Numerical modeling of elastic wave propagation in prestressed helical waveguides with the safe method

Guided waves are used to control large components such as plates and tubes. They have the advantage to spread over long distances with little loss of energy. Because of the dispersive and multimodal behavior of guided waves, simulation becomes a very helpful tool for a proper analysis of these tests. The aim of this work is to model the elastic waves propagation in helical waveguides subjected to axial load. This study requires the development of elastodynamics equations in a helical coordinate system, which is translationally invariant along the helix centerline. The semi-analytical finite element (SAFE) method may then be applied, reducing the mesh to the section of the guide (two dimensional). The eigen-problem can be solved by fixing the wavenumber or frequency. Moreover, the computation of the prestressed state is solved by a 2D model based on the asymptotic expansion in which the invariance of the helical structure is taken into account. Results for single straight and helical wires are first computed in order to validate the approach. A dispersion analysis for a seven wire strand with simplified contact conditions is then performed