NDT can be divided into active and passive methods. In the case of active methods, the structure is excited with a perturbation that propagates interacting with defects, thus, enabling the structural integrity assessment. In the passive techniques, a typical an example is the acoustic emission technique (AE) where the excitation is produced when the damage advances due to an overload or when being submitted to conditions of utilization. This excitation is called event, and the analysis of the wave propagation emitted by the source of emission allows us to obtain information not only about the defect but also the conditions of its growth and, thus, carry out the structure health monitoring (SHM) [3, 4, 5]. In both techniques, the condition of the information extracted from the tests, regarding the wave propagation properties (inherent of the structure geometry and material) influence the data extracted. In this context, the present work was developed with the main objective of presenting in detail the propagation of elastic waves in rectangular isotropic steel rod of \(15\times 5\) [mm] where the attenuation due to the material viscosity is neglected [6].